Final

A uniform meter stick is pivoted to rotate about a horizontal axis through the 25-cm mark on the stick. The stick is released from rest in a horizontal position. The moment of inertia of a uniform rod about an axis perpendicular to the rod and through the center of mass of the rod is given by (1/12)ML2. Determine the magnitude of the initial angular acceleration of the stick.
Question options:
1) 17 rad/s2
2) 13 rad/s2
3) 15 rad/s2
4) 19 rad/s2
5) 23 rad/s2

A disk (radius = 8.0 cm) that rotates about a fixed axis starts from rest and accelerates at a constant rate to an angular velocity of 4.0 rad/s in 2.0 s. What is the magnitude of the total linear acceleration of a point on the rim of the disk at the instant when the angular velocity of the disk is 1.5 rad/s?
Question options:
1) 24 cm/s2
2) 16 cm/s2
3) 18 cm/s2
4) 34 cm/s2
5) 44 cm/s2

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 starts from rest at t = 0. The wheel has a diameter of 20 cm. What is the magnitude of the total linear acceleration of a point on the outer edge of the wheel at t = 0.60 s?
Question options:
1) 0.25 m/s2
2) 0.50 m/s2
3) 0.14 m/s2
4) 0.34 m/s2
5) 0.20 m/s2

You throw a Frisbee of mass m and radius r so that it is spinning about a horizontal axis perpendicular to the plane of the Frisbee. Ignoring air resistance, the torque exerted about its center of mass by gravity is
Question options:
1) 0.
2) mgr.
3) 2mgr.
4) a function of the angular velocity.
5) small at first, then increasing as the Frisbee loses the torque given it by your hand.

A thin uniform rod (length = 1.2 m, mass = 2.0 kg) is pivoted about a horizontal, frictionless pin through one end of the rod. (The moment of inertia of the rod about this axis is ML2/3.) The rod is released when it makes an angle of 37° with the horizontal. What is the angular acceleration of the rod at the instant it is released?
Question options:
1) 9.8 rad/s2
2) 7.4 rad/s2
3) 8.4 rad/s2
4) 5.9 rad/s2
5) 6.5 rad/s2

A solid cylinder of radius R = 1.0 m and mass 10 kg rotates about its axis. When its angular velocity is 10 rad/s, its angular momentum (in kg × m2/s) is
Question options:
1) 50.
2) 20.
3) 40.
4) 25.
5) 70.

The 1560 kg solid steel door to a bank vault is 2.00 m high, 1.00 m wide and 10 cm thick. One hinge is 60.0 cm down from the top on the left hand side of the door. The other hinge is 30.0 cm up from the bottom. What horizontal force, in what direction, does the door exert on the upper hinge?
Question options:
1) 6950 N, left
2) 6950 N, right
3) 7640 N, left
4) 7640 N, right
5) 15,300 N, left

Stars originate as large bodies of slowly rotating gas. Because of gravity, these clumps of gas slowly decrease in size. The angular velocity of a star increases as it shrinks because of
Question options:
1) conservation of angular momentum
2) conservation of linear momentum
3) conservation of energy
4) the law of universal gravitation
5) conservation of mass

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 turns through 2.4 revolutions during a 2.0-s time interval. What is the angular velocity at the end of this time interval?
Question options:
1) 9.5 rad/s
2) 9.7 rad/s
3) 9.3 rad/s
4) 9.1 rad/s
5) 8.8 rad/s

A uniform rod (length = 2.4 m) of negligible mass has a 1.0-kg point mass attached to one end and a 2.0-kg point mass attached to the other end. The rod is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through a point 1.0 m from the 2.0-kg mass. The rod is released from rest when it is horizontal. What is the angular velocity of the rod at the instant the 2.0-kg mass passes through its low point?
Question options:
1) 1.7 rad/s
2) 2.2 rad/s
3) 2.0 rad/s
4) 1.5 rad/s
5) 3.1 rad/s

Particles (mass of each = 0.20 kg) are placed at the 40-cm and 100-cm marks of a meter stick of negligible mass. This rigid body is free to rotate about a frictionless pivot at the 0-cm end. The body is released from rest in the horizontal position. What is the initial angular acceleration of the body?
Question options:
1) 12 rad/s2
2) 5.9 rad/s2
3) 8.4 rad/s2
4) 5.4 rad/s2
5) 17 rad/s2

A solid sphere, spherical shell, solid cylinder and a cylindrical shell all have the same mass m and radius R. If they are all released from rest at the same elevation and roll without slipping, which reaches the bottom of an inclined plane first?
Question options:
1) solid sphere
2) spherical shell
3) solid cylinder
4) cylindrical shell
5) all take the same time

A nonuniform 2.0-kg rod is 2.0 m long. The rod is mounted to rotate freely about a horizontal axis perpendicular to the rod that passes through one end of the rod. The moment of inertia of the rod about this axis is 4.0 kg × m2. The center of mass of the rod is 1.2 m from the axis. If the rod is released from rest in the horizontal position, what is its angular speed as it swings through the vertical position?
Question options:
1) 3.4 rad/s
2) 4.4 rad/s
3) 4.3 rad/s
4) 5.8 rad/s
5) 6.8 rad/s

Two particles (m1 = 0.20 kg, m2 = 0.30 kg) are positioned at the ends of a 2.0-m long rod of negligible mass. What is the moment of inertia of this rigid body about an axis perpendicular to the rod and through the center of mass?
Question options:
1) 0.48 kg × m2
2) 0.50 kg × m2
3) 1.2 kg × m2
4) 0.80 kg × m2
5) 0.70 kg × m2

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity increases to 40 rad/s. Assume that the angular acceleration was constant during the 5.0-s interval. How many revolutions does the wheel turn through during the 5.0-s interval?
Question options:
1) 20 rev
2) 24 rev
3) 32 rev
4) 28 rev
5) 39 rev

The 1560 kg solid steel door to a bank vault is 2.00 m high, 1.00 m wide and 10 cm thick. One hinge is 60.0 cm down from the top on the left hand side of the door. The other hinge is 30.0 cm up from the bottom. What horizontal force, in what direction, does the door exert on the lower hinge?
Question options:
1) 6950 N, left
2) 6950 N, right
3) 7640 N, left
4) 7640 N, right
5) 15,300 N, left

A wheel (radius = 12 cm) is mounted on a frictionless, horizontal axle that is perpendicular to the wheel and passes through the center of mass of the wheel. A light cord wrapped around the wheel supports a 0.40-kg object. If released from rest with the string taut, the object is observed to fall with a downward acceleration of 3.0 m/s2. What is the moment of inertia (of the wheel) about the given axle?
Question options:
1) 0.023 kg × m2
2) 0.013 kg × m2
3) 0.020 kg × m2
4) 0.016 kg × m2
5) 0.035 kg × m2

A uniform rod (mass = 2.0 kg, length = 0.60 m) is free to rotate about a frictionless pivot at one end. The rod is released from rest in the horizontal position. What is the magnitude of the angular acceleration of the rod at the instant it is 60° below the horizontal?
Question options:
1) 15 rad/s2
2) 12 rad/s2
3) 18 rad/s2
4) 29 rad/s2
5) 23 rad/s2

Four identical particles (mass of each = 0.40 kg) are placed at the vertices of a rectangle (2.0 m ´ 3.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the longer sides and is parallel to the shorter sides?
Question options:
1) 2.7 kg × m2
2) 3.6 kg × m2
3) 3.1 kg × m2
4) 4.1 kg × m2
5) 1.6 kg × m2

A skater extends her arms horizontally, holding a 5-kg mass in each hand. She is rotating about a vertical axis with an angular velocity of one revolution per second. If she drops her hands to her sides, what will the final angular velocity (in rev/s) be if her moment of inertia remains approximately constant at 5 kg × m2, and the distance of the masses from the axis changes from 1 m to .1 m?
Question options:
1) 6
2) 3
3) 9
4) 4
5) 7

Identical particles are placed at the 50-cm and 80-cm marks on a meter stick of negligible mass. This rigid body is then mounted so as to rotate freely about a pivot at the 0-cm mark on the meter stick. If this body is released from rest in a horizontal position, what is the angular speed of the meter stick as it swings through its lowest position?
Question options:
1) 4.2 rad/s
2) 5.4 rad/s
3) 4.6 rad/s
4) 5.0 rad/s
5) 1.7 rad/s

