Area = 4

radius^1 α size^1

(2r^1)^2 α 2r^2 = 4A

(2r^1)^3 α 2r^3 = 8V

volume α size^3 α (diameter^1)^3

V2 α (3d^1)^3

V2 α (3V1)^3

V2 α 27V1

M α size^3

M2 α (2size)^3

M2 α 8 size

M1 α L1^3

M2 α L2^3, so…

M1/M2 α L1^3/L2^3

M2 α M1(L2^3/L1^3)

M2 α (1000 kg)(86^3 cm/145^3 cm)

M2 α 209 kg

Metabolism α M

Also…

BMR α M^3/4

Heat gained/lost α M^2/3

C1 α V^1/3

C2 α V^1/3

Take ratio and solve for C2

A α V^2/3 <--- [(V^1/3)^2 = V^2/3] A1/A2 α (V1^2/3) / (V2^2/3) Solve for A2

isomorphically with size, as we demonstrated in class. The veterinarian therefore scales the dosage for the small bull as Dose ~ ?

estimated dimensions for a gorilla.

answer. You can assume that in normal activities a gorilla’s bones typically experience no more than 20 % of the stress required to break them.

relative = 1.70 m/s

Vds = Vdw + Vws

V(ds) = tan-1 (1.2/1.2)

cos-1(1/2)

A * B = AxBx + AyBy + AzBz

(3)(6) + (9)(-2) + (0)(3)

A * B = (AyBz – AzBy)x + (AzBx – AxBz)y + (AxBy – AyBx)z

[(2)(3) – (0)(0) * x] + [(0)(0) – (3)(3) * y] +

[(3)(0) – (2)(0) *z]

NE is exactly 45 degrees

Vy = 10 * cos(45)

tan-1(2/1)

3200 * cos(18)

East: 988.85 miles

3200 * sin(18)

tan-1(800/4300)

-2A: -2x + 0t + 6z

3B: -6x+15y+3z

-C: -3x-1y-1z

V(B) = (-2,5,1)

V(C) = (3,1,1)

Find V(-2A) + V(3B) – V(C)

V(B) = (-2,5,1)

V(C) = (3,1,1)

Find V(2A) – 3[V(B) – V(C)]

cos(theta) = AxBx + AyBy + AzBz / sqroot[(Ax)^2 + (Ay)^2 + (Az)^2] * sqroot[(Bx)^2 + (By)^2 +(Bz)^2]
cos (theta) = -0.690065559

theta = Cos^-1 (-0.69006559)

convert to radians

B: (-3,0,1)

C: (-1,-1,2)

Scalar Product = -10 from A * B

What is the angle between A & B in radians (1 sigfig)?

to the right

V(mf) = V(mo) – V(0f)

to the left

V(mf) = V(mo) + V(of)

to the left

V(mf) = V(mo) – V(of)

T = (L/V-Vo) * S

tan^-1(80/425)

V(ac) = sqroot [(Vab)^2 – (Vbc)^2]

A = 6.0xˆ + 4.0yˆ − 2.0zˆ

B = 5.0xˆ − 6.0yˆ − 3.0zˆ

A = 2xˆ + 3yