Honors Physics EXAM

thermodynamics, electromagnetism, optics, vibrations and mechanical waves, and mechanics
elements of physics
series of steps used by scientists to test a theory
1. make observations
2. create and test a hypothesis
3. interpret the results
4. form conclusions based on the results
scientific method
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pattern, plan, representation, or description designed to show the structure or workings of an object, system, or concept
model
particles or interacting components considered to be a distinct physical entity for the purpose of study- what to study when making a model
ex: a ball and anything affecting its motion
system
explanation based on research and observation that can be tested
hypothesis
experiment testing only one factor at a time using a control group and an experimental group
controlled experiment
1 x 10^-6 s
If a radio wave has a period of 1 µs, what is the wave’s period in seconds?
a. 1 x 10^-8 m
b. 1 x 10^-5 mm
c. 1 x 10^-2 µm
A hydrogen atom has a diameter of about 10 nm.
a. Express this diameter in meters.
b. Express this diameter in millimeters.
c. Express this diameter in micrometers.
1.440 x 10^3 kg
The average mass of an automobile in the U.S. is about 1.44 x 10^6 g. Express this mass in kilograms.
description of how close a measurement is to the correct or accepted value of the quantity measured
accuracy
degree of exactness of a measurement
precision
digits in a measurement know with certainty plus one estimated digit- always use scientific notation
significant figures
round to the first column from the left with an estimated digit- the smallest number of decimal places
rule for adding and subtracting significant figures
round to the same number of digits as the measurement with the smallest number of significant figures
rule for multiplying and dividing significant figures
a. .67
b. 14
c. 778.92
d. 797.5
Perform these calculations using the rules for significant figures.
a. 26 x .02584
b. 15.3 ÷ 1.1
c. 782.45 – 3.5328
d. 63.258 + 734.2
system for specifying the precise location of objects in space and time that remains fixed with an origin throughout the procedure
frame of reference
change in position of an object- does not always equal distance traveled, can be positive or negative
∆x = xf – xi
displacement
total displacement divided by the time during which the displacement occurred- not the same as speed because speed has no direction, can be positive or negative
Vavg = ∆x ÷ ∆t = (xf – xi) ÷ (tf – ti)
average velocity
velocity of an object at some instant of at a specific point in the object’s path- can be found by drawing a line tangent to a specific point on a graph and finding the slope of the line
instantaneous velocity
24 s
What is the shortest possible time in which a bacterium could travel a distance of 8.4 cm across a Petri dish at a constant speed of 3.5 mm/s
a. 2.5 m/s to the south
b. 2.27 m/s to the north
c. 0 m/s
An athlete swims from the north end to the south end of a 50.0 m pool in 20.0 s and makes the return trip to the starting position in 22.0s.
a. What is the average velocity for the first half of the swim?
b. What is the average velocity for the second half of the swim?
c. What is the average velocity for the whole trip?
rate at which velocity changes over time if an object changes sped, direction, or both- can be positive, negative, or 0 depending on the object’s velocity
a = ∆v ÷ ∆t = (vf – vi) ÷ (tf – ti)
acceleration
vf = vi = a∆t
final velocity with constant acceleration
∆x = 1/2(vi + vf)∆t
displacement of an object with a constant acceleration
can also be used to find displacement required for an object to reach a certain speed or come to a stop
∆x = vi∆t + 1/2a∆t^2
∆y = a/2at^2 for horizontal projectiles
displacement of an object with a constant acceleration over a certain period of time
vf^2 = vi^2 + 2a∆x
final velocity after any displacement
.85 s
Marissa’s car accelerates uniformly at a rate of +2.60 m/s^2. How long does it take for Marissa’s car to accelerate from a speed of 24.6 m/s to a speed of 26.8 m/s?
positive
A bowling ball with a negative initial velocity slows down as it rolls down the lane toward the pins. Is the bowling ball’s acceleration positive or negative?
a. +5.0 m/s^2
b. +16 m
c. +6.4 m/s
Nathan accelerates his skateboard uniformly along a straight path from rest to 12.5 m/s in 2.5 s.
a. What is Nathan’s acceleration?
b. What is Nathan’s displacement during the 2.5 s time interval?
c. What is Nathan’s average velocity during the 2.5 s interval?
motion of a body when only the force of gravity is acting upon it- acceleration = 9.8 m/s^2, even when thrown upward an object will still have an acceleration of -9.8 m/s^2
free fall
a. The coin’s velocity decreases, becomes 0 at the peak, then increases as it comes back down
b. Remains constant
A coin is tossed vertically in the air.
a. What happens to its velocity while it is in the air?
b. Does its acceleration increase, decrease, or remain constant while it is in the air?