Four identical particles (mass of each = 0.24 kg) are placed at the vertices of a rectangle (2.0 m ´ 3.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the center of mass of the body and is parallel to the shorter sides of the rectangle?
Question options:
1) 2.4 kg × m2
2) 2.2 kg × m2
3) 1.9 kg × m2
4) 2.7 kg × m2
5) 8.6 kg × m2

A car of mass 1000 kg moves with a speed of 50 m/s on a circular track of radius 100 m. What is the magnitude of its angular momentum (in kg × m2/s) relative to the center of the race track?
Question options:
1) 5.0 ´ 102
2) 5.0 ´ 106
3) 2.5 ´ 104
4) 2.5 ´ 106
5) 5.0 ´ 103

A wheel rotating about a fixed axis has an angular position given by q = 3.0 – 2.0t3, where q is measured in radians and t in seconds. What is the angular acceleration of the wheel at t = 2.0 s?
Question options:
1) -1.0 rad/s2
2) -24 rad/s2
3) -2.0 rad/s2
4) -4.0 rad/s2
5) -3.5 rad/s2

A space station out beyond the solar system is rotating with constant angular velocity. A spaceship heading into the station along a diameter of the station, uses its rockets to brake, and then docks inside the station. When the spaceship docks, the angular momentum of the system consisting of the station and ship
Question options:
1) is less than the original angular momentum of the station.
2) is the same as the original angular momentum of the station.
3) is greater than the original angular momentum of the station.
4) is less than the original angular momentum of the station, but the angular velocity increases.
5) is greater than the original angular momentum of the station, but the angular velocity decreases.

A uniform rod of length (L = 2.0 m) and mass (M = 1.5 kg) is pivoted about a horizontal frictionless pin through one end. The rod is released from rest at an angle of 30° below the horizontal. What is the angular speed of the rod when it passes through the vertical position? (The moment of inertia of the rod about the pin is 2.0 kg-m2.)
Question options:
1) 3.5 rad/s
2) 2.7 rad/s
3) 3.1 rad/s
4) 2.3 rad/s
5) 1.6 rad/s

A wheel rotates about a fixed axis with a constant angular acceleration of 4.0 rad/s2. The diameter of the wheel is 40 cm. What is the linear speed of a point on the rim of this wheel at an instant when that point has a total linear acceleration with a magnitude of 1.2 m/s2?
Question options:
1) 39 cm/s
2) 42 cm/s
3) 45 cm/s
4) 35 cm/s
5) 53 cm/s

At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s. Two seconds later it has turned through 5.0 complete revolutions. What is the angular acceleration of this wheel?
Question options:
1) 17 rad/s2
2) 14 rad/s2
3) 20 rad/s2
4) 23 rad/s2
5) 13 rad/s2

A cylinder rotating about its axis with a constant angular acceleration of 1.6 rad/s2 starts from rest at t = 0. At the instant when it has turned through 0.40 radian, what is the magnitude of the total linear acceleration of a point on the rim (radius = 13 cm)?
Question options:
1) 0.31 m/s2
2) 0.27 m/s2
3) 0.35 m/s2
4) 0.39 m/s2
5) 0.45 m/s2

A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 30° above the horizontal. What is the angular acceleration of the rod at the instant it is released?
Question options:
1) 4.7 rad/s2
2) 6.9 rad/s2
3) 6.4 rad/s2
4) 5.6 rad/s2
5) 4.2 rad/s2

A uniform rod (length = 2.0 m) is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through the rod at a point 0.50 m from one end of the rod. If the rod is released from rest in a horizontal position, what is the angular speed of the rod as it rotates through its lowest position?
Question options:
1) 3.5 rad/s
2) 3.8 rad/s
3) 4.1 rad/s
4) 2.0 rad/s
5) 5.6 rad/s

A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at the horizontal position. What is the angular acceleration of the rod at the instant the rod makes an angle of 70° with the horizontal?
Question options:
1) 3.7 rad/s2
2) 1.3 rad/s2
3) 2.5 rad/s2
4) 4.9 rad/s2
5) 1.9 rad/s2

Four identical particles (mass of each = 0.40 kg) are placed at the vertices of a rectangle (2.5 m ´ 4.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the shorter sides and is parallel to the longer sides?
Question options:
1) 2.2 kg × m2
2) 2.8 kg × m2
3) 2.5 kg × m2
4) 3.1 kg × m2
5) 1.6 kg × m2

A uniform rod is 3.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 27° above the horizontal. What is the angular speed of the rod as it passes through the horizontal position?
Question options:
1) 3.0 rad/s
2) 2.8 rad/s
3) 2.1 rad/s
4) 2.5 rad/s
5) 3.4 rad/s

A horizontal disk with a radius of 10 cm rotates about a vertical axis through its center. The disk starts from rest at t = 0 and has a constant angular acceleration of 2.1 rad/s2. At what value of t will the radial and tangential components of the linear acceleration of a point on the rim of the disk be equal in magnitude?
Question options:
1) 0.55 s
2) 0.63 s
3) 0.69 s
4) 0.59 s
5) 0.47 s

A uniform rod (mass = 1.5 kg) is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest in a horizontal position. What is the angular speed of the rod when the rod makes an angle of 30° with the horizontal? (The moment of inertia of the rod about the pin is 2.0 kg × m2).
Question options:
1) 2.2 rad/s
2) 3.6 rad/s
3) 2.7 rad/s
4) 3.1 rad/s
5) 1.8 rad/s

At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration of -0.40 rad/s2 has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad. What is the angular position of the wheel at t = 2.0 s?
Question options:
1) 4.9 rad
2) 4.7 rad
3) 4.5 rad
4) 4.3 rad
5) 4.1 rad

The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off. The turntable comes to rest 2.5 s after being turned off. Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration.
Question options:
1) 12 rad
2) 8.0 rad
3) 10 rad
4) 16 rad
5) 6.8 rad

A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis. It completes the first revolution 6.0 s after it started. How long after it started will the wheel complete the second revolution?
Question options:
1) 9.9 s
2) 7.8 s
3) 8.5 s
4) 9.2 s
5) 6.4 s

Three particles, each of which has a mass of 80 g, are positioned at the vertices of an equilateral triangle with sides of length 60 cm. The particles are connected by rods of negligible mass. What is the moment of inertia of this rigid body about an axis that is parallel to one side of the triangle and passes through the respective midpoints of the other two sides?
Question options:
1) 0.018 kg × m2
2) 0.020 kg × m2
3) 0.016 kg × m2
4) 0.022 kg × m2
5) 0.032 kg × m2

A merry-go-round of radius R = 2.0 m has a moment of inertia I = 250 kg × m2, and is rotating at 10 rpm. A child whose mass is 25 kg jumps onto the edge of the merry-go-round, heading directly toward the center at 6.0 m/s. The new angular speed (in rpm) of the merry-go-round is approximately
Question options:
1) 10
2) 9.2
3) 8.5
4) 7.1
5) 6.4

A wheel (radius = 0.20 m) starts from rest and rotates with a constant angular acceleration of 2.0 rad/s2. At the instant when the angular velocity is equal to 1.2 rad/s, what is the magnitude of the total linear acceleration of a point on the rim of the wheel?
Question options:
1) 0.40 m/s2
2) 0.29 m/s2
3) 0.69 m/s2
4) 0.49 m/s2
5) 0.35 m/s2

A hockey puck traveling at speed v on essentially frictionless ice collides elastically with one end of a straight stick lying flat on the ice. In this collision
Question options:
1) momentum is conserved.
2) angular momentum is conserved.
3) energy is conserved.
4) all of the above are conserved.
5) only momentum and angular momentum are conserved.

Particles (mass of each = 0.40 kg) are placed at the 60-cm and 100-cm marks of a meter stick of negligible mass. This rigid body is free to rotate about a frictionless pivot at the 0-cm end. The body is released from rest in the horizontal position. What is the magnitude of the initial linear acceleration of the end of the body opposite the pivot?
Question options:
1) 15 m/s2
2) 9.8 m/s2
3) 5.8 m/s2
4) 12 m/s2
5) 4.7 m/s2

A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s2. In a 4.0-s interval the wheel turns through an angle of 80 radians. Assuming the wheel started from rest, how long had it been in motion at the start of the 4.0-s interval?
Question options:
1) 2.5 s
2) 4.0 s
3) 3.5 s
4) 3.0 s
5) 4.5 s

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity decreases to 10 rad/s. Assume that the angular acceleration is constant during the 5.0-s interval. How many radians does the wheel turn through during the 5.0-s interval?
Question options:
1) 95 rad
2) 85 rad
3) 65 rad
4) 75 rad
5) 125 rad

The quantity with the same units as force times time, Ft, with dimensions MLT-1 is

Question options:
1) mv
2) mvr
3) mv2r
4) ma
5)
mar

A uniform ladder 15 ft long is leaning against a frictionless wall at an angle of 53° above the horizontal. The weight of the ladder is 30 pounds. A 75-lb boy climbs 6.0-ft up the ladder. What is the magnitude of the friction force exerted on the ladder by the floor?
Question options:
1) 43 lb
2) 34 lb
3) 38 lb
4) 47 lb
5) 24 lb

How large a force is necessary to stretch a 2-mm diameter copper wire (Y = 11 ´ 1010 N/m2) by 1%?
Question options:
1) 2 163 N
2) 3 455 N
3) 6 911 N
4) 11 146 N
5) 5 420 N

A 20-m long steel wire (cross-section 1 cm2, Young’s modulus 2 ´ 1011 N/m2), is subjected to a load of 25,000 N. How much will the wire stretch under the load?
Question options:
1) 0.25 cm
2) 2.5 cm
3) 12.5 cm
4) 25 cm
5) 1.25 cm

A horizontal meter stick supported at the 50-cm mark has a mass of 0.50 kg hanging from it at the 20-cm mark and a 0.30 kg mass hanging from it at the 60-cm mark. Determine the position on the meter stick at which one would hang a third mass of 0.60 kg to keep the meter stick balanced.
Question options:
1) 74 cm
2) 70 cm
3) 65 cm
4) 86 cm
5) 62 cm

Angie says that an object is in equilibrium if the net torques about the center of mass is zero. Robbie says that an object is in equilibrium if the sum of external forces is zero. Which one, if either, is correct?
Question options:
1) Both are correct: an object is in equilibrium if either condition holds.
2) Neither is correct: both conditions must hold simultaneously.
3) Neither is correct: the net external force and the net external torque about any axis must be zero.
4) Neither is correct: an object is in equilibrium only if its velocity is zero in all coordinate systems.
5) Both are correct: if the sum of the external forces is zero, the net torque about any axis is automatically zero, and vice versa.

John is carrying a shovelful of snow. The center of mass of the 3.00 kg of snow he is holding is 15.0 cm from the end of the shovel. He is pushing down on the opposite end of the shovel with one hand and holding it up 30.0 cm from that end with his other hand. Ignore the mass of the shovel. Sarah says that his hand pushing down on the shovel must be exerting a greater force than the hand pushing up. James says it is just the reverse. Which one, if either, is correct?
Question options:
1) Sarah, because the hand pushing down must exert a greater force to match the torque exerted by the snow.
2) James, because, depending on the location of the axis of rotation, the hand pushing down can counteract the torque exerted by the snow.
3) James, because the hand pushing up must exert a force that equals the sum of the force of the hand pushing down and the weight of the snow.
4) James, because both (b) and (c) above are correct.
5) Neither, because the hands exert forces of equal magnitudes.

The answer to a question is [MLT-1]. The question is “What are the dimensions of
Question options:
1) mr?”
2) mvr?”
3) ma?”
4) mat?”
5)
mvrr

How large a pressure increase (in ATM) must be applied to water if it is to be compressed in volume by 1%? The bulk modulus of water is 2 ´ 109 N/m2 and 1 ATM = 105 N/m2.
Question options:
1) 50 ATM
2) 100 ATM
3) 1 080 ATM
4) 400 ATM
5) 200 ATM

A problem may be solved more easily when alternative representations are used. The best strategy is to formulate representations in an order that assists in understanding the physical principles involved. Of the orders given below, the one that will work best most often is
Question options:
1) pictorial representation, mathematical representation, tabular representation, mental representation.
2) pictorial representation, mental representation, mathematical representation, tabular representation.
3) mathematical representation, pictorial representation, tabular representation, mental representation.
4) mathematical representation, tabular representation, mental representation, pictorial representation.
5) mental representation, pictorial representation, tabular representation, mathematical representation.

For the wave described by y = 0.02 sin (kx) at t = 0 s, the first maximum at a positive x coordinate occurs where x = 4 m. Where on the positive x axis does the second maximum occur?
Question options:
1) 20 m
2) 18 m
3) 24 m
4) 28 m
5) 16 m

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 3 sin (2x) cos 5t where x is in m and t is in s. What is the wavelength of the interfering waves?
Question options:
1) 3.14 m
2) 1.00 m
3) 6.28 m
4) 12.0 m
5) 2.00 m

The path difference between two waves is 5m. If the wavelength of the waves emitted by the two sources is 4m, what is the phase difference (in degrees)?
Question options:
1) 90
2) 400
3) 1.57
4) 7.85
5) 15

Transverse waves are traveling on a 1.00-m long piano string at 500 m/s. If the points of zero vibration occur at one-half wavelength, (where the string is fastened at both ends), find the frequency of vibration.
Question options:
1) 250 Hz
2) 500 Hz
3) 1000 Hz
4) 2000 Hz
5) 2500 Hz

If y = 0.02 sin (30x – 400t) (SI units), the wave number is
Question options:
1) 30 m-1
2) 30/2p m-1
3) 400/2p m-1
4) 400 m-1
5) 60p m-1

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2 sin (4x) cos (3t) where x is in m and t is in s. What is the speed (in m/s) of the interfering waves?
Question options:
1) 0.75
2) 0.25
3) 1.3
4) 12
5) 3.0

Write the equation of a wave, traveling along the +x axis with an amplitude of 0.02 m, a frequency of 440 Hz, and a speed of 330 m/sec.
Question options:
1) y = 0.02 sin [880p (x/330 – t)] 2) y = 0.02 cos [880p x/330 – 440t] 3) y = 0.02 sin [880p(x/330 + t)] 4) y = 0.02 sin [2p(x/330 + 440t)] 5) y = 0.02 cos [2p(x/330 + 440t)]

A point source emits sound with a power output of 100 watts. What is the intensity (in W/m2) at a distance of 10.0 m from the source?
Question options:
1) 7.96 ´ 10-2
2) 7.96 ´ 10-1
3) 7.96 ´ 100
4) 7.96 ´ 101
5) 7.96 ´ 10-3

Four wave functions are given below. Rank the wave functions in order of the magnitude of the frequencies of the waves, from least to greatest.

I. y(x, t) = 5sin(4x – 20t + 4)
II. y(x, t) = 5sin(3x – 12t + 5)
III. y(x, t) = 5cos(4x + 24t + 6)
IV. y(x, t) = 14cos(2x – 8t + 3)
Question options:
1) IV, II, I, III
2) IV = II, I, III
3) III, I, II, IV
4) IV, I, II, III
5) III, IV, II, I

If y = 0.02 sin (30x – 400t) (SI units), the wavelength of the wave is
Question options:
1) p/15 m
2) 15/p m
3) 60p m
4) 4.2 m
5) 30 m

Two instruments produce a beat frequency of 5 Hz. If one has a frequency of 264 Hz, what could be the frequency of the other instrument?
Question options:
1) 269 Hz
2) 254 Hz
3) 264 Hz
4) 5 Hz
5) 274 Hz

Calculate the displacement amplitude (in m) of a 20 kHz sound wave in helium if it has a pressure amplitude of 8 ´ 10-3 N/m2. (r = 0.179 kg/m3, v = 972 m/s.)
Question options:
1) 2.9 ´ 10-10
2) 3.7 ´ 10-10
3) 7.8 ´ 10-9
4) 2.4 ´ 10-9
5) 1.9 ´ 10-10

Determine the intensity (in W/m2) of a harmonic longitudinal wave with a pressure amplitude of 8 ´ 10-3 N/m2 propagating down a tube filled with helium. (r = 0.179 kg/m3, v = 972 m/s.)
Question options:
1) 3.7 ´ 10-7
2) 1.8 ´ 10-7
3) 9.2 ´ 10-8
4) 4.6 ´ 10-8
5) 1.5 ´ 10-9