11 m
A pebble is dropped down a well and hits the water 1.5 s later. How far did the pebble fall?
physical quantity that has magnitude but no direction
ex: speed and volume
scalar
physical quantity with both direction and magnitude
ex: velocity, displacement, acceleration
vector
vector that represent the sum of two or more vectors- must be drawn tip to tail
a^2 + b^2 = c^2 to find magnitude
tan-1(o/a) = θ to find direction (angle)
cosθ = a/h or sinθ = o/h to find velocity when given the angle
resultant
126 m above the horizontal
A roller coaster moves 85 m horizontally, then travels 45 m at an angle of 30.0˚ above the horizontal. What is the displacement from its starting point?
205 km/h at 75˚ north of east
A pilot sets the plane’s controls thinking the plane will fly at 2.50 x 10^2 km/h to the south. If the wind blows at 75 km/h toward the southeast, what is the plane’s resultant velocity?
projections of a vector along the axes of a coordinate system
components
a. 5.8 m/s at 59˚ downriver
b. 6.1 m/s at 9.5˚ from the direction the wave is traveling
Find the magnitude and direction of the resultant velocity vector for the following perpendicular velocities:
a. A fish swimming at 3.0 m/s relative to the water across a river that moves at 5.0 m/s.
b. A surfer traveling at 1.0 m/s relative to the water across a wave that is traveling at 6.0 m/s.
curved path an object follows when thrown, launched, or otherwise projected near Earth’s surface
projectile motion
always considered constant in a projectile
∆x = vx∆t
horizontal motion of a projectile
vy = vi(sinθ)
vertical component of a projectile
vx = vi(cosθ)
horizontal component of a projectile
5.05 s; 454 m
A tornado lifts a car to a height of 125 m above the ground then flings the car horizontally with a speed of 90.0 m/s. How long does the car take to reach the ground? How far does the car travel horizontally before hitting the ground?
69.4 m/s at 64.4˚ below the horizontal
A rescue plane traveling horizontally at 30.0 m/s at a height of 200 m above the ground drops a package of emergency rations to a stranded party of explorers. Find the velocity of the package just before it hits the ground.
10 m/s in the opposite direction
A woman on a 10-speed bicycle travels at 9 m/s relative to the ground as she passes a little boy on a tricycle traveling at 1 m/s relative to the ground in the opposite direction. How fast does the boy appear to be moving to the woman?
1.51 m/s at 5.7˚ north of east
A girl in an airport rolls a ball north at .15 m/s on a moving walkway that moves east at 1.50 m/s. What is the ball’s velocity relative to the ground?
an action exerted on an object which may change the object’s state of rest or motion
force
force that results from physical contact
ex: catching a football, pushing a wagon
contact force
force that does not involve physical contact between objects
ex: gravity, attraction or repulsion of electric charges
field force
an object at rest remains at rest, and an object in motion stays in motion with a constant velocity unless acted on by an external force- law of inertia
Newton’s First Law
tendency of an object to resist being moved or resist a change in speed or direction- proportional to an object’s mass
inertia
a single force that acts on an object as a result of the interaction between the object and its environment
external force
vector sum of all forces acting on an object
Fnet = ?Vg = mfg for objects in a liquid
net force
state at which the net force of an object is 0
equilibrium
If a car is traveling westward at a constant velocity of 20 m/s, what is the net force acting on the car?
-3674 N
If a car is accelerating downhill under a net force of 3674N, what additional force would cause the car to have a constant velocity?
the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass
∑F = ma
Newton’s Second Law
for every action, there is an equal but opposite reaction- there is always an action force and a reaction force
Newton’s Third Law
a. 12 N
b. 3.0 m/s^2
A 6.0 kg object undergoes an acceleration of 2.0 m/s^2.
a. What is the magnitude of the net force acting on the object?
b. If this same force is applied to a 4.0 kg object, what acceleration is produced?