An organ pipe open at both ends has a radius of 4.0 cm and a length of 6.0 m. What is the frequency (in Hz) of the third harmonic? (Assume the velocity of sound is 344 m/s.)
Question options:
1) 76
2) 86
3) 54
4) 28
5) 129

A piano string of density 0.0050 kg/m is under a tension of 1350 N. Find the velocity with which a wave travels on the string.
Question options:
1) 260 m/s
2) 520 m/s
3) 1040 m/s
4) 2080 m/s
5) 4160 m/s

If y = 0.02 sin (30x – 400t) (SI units) and if the mass density of the string on which the wave propagates is .005 kg/m, then the transmitted power is
Question options:
1) 1.03 W
2) 2.13 W
3) 4.84 W
4) 5.54 W
5) 106 W

How fast (in m/s) is the Concorde moving if it reaches Mach 1.5? (The speed of sound in air is 344 m/s.)
Question options:
1) 229
2) 516
3) 416
4) 728
5) 858

Ocean waves with a wavelength of 120 m are coming in at a rate of 8 per minute. What is their speed?
Question options:
1) 8.0 m/s
2) 16 m/s
3) 24 m/s
4) 30 m/s
5) 4.0 m/s

When you hear the horn of a car that is approaching you, the frequency that you hear is larger than that heard by a person in the car because
Question options:
1) wave crests are farther apart by the distance the car travels in one period.
2) wave crests are closer together by the distance the car travels in one period.
3) the car gets ahead of each wave crest before it emits the next one.
4) the speed of sound in air is increased by the speed of the car.
5) a speeding car emits more wavecrests in each period.

You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 6 cm wide but still 5 mm high. You must move your hand up and down once,
Question options:
1) the same distance up as before, but take a shorter time.
2) the same distance up as before, but take a longer time.
3) a smaller distance up, but take a shorter time.
4) a greater distance up, but take a longer time.
5) a greater distance up, but take the same time.

The variation in the pressure of helium gas, measured from its equilibrium value, is given by DP = 2.9 ´ 10-5 cos (6.2x – 3000t) where x and t have units m and s, and DP is measured in N/m2. Determine the frequency (in Hz) of the wave.
Question options:
1) 1500
2) 477
3) 1.01
4) 0.32
5) 239

A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren relative to the police car is 500 Hz, what is the frequency heard by an observer in the truck as the police car approaches the truck? (The speed of sound in air is 343 m/s.)
Question options:
1) 396
2) 636
3) 361
4) 393
5) 617

A sculptor strikes a piece of marble with a hammer. Find the speed of sound through the marble (in km/s). (The Young’s modulus is 50 ´ 109 N/m2 and its density is 2.7 ´ 103 kg/m3.)
Question options:
1) 5.1
2) 4.3
3) 3.5
4) 1.3
5) 1.8

Two tuning forks with frequencies 264 and 262 Hz produce “beats”. What is the beat frequency (in Hz)?
Question options:
1) 4
2) 2
3) 1
4) 3
5) 0 (no beats are produced)

A string is stretched and fixed at both ends, 200 cm apart. If the density of the string is 0.015 g/cm, and its tension is 600 N, what is the wavelength (in cm) of the first harmonic?
Question options:
1) 600
2) 400
3) 800
4) 1000
5) 200

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 4 sin (5x) cos (6t) where x is in m and t is in s. What is the approximate frequency of the interfering waves?
Question options:
1) 3 Hz
2) 1 Hz
3) 6 Hz
4) 12 Hz
5) 5 Hz

A 100-m long transmission cable is suspended between two towers. If the mass density is 2.01 kg/m and the tension in the cable is 3.00 ´ 104 N, what is the speed of transverse waves on the cable?
Question options:
1) 60 m/s
2) 122 m/s
3) 244 m/s
4) 310 m/s
5) 1500 m/s

If y = 0.02 sin (30x – 400t) (SI units), the velocity of the wave is
Question options:
1) 3/40 m/s
2) 40/3 m/s
3) 60p/400 m/s
4) 400/60p m/s
5) 400 m/s

Four wave functions are given below.Rank the wave functions in order of the magnitude of the wave speeds, from least to greatest.

I. y(x, t) = 5sin(4x – 20t + 4)
II. y(x, t) = 5sin(3x – 12t + 5)
III. y(x, t) = 5cos(4x + 24t + 6)
IV. y(x, t) = 14cos(2x – 8t + 3)
Question options:
1) IV, II, I, III
2) IV = II, I, III
3) III, I, II, IV
4) IV, I, II, III
5) III, IV, II, I

Do not try the following: it could kill you. This question is only about a hypothetical possibility.) If you were standing below an object falling at terminal velocity, as it approached you, you would hear the sound
Question options:
1) drop in frequency.
2) stay at the same frequency.
3) increase in frequency.
4) decrease in loudness.
5) stay at the same loudness.

To decrease the intensity of the sound you are hearing from your speaker system by a factor of 36, you can
Question options:
1) reduce the amplitude by a factor of 12 and increase your distance from the speaker by a factor of 3.
2) reduce the amplitude by a factor of 4 and increase your distance from the speaker by a factor of 3.
3) reduce the amplitude by a factor of 2 and increase your distance from the speaker by a factor of 3.
4) reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 4.
5) reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 12.

A student attaches a length of nylon fishing line to a fence post. She stretches it out and shakes the end of the rope in her hand back and forth to produce waves on the line. The most efficient way for her to increase the wavelength is to
Question options:
1) increase the tension on the hose and shake the end more times per second.
2) decrease the tension on the hose and shake the end more times per second.
3) increase the tension on the hose and shake the end fewer times per second.
4) decrease the tension on the hose and shake the end fewer times per second.
5) keep the tension and frequency the same but increase the length of the hose.

The speed of a 10-kHz sound wave in seawater is approximately 1500 m/s. What is its wavelength in sea water?
Question options:
1) 5.0 cm
2) 10 cm
3) 15 cm
4) 20 cm
5) 29 cm

While you are sounding a tone on a toy whistle, you notice a friend running toward you. If you want her to hear the same frequency that you hear even though she is approaching, you must
Question options:
1) stay put.
2) run towards her at the same speed.
3) run away from her at the same speed.
4) stay put and play a note of higher frequency.
5) run towards her and play a note of higher frequency.

An earthquake emits both S-waves and P-waves which travel at different speeds through the Earth. A P-wave travels at 9000 m/s and an S-wave travels at 5000 m/s. If P-waves are received at a seismic station 1.00 minute before an S-wave arrives, how far away is the earthquake center?
Question options:
1) 88.9 km
2) 1200 km
3) 675 km
4) 240 km
5) 480 km

A very long string is tied to a rigid wall at one end while the other end is attached to a simple harmonic oscillator. Which of the following can be changed by changing the frequency of the oscillator?
Question options:
1) The speed of the waves traveling along the string.
2) The tension in the string.
3) The wavelength of the waves on the string.
4) All of the above.
5) None of the above.

A wave generated in a medium is a longitudinal wave when
Question options:
1) there is a net transport of matter by the wave.
2) the molecules of the medium are unable to exert forces on each other.
3) molecular displacements are parallel to the wave velocity.
4) molecular displacements are perpendicular to the wave velocity.
5) the density of the medium is less than the density of water.

If y = 0.02 sin (30x – 400t) (SI units), the frequency of the wave is
Question options:
1) 30 Hz
2) 15/p Hz
3) 200/p Hz
4) 400 Hz
5) 800p Hz

A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren is 500 Hz relative to the police car, what is the change in frequency (in Hz) heard by an observer in the truck as the two vehicles pass each other? (The speed of sound in air is 343 m/s.)
Question options:
1) 242
2) 238
3) 240
4) 236
5) 234

Calculate the pressure amplitude (in N/m2) of a 500 Hz sound wave in helium if the displacement amplitude is equal to 5 ´ 10-8 m. (r = 0.179 kg/m3, v = 972 m/s.)
Question options:
1) 3.5 ´ 10-2
2) 1.6 ´ 10-2
3) 2.7 ´ 10-2
4) 4.2 ´ 10-2
5) 2.0 ´ 10-2

Bats can detect small objects such as insects that are of a size on the order of a wavelength. If bats emit a chirp at a frequency of 60 kHz and the speed of soundwaves in air is 330 m/s, what is the smallest size insect they can detect?
Question options:
1) 1.5 mm
2) 3.5 mm
3) 5.5 mm
4) 7.5 mm
5) 9.8 mm

The lowest A on a piano has a frequency of 27.5 Hz. If the tension in the 2.00-m string is 308 N, and one-half wavelength occupies the string, what is the mass of the wire?
Question options:
1) 0.025 kg
2) 0.049 kg
3) 0.051 kg
4) 0.081 kg
5) 0.037 kg

Calculate the intensity level in dB of a sound wave that has an intensity of 15 ´ 10-4 W/m2.
Question options:
1) 20
2) 200
3) 92
4) 9
5) 10

A string is stretched and fixed at both ends, 200 cm apart. If the density of the string is 0.015 g/cm, and its tension is 600 N, what is the fundamental frequency?
Question options:
1) 316 Hz
2) 632 Hz
3) 158 Hz
4) 215 Hz
5) 79 Hz

Drummers like to have high-pitched cymbals that vibrate at high frequencies. To obtain the highest frequencies, a cymbal of a fixed size should be made of a material
Question options:
1) with a low Young’s modulus and a low density.
2) with a low Young’s modulus and a high density.
3) with a high Young’s modulus and a low density.
4) with a high Young’s modulus and a high density.
5) composed of a metal-plastic laminate.

The Young’s modulus for aluminum is 7.02 ´ 1010 N/m2. If the speed of sound in aluminum is measured to be 5.10 km/s, find its density (in kg/m3).
Question options:
1) 11.3 ´ 103
2) 7.80 ´ 103
3) 2.70 ´ 103
4) 29.3 ´ 103
5) 1.40 ´ 103

A car moving at 36 m/s passes a stationary police car whose siren has a frequency of 500 hz. What is the change in the frequency (in Hz) heard by an observer in the moving car as he passes the police car? (The speed of sound in air is 343 m/s.)
Question options:
1) 416
2) 208
3) 105
4) 52
5) 552

By what factor will an intensity change when the corresponding sound level increases by 3 dB?
Question options:
1) 3
2) 0.5
3) 2
4) 4
5) 0.3

A clarinet behaves like a tube closed at one end. If its length is 1.0 m, and the velocity of sound is 344 m/s, what is its fundamental frequency (in Hz)?
Question options:
1) 264
2) 140
3) 86
4) 440
5) 172

A vertical tube one meter long is open at the top. It is filled with 75 cm of water. If the velocity of sound is 344 m/s, what will the fundamental resonant frequency be (in Hz)?
Question options:
1) 3.4
2) 172
3) 344
4) 1.7
5) 688

An organ pipe open at both ends is 1.5 m long. A second organ pipe that is closed at one end and open at the other is 0.75 m long. The speed of sound in the room is 330 m/s. Which of the following sets of frequencies consists of frequencies which can be produced by both pipes?
Question options:
1) 110 Hz, 220 Hz, 330 Hz
2) 220 Hz, 440 Hz, 660 Hz
3) 110 Hz, 330 Hz, 550 Hz
4) 330 Hz, 440 Hz, 550 Hz
5) 220 Hz, 660 Hz, 1100 Hz

The variation in the pressure of helium gas, measured from its equilibrium value, is given by DP = 2.9 ´ 10-5 cos (6.2x – 3000t) where x and t have units m and s. Determine the speed (in m/s) of the wave.
Question options:
1) 1515
2) 153
3) 484
4) 828
5) 101

A stretched string is observed to vibrate in three equal segments when driven by a 480 Hz oscillator. What is the fundamental frequency of vibration for this string?
Question options:
1) 480 Hz
2) 320 Hz
3) 160 Hz
4) 640 Hz
5) 240 Hz

Two strings are respectively 1.00 m and 2.00 m long. Which of the following wavelengths, in meters, could represent harmonics present on both strings?
Question options:
1) 0.800, 0.670, 0.500
2) 1.33, 1.00, 0.500
3) 2.00, 1.00, 0.500
4) 2.00, 1.33, 1.00
5) 4.00, 2.00, 1.00

A person standing in the street is unaware of a bird dropping that is falling from a point directly above him with increasing velocity. If the dropping were producing sound of a fixed frequency, as it approaches the person would hear the sound
Question options:
1) drop in frequency.
2) stay at the same frequency.
3) increase in frequency.
4) decrease in loudness.
5) stay at the same loudness.

A point source emits sound waves with a power output of 100 watts. What is the sound level (in dB) at a distance of 10 m?
Question options:
1) 139
2) 119
3) 129
4) 109
5) 10

If y = 0.02 sin (30x – 400t) (SI units), the angular frequency of the wave is
Question options:
1) 30 rad/s
2) 30/2p rad/s
3) 400/2p rad/s
4) 400 rad/s
5) 40/3 rad/s

By what factor is the intensity of sound at a rock concert louder than that of a whisper when the two intensity levels are 120 dB and 20 dB respectively?
Question options:
1) 1012
2) 108
3) 106
4) 1010
5) 1011

A length of organ pipe is closed at one end. If the speed of sound is 344 m/s, what length of pipe (in cm) is needed to obtain a fundamental frequency of 50 Hz?
Question options:
1) 28
2) 86
3) 344
4) 172
5) 688

The fundamental frequency of a above middle C on the piano is 440 Hz. This is the tenor high A, but a convenient note in the mid-range of women’s voices. When we calculate the wavelength, we find that it is
Question options:
1) much shorter than the length of either a man’s or woman’s lips.
2) shorter than the length of a man’s lips, but about the length of a woman’s lips.
3) longer than a woman’s lips, but about the length of a man’s lips.
4) much longer than the length of either a man’s or a woman’s lips.
5) about the same length as either a man’s or woman’s lips.

When two organ pipes open at both ends sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes?
Question options:
1) 440, 880 and 1320 Hz.
2) 660, 1320 and 1980 Hz.
3) 880, 1320 and 1760 Hz.
4) 1320, 2640 and 3960 Hz.
5) They have no overtones in common.

You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 6 cm wide and 7 mm high. You must move your hand up and down once,
Question options:
1) the same distance up as before, but take a shorter time.
2) the same distance up as before, but take a longer time.
3) a smaller distance up, but take a shorter time.
4) a greater distance up, but take a longer time.
5) a greater distance up, but take the same time.

Superposition of waves can occur
Question options:
1) in transverse waves.
2) in longitudinal waves.
3) in sinusoidal waves.
4) in all of the above.
5) only in (a) and (c) above.

Which of the following wavelengths could NOT be present as a standing wave in a 2 m long organ pipe open at both ends?
Question options:
1) 4 m
2) 2 m
3) 1 m
4) 0.89 m
5) 0.5 m

The velocity of sound in sea water is 1533 m/s. Find the bulk modulus (in N/m2) of sea water if its density is 1.025 ´ 103 kg/m3.
Question options:
1) 2.6 ´ 109
2) 2.2 ´ 109
3) 2.0 ´ 109
4) 2.4 ´ 109
5) 2.8 ´ 109

A stone is thrown into a quiet pool of water. With no fluid friction, the amplitude of the waves falls off with distance r from the impact point as
Question options:
1) 1/r3
2) 1/r2
3) 1/r3/2
4) 1/r1/2
5) 1/r

The variation in the pressure of helium gas, measured from its equilibrium value, is given by DP = 2.9 ´ 10-5 cos (6.2x – 3000t) where x and t have units m and s, and DP is measured in N/m2. Determine the wavelength (in m) of the wave.
Question options:
1) 1500
2) 0.32
3) 477
4) 1.01
5) 0.50

A jet plane has a sound level of 150 dB. What is the intensity in W/m2?
Question options:
1) 1
2) 100
3) 10
4) 1000
5) 10000

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2 sin (px) cos (3pt) where x is in m and t is in s. What is the distance (in m) between the first two antinodes?
Question options:
1) 8
2) 2
3) 4
4) 1
5) 0.5

A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren is 500 Hz relative to the police car, what is the frequency heard by an observer in the truck after the police car passes the truck? (The speed of sound in air is 343 m/s.)
Question options:
1) 361
2) 636
3) 393
4) 396
5) 383

Which of the following wavelengths could NOT be present as a harmonic on a 2 m long string?
Question options:
1) 4 m
2) 2 m
3) 1 m
4) 0.89 m
5) 0.5 m