1.6 m/s^2 at 65˚ north of east
The forces acting on a sailboat are 390 N north and 189 N east. If the boat has a mass of 270 kg including the crew, what are the magnitude and direction of the boat’s acceleration?
measure of the gravitational force exerted on an object- its value can change with the location of the object in the universe
Fg = mag
Fg = Gmmp/r^2
weight
force that acts on a surface in a direction perpendicular to the surface- not always perpendicular to gravity
Fn = mg(cosθ)
normal force
force that resists the initiation of sliding motion between two surfaces that are in contact and at rest- as long as the object does not move, it is equal and opposite to the applied force
Fs = -Fapplied
µs = Fsmax/Fn for the coefficient
static friction
force that opposes the movement of two surfaces that are in contact and sliding over each other
Fnet = Fapplied – Fk
µk = Fk/Fn for coefficient
kinetic friction
ratio of the magnitude of the force of friction between two objects in contact to the magnitude of the normal force
Ff = µFn to find magnitude of the force of friction if the coefficient and normal force are given
coefficient of friction
a. 3.70 N
b. 58.5 N
A bag of sugar has a mass of 2.26 kg.
a. What is its weight in Newtons on the moon, where the acceleration due to gravity is 1/6 of Earth’s?
b. What is its weight on Jupiter, where the acceleration due to gravity is 2.64 times that of Earth?
a. 34 N
b. 39 N
A 2.0 kg block on an incline at a 60˚ angle is held in equilibrium by a horizontal force.
a. Determine the magnitude of this horizontal force.
b. Determine the magnitude of the normal force on the block.
.37; .32
A 55 kg ice skater is at rest on a flat skating rink. A 198 N horizontal force is needed to set her in motion. After the skater is in motion, a 175 N force keeps her moving at a constant velocity. Find the coefficients of static and kinetic friction between the skates and the ice.
the product of the component of a force along the direction of displacement and the magnitude of the displacement- can be positive or negative
W = Fdcosθ
work
a. negative
b. positive
c. negative
Indicate whether the work done on the second object will be positive or negative.
a. The road exerts a friction force on a speeding car skidding to a stop.
b. A rope exerts a force on a bucket as it is raised up a well.
c. Air exerts a force on a parachute as the parachutist falls to Earth.
a. 8.28 x 10^3 J
b. -7.92 x 10^3 J
c. 3.6 x 10^2 J
A worker pushes a 1.50 x 10^3 crate with a horizontal force of 345 N a distance of 24.0 m. µk = .220.
a. How much work is done by the worker on the crate?
b. How much work is done by the floor on the crate?
c. What is the net work done on the crate?
energy of an object due to the object’s motion
KE = 1/2mv^2
kinetic energy
net work done by all forces acting on an object equals the change in the object’s kinetic energy
Wnet = ∆KE
work-kinetic energy theorem
energy associated with an object because of its position, shape, or condition
potential energy
the potential energy stored in the gravitational fields of interacting bodies- must be measured relative to some zero level
PEg = mgh
gravitational potential energy
energy available for use when a deformed elastic object returns to its original position- stored in any compressed or stretched object
PEelastic = 1/2kx^2 where k is the spring constant measured in N/m
elastic potential energy
4.4 x 10^-3 J
A pinball hits a bumper, giving the ball a speed of 42 cm/s. If the ball has a mass of 50 g, what is its kinetic energy in Joules?
2.8 m/s
A student slides a .75 kg book across a table a distance of 1.2 m. Given that µ = .34, use the work-kinetic energy theorem to find the book’s initial speed.
6.18 x 10^-2 J
A spoon with a mass of 30.0 g is raised 21.0 cm above a table. What is the spoon’s gravitational potential energy?
sum of kinetic energy and all forms of potential energy- is always conserved in the absence of friction
ME = KE + ∑PE
MEi = MEf
mechanical energy
2.93 m/s
If the spring of a jack-in-the-box is compressed 8.0 cm from its relaxed length and then released, what is the speed of the 50.0 g toy head when the spring returns to its natural length if k = 80.0 N/m?
quantity that measures the rate at which work is done or energy is transformed- 1hp = 746 W
P = W/∆t
P = Fv
power
12.3 s; 2.45 x 10^3 J
A 50.0 kg student climbs a 5.0 m rope at a constant speed. If the student’s power output is 200.0 W, how long does it take the student to climb the rope? How much work does the student do?