A car approaches a stationary police car at 36 m/s. The frequency of the siren (relative to the police car) is 500 Hz. What is the frequency (in Hz) heard by an observer in the moving car as he approaches the police car? (Assume the velocity of sound in air is 343 m/s.)
Question options:
1) 220
2) 448
3) 5264
4) 552
5) 383

The wavelength of light visible to the human eye is on the order of 5 ´ 10-7 m. If the speed of light in air is 3 ´ 108 m/s, find the frequency of the lightwave.
Question options:
1) 3 ´ 107 Hz
2) 4 ´ 109 Hz
3) 5 ´ 1011 Hz
4) 6 ´ 1014 Hz
5) 4 ´ 1015 Hz

It is possible to hear an approaching train before you can see it by listening to the sound wave through the track. If the elastic modulus is 2.0 ´ 1011 N/m2 and the density of steel is 7.8 ´ 103 kg/m3, approximately how many times faster is the speed of sound in the track than in air? (vair » 340 m/s.)
Question options:
1) 20
2) 5
3) 10
4) 15
5) 25

Water pressurized to 3.5 ´ 105 Pa is flowing at 5.0 m/s in a horizontal pipe which contracts to 1/3 its former area. What are the pressure and velocity of the water after the contraction?
Question options:
1) 2.5 ´ 105 Pa, 15 m/s
2) 3.0 ´ 105 Pa, 10 m/s
3) 3.0 ´ 105 Pa, 15 m/s
4) 4.5 ´ 105 Pa, 1.5 m/s
5) 5.5 ´ 105 Pa, 1.5 m/s

Find the pressure in atmospheres at the base of Dworshak Dam if the water in the reservoir is 200 meters deep. (105 N/m2 = 1 ATM.)
Question options:
1) 20.6 ATM
2) 24.7 ATM
3) 29.4 ATM
4) 196 ATM
5) 75 ATM

A Boeing 737 airliner has a mass of 20,000 kg and the total area of both wings (top or bottom) is 100 m2. What is the pressure difference between the top and bottom surface of each wing when the airplane is in flight at a constant altitude?
Question options:
1) 1960 N/m2
2) 3920 N/m2
3) 7840 N/m2
4) 4560 N/m2
5) 3070 N/m2

An empty spice bottle has an inner volume of 1.31 ´ 10-4 m3. It has a mass of 112 g when filled with air, and it displaces 1.63 ´ 10-4 m3 of water when fully submerged. What volume of mercury (rHg = 13.6 ´ 103 kg/m3) must be added to the bottle so that it will just be submerged?
Question options:
1) 3.74 cm3
2) 12.0 cm3
3) 101 cm3
4) 147 cm3
5) 237 cm3

A hole is punched in a full milk carton, 10 cm below the top. What is the initial velocity of outflow?
Question options:
1) 1.4 m/s
2) 2.0 m/s
3) 2.8 m/s
4) 3.9 m/s
5) 2.8 m/s

Determine the minimum area of a flat ice floe 1.0 meter thick if it is to support a 2000-kg car above seawater. (rice = 920 kg/m3, rsea = 1020 kg/m3.)
Question options:
1) 20 m2
2) 40 m2
3) 60 m2
4) 80 m2
5) 100 m2

An empty spice bottle has an inner volume of 1.31 ´ 10-4 m3. It has a mass of 112 g when filled with air, and it displaces 1.63 ´ 10-4 m3 of water when fully submerged. What fraction of the total volume of the bottle will be beneath the surface when it is placed in a tank of water?
Question options:
1) 0.69
2) 0.81
3) 0.85
4) 1.00
5) 1.46

How much power is theoretically available from a mass flow of 1000 kg/s of water when it falls a vertical distance of 100 meters?
Question options:
1) 980 kW
2) 98 kW
3) 4900 W
4) 980 W
5) 9600 W

A wind of velocity 10 m/s is blowing through a wind generator with blade radius 5.0 meters. What is the maximum power output if 30% of the wind’s energy can be extracted? rair = 1.25 kg/m3.
Question options:
1) 7.2 kW
2) 14.7 kW
3) 21.3 kW
4) 29.4 kW
5) 39.6 kW

A waiter in a restaurant fills a pitcher full of water and ice so that water would spill out if any more were added. As the ice starts to melt
Question options:
1) the water level in the pitcher falls.
2) the water level in the pitcher remains the same.
3) water starts to flow out the spout of the pitcher.
4) the pressure on the bottom of the pitcher decreases.
5) the pressure on the bottom of the pitcher increases.

People can snorkel down to a depth of roughly one meter. This means that the maximum pressure their lungs can exert on the air they expel is roughly
Question options:
1) 9800 N.
2) 9800 Pa.
3) 9800 ATM.
4) 19 600 N.
5) 19 600 N/m2.

Water is sent from a firehose at 30.0 m/s at an angle of 30° above the horizontal. What is the maximum height reached by the water?
Question options:
1) 7.50 m
2) 11.5 m
3) 15.0 m
4) 19.0 m
5) 30.0 m

A blimp is filled with 200 m3 of helium. How much mass can the balloon lift? The density of helium is 1/7 that of air, and the density of air is 1/800 that of water.
Question options:
1) 115 kg
2) 214 kg
3) 315 kg
4) 415 kg
5) 37 kg

In a wind tunnel the pressure on the top surface of a model airplane wing is 8.8 ´ 104 N/m and the pressure on the bottom surface is 9.0 ´ 104 N/m2. If the area of the top and bottom surfaces of each wing is 2.0 m2, what is the total lift on the model airplane?
Question options:
1) 2.0 ´ 103 N
2) 8.0 ´ 103 N
3) 1.6 ´ 104 N
4) 3.6 ´ 104 N
5) 1.0 ´ 103 N

Find the average density of a white dwarf star if it has a mass equal to that of the sun (2.0 ´ 1030 kg) and a radius equal to that of the Earth (6.4 ´ 106 m).
Question options:
1) 9.0 ´ 106 kg/m3
2) 1.8 ´ 107 kg/m3
3) 1.8 ´ 109 kg/m3
4) 3.6 ´ 1010 kg/m3
5) 9.0 ´ 107 kg/m3

Some species of whales can dive to depths of 1 kilometer. What is the total pressure they experience at this depth? (rsea = 1020 kg/m3 and 105 N/m2 = 1 ATM.)
Question options:
1) 9 ATM
2) 90 ATM
3) 101 ATM
4) 111 ATM
5) 130 ATM

Melanie says that when a diver enters an underwater cave of height h, the pressure on her is no greater than mgh. Rosalind says that if the bottom of the cave is a distance H below the water surface, the pressure on the soles of the diver’s feet is mgH. Which one, if either, is correct? (The density of water is rW.)
Question options:
1) Melanie, because the roof of the cave absorbs the water pressure from above.
2) Melanie, because only the fluid directly above any volume of the fluid can contribute to the pressure on that volume.
3) Rosalind, because a fluid exerts equal pressure in all directions.
4) Rosalind, because the pressure also depends on the density, rc, of the material above the cave roof, so that p = rcg(H – h) + rWgh.
5) Melanie, because the pressure equals p = rWgH – rcg(H – h).

What is the total force acting inward on a spherical bathysphere of diameter 2.00 m at an ocean depth of 1000 m? (The pressure inside the bathysphere is, hopefully, 1 ATM.) r(sea water) = 1.02 ´ 103 kg/m3.
Question options:
1) 1.26 ´ 104 N
2) 1.26 ´ 106 N
3) 1.26 ´ 108 N
4) 1.26 ´ 1010 N
5) 1.26 ´ 102 N

All people come very close to being able to float in water. What therefore is the volume (in cubic meters) of a 50-kg woman?
Question options:
1) 0.007
2) 0.035
3) 0.050
4) 0.070
5) 0.085

What is the total mass of the Earth’s atmosphere? The radius of the Earth is 6.4 ´ 106 m, and 1 ATM = 105 N/m2.
Question options:
1) 5 ´ 1016 kg
2) 1 ´ 1018 kg
3) 5 ´ 1018 kg
4) 1 ´ 1020 kg
5) 5 ´ 109 kg

A police crime lab is trying to determine whether someone was murdered or died as a result of an accident. He was struck in the temple by a 4.20 kg sculpture that is alleged to have fallen off a bookcase. The sculpture presumably fell a distance of 1.43 m and the corner that struck him had an area of 0.25 cm2. If the time for the sculpture to stop was 1.00 ms, the pressure on his temple, in N/m2, was
Question options:
1) 8.88 ´ 104.
2) 1.65 ´ 105.
3) 1.65 ´ 106.
4) 8.88 ´ 108.
5) 1.65 ´ 109.

When water freezes, it expands about 9 percent. What would be the pressure increase inside your automobile engine block if the water in there froze? The bulk modulus of ice is 2.0 ´ 109 N/m2, and 1 ATM = 105 N/m2.
Question options:
1) 18 ATM
2) 360 ATM
3) 1080 ATM
4) 1800 ATM
5) 600 ATM

The pressure inside a commercial airliner is maintained at 1 ATM (105 N/m2). What is the outward force exerted on a 1 m ´ 2 m cabin door if the outside pressure (at 10 km height) is 0.3 ATM?
Question options:
1) 1.4 ´ 102 N
2) 1.4 ´ 103 N
3) 1.4 ´ 104 N
4) 1.4 ´ 105 N
5) 7.0 ´ 103 N

Air within the funnel of a large tornado may have a pressure of only 0.2 ATM. What is the approximate outward force on a (5 m ´ 10 m) wall if a tornado suddenly envelops the house? (1 ATM = 105 N/m2.)
Question options:
1) 4 ´ 103 N
2) 4 ´ 104 N
3) 4 ´ 105 N
4) 4 ´ 106 N
5) 7 ´ 105 N

A hydraulic lift raises a 2000-kg automobile when a 500-N force is applied to the smaller piston. If the smaller piston has an area of 10 cm2, what is the cross-sectional area of the larger piston?
Question options:
1) 40 cm2
2) 80 cm2
3) 196 cm2
4) 392 cm2
5) 160 cm2

Water is flowing at 4.0 m/s in a circular pipe. If the diameter of the pipe decreases to 1/2 its former value, what is the velocity of the water downstream?
Question options:
1) 1.0 m/s
2) 2.0 m/s
3) 8.0 m/s
4) 16 m/s
5) 4.0 m/s

A fountain sends water to a height of 100 meters. What must be the pressurization (above atmospheric) of the water system? 1 ATM = 105 N/m2.
Question options:
1) 1.0 ATM
2) 4.2 ATM
3) 7.2 ATM
4) 9.8 ATM
5) 8.2 ATM

A cube of water ice (r = 0.917 ´ 103 kg/m3) is placed in mercury (r = 13.6 ´ 103 kg/m3), which is liquid at 0° Celsius. If we ignore any possible melting of the ice cube and problems with the surface tension of mercury, the fraction of the ice cube that floats above the surface of the mercury is
Question options:
1) 0.0674.
2) 0.0735.
3) 0.926.
4) 0.933.
5) 1.00.

Two identical fish, both at sea level, float in two identical aquariums with identical quantities of water. Fish A is in Alaska, so it weighs more than fish B at the equator, since g is larger at sea level in Alaska. Which statement is correct.
Question options:
1) A comparison is impossible unless they are both floating at the same level.
2) Fish A displaces a greater quantity of water than fish B.
3) Fish B displaces a greater quantity of water than fish A.
4) They both displace the same quantity of water.
5) Fish A has a smaller acceleration than Fish B when equal horizontal forces are applied to each, because Fish A weighs more.

What fraction of an iceberg is submerged? (rice = 917 kg/m3, rsea = 1.03 ´ 103 kg/m3.)
Question options:
1) 95%
2) 93%
3) 91%
4) 89%
5) 77%

A wood block is placed on top of the ice in a large bowl half full of ice. The bowl is then filled to the brim with water, with the wood block riding on top of the ice. As the ice melts,
Question options:
1) the density of the water decreases.
2) the water level falls below the rim.
3) the water level rises and water spills out of the bowl.
4) the water level does not change.
5) the wood block descends, causing water to spill out of the bowl.

he water level in a reservoir is maintained at a constant level. What is the exit velocity in an outlet pipe 3.0 m below the water surface?
Question options:
1) 2.4 m/s
2) 3.0 m/s
3) 5.4 m/s
4) 7.7 m/s
5) 49 m/s

A stonecutter’s chisel has an edge area of 0.7 cm2. If the chisel is struck with a force of 42 N, what is the pressure exerted on the stone?
Question options:
1) 600 N/m2
2) 30 000 N/m2
3) 300 000 N/m2
4) 600 000 N/m2
5) 6 000 N/m2

A supertanker filled with oil has a total mass of 6.1 ´ 108 kg. If the dimensions of the ship are those of a rectangular box 300 meters long, 80 meters wide, and 40 meters high, determine how far the bottom of the ship is below sea level. (rsea = 1020 kg/m3.)
Question options:
1) 10 m
2) 15 m
3) 20 m
4) 25 m
5) 30 m

The amplitude of a system moving with simple harmonic motion is doubled. The total energy will then be
Question options:
1) 4 times larger
2) 3 times larger
3) 2 times larger
4) the same as it was
5) half as much

When a damping force is applied to a simple harmonic oscillator which has angular frequency w0 in the absence of damping, the new angular frequency w is such that
Question options:
1) w < w0. 2) w = w0. 3) w > w0.
4) wT < w0T0. 5) wT > w0T0.

Suppose it were possible to drill a frictionless cylindrical channel along a diameter of the Earth from one side of the Earth to another. A body dropped into such a channel will only feel the gravitational pull of mass within a sphere of radius equal to the distance of the mass from the center of the Earth. The density of the Earth is 5.52 ´ 103 kg/m3 and G = 6.67 ´ 10-11 N × m2/kg2. The mass will oscillate with a period of
Question options:
1) 84.4 min.
2) 169 min.
3) 24.0 h.
4) 1130 h.
5) 27.2 d.

A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = 5 sin (pt + p/3). The phase (in rad) of the motion at t = 2 s is
Question options:
1) 7p/3
2) p/3
3) p
4) 5p/3
5) 2p

A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = 5.0 sin (pt + p/3). The velocity (in m/s) of the body at t = 1.0 s is
Question options:
1) +8.0
2) -8.0
3) -14
4) +14
5) -5.0

The motion of a particle connected to a spring is described by x = 10 sin (pt). At what time (in s) is the potential energy equal to the kinetic energy?
Question options:
1) 0
2) 0.25
3) 0.50
4) 0.79
5) 1.0

In an inertia balance, a body supported against gravity executes simple harmonic oscillations in a horizontal plane under the action of a set of springs. If a 1.00 kg body vibrates at 1.00 Hz, a 2.00 kg body will vibrate at
Question options:
1) 0.500 Hz.
2) 0.707 Hz.
3) 1.00 Hz.
4) 1.41 Hz.
5) 2.00 Hz.

When a damping force is applied to a simple harmonic oscillator which has period T0 in the absence of damping, the new period T is such that
Question options:
1) T < T0. 2) T = T0. 3) T > T0.
4) wT < w0T0. 5) wT > w0T0.

A 2.00 m-long 6.00 kg ladder pivoted at the top hangs down from a platform at the circus. A 42.0 kg trapeze artist climbs to a point where her center of mass is at the center of the ladder and swings at the systems natural frequency. The angular frequency (in s-1) of the system of ladder and woman is
Question options:
1) 1.01.
2) 2.01.
3) 4.03.
4) 8.05.
5) 16.2.