613 W; 2.45 x10^3 J
A motor-driven winch pulls a 50.0 kg student 5.00 m up a rope at a constant speed of 1.25 m/s. How much power does the motor use in raising the student? How much work does the motor do on the student?
quantity defined as the product of the mass and velocity of an object- is always conserved although it may transfer from one object to another
p = mv
F∆t = ∆p
p1i + p2i = p1f + p2f
momentum
product of the force and time over which the force acts- is equal and opposite in all collisions involving isolated objects
F∆t
F∆t = ∆p
F1∆t = -F2∆t
impulse
a. momentum increases by a factor of 2
b. kinetic energy increases by 4
The speed of a particle is doubled.
a. By what factor is its momentum changed?
b. What happens to its kinetic energy?
a. 31.0 m/s
b. the bullet
A pitcher claims he can throw a .145 kg baseball with as much momentum as a speeding bullet. Assume that a 3.00 g bullet moves at a speed of 1.50 x 10^3 m/s.
a. What must the baseball’s speed be if the claim is valid?
b. Which has greater kinetic energy, the ball or the bullet?
a. 2.6 kgm/s downfield
b. 1.3 x 10^2 N downfield
A .42 kg soccer ball is moving downfield with a velocity of 12 m/s. A player kicks the ball so that it has a final velocity of 18 m/s downfield.
a. What is the change in the ball’s momentum?
b. Find the constant force exerted by the player on the ball if they are in contact for .020 s.
a. The ball will move away at 7.0 m/s.
b. The momentum gained by the ball must be equal to and opposite that of the student.
c. The student and the ball will move to the right at 1.5 m/s.
d. The student’s initial momentum is 0. When the student catches the ball, some of the ball’s momentum goes to the student.
A 44 kg student on ice skates is playing with a 22 kg exercise ball. Explain what happens during the following situations:
a. The student is holding the ball and both are at rest. The student then throws the ball horizontally, causing the student to glide backat 3.5 m/s.
b. What happens to the ball in part a in terms of the momentum of the ball and the momentum of the student?
c. The student is initially at rest. He then catches the ball, which is initially moving to the right at 4.6 m/s.
d. What happens in part c in terms of the momentum of the student and the momentum of the ball?
61 m/s
High-speed stroboscopic photograph show the head of a 250 g golf club traveling at 55.0 m/s just before it strikes a 46 g golf ball sitting at rest on a tee. After the collision, the club continues to travel in the same direction at 42.0 m/s. Use the law of conservation of momentum to find the speed of the gold ball after the collision.
collision in which two objects stick together after colliding- momentum is conserved but kinetic energy is not
mv1i + mv2i = (m1 + m2)vf
perfectly inelastic collision
collision in which the total momentum and total kinetic energy are conserved
mv1i + mv2i = mv1f +mv2f
1/2mv1i^2 +1/2mv2i^2 = 1/2mv1f^2 +1/2mv2f^2
elastic collision
a. 1.1 m/s to the south
b. 1.4 x 10^3 J
A 95.0 kg fullback moving south with a speed of 5.0 m/s has a perfectly inelastic collision with a 90.0 kg opponent moving north at 3.0 m/s.
a. Calculate the velocity of the players just after the tackle.
b. Calculate the decrease in total kinetic energy as a result of the collision.
a. 3.5 m/s
b. 0 J
c. 0 J
Two .40 kg soccer balls collide elastically in a head-on collision. The first ball starts at rest, and the second ball has a speed of 3.5 m/s. After the collision, the second ball is at rest.
a. What is the final speed of the first ball?
b. What is the kinetic energy of the first ball before the collision?
c. What is the kinetic energy of the second ball after the collision?
speed of an object in circular motion- depends on an object’s distance from the center of its path
tangential speed
acceleration directed toward the center of a circular path
ac = vt^2/r
centripetal acceleration
net force on an object in circular motion
ex: friction, gravity
Fc = mac
centripetal force
14 m/s
A girl on a spinning amusement park ride is 12 m from the center of the ride and has a centripetal acceleration of 17 m/s^2. What is her tangential speed?
1.36 x 10^3 N
A 90 kg person rides a spinning amusement park ride with a radius of 11.5 m. If his tangential speed is 13.2 m/s, what is the magnitude of the centripetal force acting on the rider?
mutual force of attraction between particles of matter- acts between all masses
Fg = G (m1m2÷r^2)
gravitational force
is equal to free-fall acceleration
g = Fg/m
g = Gmp/r^2
gravitational field strength
a. 636 N
b. 475 N
c. 678 N
d. 656 N
Earth has a mass of 5.97 x 10^24 kg and a radius of 6.38 x 10^6 m, while Saturn has a mass of 5.68 x 10^26 kg and a radius of 6.03 x 10^7 m. Find the weight of a 65.0 kg person at each of the following locations:
a. on the surface of Earth
b. 1000 km above the surface of Earth
c. on the surface of Saturn
d. 1000 km above the surface of Saturn
6.5 m/s^2
What is the magnitude of g at a height above Earth’s surface where free-fall acceleration equals 6.5 m/s^2?
planets travel in elliptical orbits around the sun, which is at one of the focal points
Kepler’s First Law
planets closer to the sun travel faster
Kepler’s Second Law
T1^2/T2^2 = r1^3/r2^3
T^2 = (4π^2/Gm)r^3
Kepler’s Third Law
T = 2π(√r^3/Gm)
vt = (√G(m/r))
where m = mass of central object being orbited
orbital period and speed
vt = 1.02 x 10^3 m/s
T = 2.37 x 10^6 s or 27.4 days
Find the orbital speed and period of Earth’s moon if r = 3.84 x 10^8 m.
quantity that measures the ability of a force to rotate an object around some axis- can be positive (ccw) or negative (cw) and is conserved only in the absence of friction
? = Fdsinθ
∑? = F1d1 – F2d2
torque
perpendicular distance from the axis to a line drawn along the direction of the force
lever arm
machine’s ability to change the direction or magnitude of an input force
MA = Fout/Fin
MA = din/dout only in the absence of friction
mechanical advantage
ratio of useful work output to useful work input- for all real machines is less than 1 due to friction
eff = Wout/Win
efficiency
130 N
The efficiency of a squeaky pulley system is 73%. What force is exerted on the machine if a rope is pulled 18.0 m to raise a 58 kg mass a height of 3.0 cm?
2.7
A person lifts a 950 N box by pushing it up an incline. If he exerts a force of 350 N along the incline, what is the incline’s mechanical advantage?
nonsolid state of matter in which the atoms or molecules are free to move past each other- liquid or gas
fluid
concentration of matter of an object- no standard for gases
? = m/V
mass density
upward force exerted by a liquid on an object immersed or floating on the liquid
Fb = mfg
Fb = mog if floating
buoyant force
any object completely or partially submerged in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object
Fb = mfg
Archimedes’ Principle
9.92 x 10^2 kg/m^3
A submerged submarine alters its buoyancy so that it initially accelerates upward at .325 m/s^2. What is the submarine’s average density at this time if the density of sea water is 1.025 x 10^3 kg/m^3?
magnitude of the force on a surface per unit area- 1.01 x 10^5 Pa = 1 N/m^2 = 1 atm
P = F/A
P = ?hg for gauge pressure
P = P0 + ?hg as a function of depth for absolute pressure
pressure
pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and walls of the container
Pinc = F1/A1 = F2/A2
Pascal’s Principle
3.59 x 10^6 Pa
Water is to be pumped to the top of the Empire State Building, which is 366 m high. What gauge pressure is needed at the base of the building to lift the water up that high if the density of water is 1.00 x 10^3 kg/m^3?
when every particle of a fluid passes a particular point along the same smooth path
laminar flow
when the flow of a fluid becomes irregular
turbulent flow
fluid with no internal friction (viscosity) and is incompressible
ideal fluid
A1v1 = A2v2
continuity
the pressure in a fluid decreases as the fluid’s velocity increases
ex: an airplane’s wings are angled to increase pressure under the wings to create lift
Bernoulli’s Principle
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