A body oscillates with simple harmonic motion along the x-axis. Its displacement varies with time according to the equation x = 5.0 sin (pt). The acceleration (in m/s2) of the body at t = 1.0 s is approximately
Question options:
1) 3.5
2) 49
3) 14
4) 43
5) 4.3

Simple harmonic oscillations can be modeled by the projection of circular motion at constant angular velocity onto a diameter of the circle. When this is done, the analog along the diameter of the centripetal acceleration of the particle executing circular motion is
Question options:
1) the displacement from the center of the diameter of the projection of the position of the particle on the circle.
2) the projection along the diameter of the velocity of the particle on the circle.
3) the projection along the diameter of tangential acceleration of the particle on the circle.
4) the projection along the diameter of centripetal acceleration of the particle on the circle.
5) meaningful only when the particle moving in the circle also has a non-zero tangential acceleration

What is the kinetic energy of a 200-kg satellite as it follows a circular orbit of radius 8.0 ´ 106 m around the Earth? (Mass of Earth = 6.0 ´ 1024 kg.)
Question options:
1) 5.0 ´ 109 J
2) 1.0 ´ 1010 J
3) 1.5 ´ 1010 J
4) 2.0 ´ 1010 J
5) 2.5 ´ 109 J

A 50-kg satellite circles the Earth in an orbit with a period of 120 min. What minimum energy is required to change the orbit to another circular orbit with a period of 180 min? (Earth: radius = 6.4 ´ 106 m, mass = 6.0 ´ 1024 kg)
Question options:
1) 2.9 ´ 108 J
2) 3.5 ´ 108 J
3) 4.1 ´ 108 J
4) 4.7 ´ 108 J
5) 5.9 ´ 108 J

A satellite is in a circular orbit about the Earth at an altitude at which air resistance is negligible. Which of the following statements is true?
Question options:
1) There is only one force acting on the satellite.
2) There are two forces acting on the satellite, and their resultant is zero.
3) There are two forces acting on the satellite, and their resultant is not zero.
4) There are three forces acting on the satellite.
5) None of the preceding statements are correct.

What is the escape speed from a planet of mass M and radius R if M = 3.2 ´ 1023 kg and R = 2.4 ´ 106 m?
Question options:
1) 5.5 km/s
2) 4.2 km/s
3) 5.2 km/s
4) 4.8 km/s
5) 3.7 km/s

Planet Zero has a mass of 5.0 ´ 1023 kg and a radius of 2.0 ´ 106 m. A space probe is launched vertically from the surface of Zero with an initial speed of 4.0 km/s. What is the speed of the probe when it is 3.0 ´ 106 m from Zero’s center?
Question options:
1) 3.0 km/s
2) 2.2 km/s
3) 1.6 km/s
4) 3.7 km/s
5) 5.9 km/s

Which of the following quantities is conserved for a planet orbiting a star in a circular orbit? Only the planet itself is to be taken as the system; the star is not included.
Question options:
1) Momentum and energy.
2) Energy and angular momentum.
3) Momentum and angular momentum.
4) Momentum, angular momentum and energy.
5) None of the above.

What is the magnitude of the free-fall acceleration at a point that is a distance 2R above the surface of the Earth, where R is the radius of the Earth?
Question options:
1) 4.8 m/s2
2) 1.1 m/s2
3) 3.3 m/s2
4) 2.5 m/s2
5) 6.5 m/s2

A satellite circles planet Roton every 2.8 h in an orbit having a radius of 1.2 ´ 107 m. If the radius of Roton is 5.0 ´ 106 m, what is the magnitude of the free-fall acceleration on the surface of Roton?
Question options:
1) 31 m/s2
2) 27 m/s2
3) 34 m/s2
4) 40 m/s2
5) 19 m/s2

A 50-kg satellite circles planet Cruton every 5.6 h in an orbit with a radius of 12 ´ 106 m. What is the magnitude of the gravitational force on the satellite by planet Cruton?
Question options:
1) 63 N
2) 58 N
3) 68 N
4) 73 N
5) 50 N

A spaceship of mass m circles a planet (mass = M) in an orbit of radius R. How much energy is required to transfer the spaceship to a circular orbit of radius 3R?
Question options:
1) GmM/(2R)
2) GmM/(3R)
3) GmM/(4R)
4) GmM/(6R)
5) 3GmM/(4R)

Two identical planets orbit a star in concentric circular orbits in the star’s equatorial plane. Of the two, the planet that is farther from the star must have
Question options:
1) the smaller period.
2) the greater period.
3) the smaller gravitational mass.
4) the larger gravitational mass.
5) the larger universal gravitational constant.

A satellite is placed in a geosynchronous orbit. In this equatorial orbit with a period of 24 hours, the satellite hovers over one point on the equator. Which statement is true for a satellite in such an orbit?
Question options:
1) There is no gravitational force on the satellite.
2) There is no acceleration toward the center of the Earth.
3) The satellite is in a state of free fall toward the Earth.
4) There is a tangential force that helps the satellite keep up with the rotation of the Earth.
5) The force toward the center of the Earth is balanced by a force away from the center of the Earth.

Planet Roton has a mass of 4.0 ´ 1023 kg and a radius of 2.0 ´ 106 m. With what speed should a space probe be launched from the surface of Roton so as to achieve a maximum distance of 3.0 ´ 106 m from the center of Roton?
Question options:
1) 4.2 km/s
2) 3.9 km/s
3) 3.0 km/s
4) 3.4 km/s
5) 6.0 km/s

What is the gravitational force on a 20-kg satellite circling the Earth (radius = 6.4 ´ 106 m, mass = 6.0 ´ 1024 kg) with a period of 5.0 h?
Question options:
1) 88 N
2) 55 N
3) 36 N
4) 98 N
5) 18 N

Three galaxies, each of mass M = 4.0 ´ 1041 kg, lie in a plane at the corners of an equilateral triangle with sides of 5.0 ´ 1022 m length. The magnitude of the force the other two galaxies exert on each galaxy is
Question options:
1) 4.3 ´ 1027 N.
2) 6.4 ´ 1027 N.
3) 7.4 ´ 1027 N.
4) 8.6 ´ 1027 N.
5) 4.3 ´ 1028 N.

A spacecraft (mass = m) orbits a planet (mass = M) in a circular orbit (radius = R). What is the minimum energy required to send this spacecraft to a distant point in space where the gravitational force on the spacecraft by the planet is negligible?
Question options:
1) GmM/(4R)
2) GmM/R
3) GmM/(2R)
4) GmM/(3R)
5) 2GmM/(5R)

The period of a satellite circling planet Nutron is observed to be 84 s when it is in a circular orbit with a radius of 8.0 ´ 106 m. What is the mass of planet Nutron?
Question options:
1) 6.2 ´ 1028 kg
2) 5.0 ´ 1028 kg
3) 5.5 ´ 1028 kg
4) 4.3 ´ 1028 kg
5) 3.7 ´ 1028 kg

Carla and Jenny are arguing about whether or not it is possible to escape the gravitational field of the Earth. Carla shows Jenny the system below where mass m is rE (not the Earth’s radius) distant from Earth and rP (not planet P’s radius) distant from planet P. Carla states that the mass m has escaped if FP on m = -FE on M. Which one, if either, is correct, and why?
Question options:
1) Carla, because the total gravitational force on m is zero at that point.
2) Carla, because there is no gravitational force from Earth on m at that point.
3) Carla, because there is no gravitational force on m from Earth when r > rE.
4) Jenny, because there is a gravitational force on m from Earth no matter how great the distance from the Earth.
5) Jenny, because the gravitational force from the Earth can only be blocked by a body that is larger than the Earth.

The period of oscillation of an object in a frictionless tunnel running through the Earth is 84.3 min. What is the period of oscillation of an object in a similar tunnel on the Moon? (RE = 6.37 ´ 106 m; RM = 1.74 ´ 106 m; ME = 5.98 ´ 1024 kg; MM = 7.36 ´ 1022 kg.)
Question options:
1) 6.03 ´ 10-3 min.
2) 0.713 min.
3) 84.3 min.
4) 108.5 min.
5) 139.6 min

Two stars of masses M and 6M are separated by a distance D. Determine the distance (measured from M) to a point at which the net gravitational force on a third mass would be zero.
Question options:
1) 0.41 D
2) 0.33 D
3) 0.37 D
4) 0.29 D
5) 0.14 D

When two solid spheres of the same material and same radius r are in contact, the magnitude of the gravitational force each exerts on the other is directly proportional to
Question options:
1) r.
2) r2.
3) r3.
4) r4.
5) r6.

Planet Zero has a mass of 4.0 ´ 1023 kg and a radius of 2.0 ´ 106 m. A 10-kg space probe is launched vertically from the surface of Zero with an initial kinetic energy of 8.0 ´ 107 J. What maximum distance from the center of Zero is achieved by the probe?
Question options:
1) 3.2 ´ 106 m
2) 4.0 ´ 106 m
3) 6.0 ´ 106 m
4) 5.0 ´ 106 m
5) 2.5 ´ 106 m

In an isolated system of two bodies that exert gravitational forces on one another, the quantity (quantities) that remain(s) constant is(are)
Question options:
1) the total energy of the system.
2) the total angular momentum of the system.
3) the angular positions of the two bodies.
4) all of the above.
5) only (a) and (b) above.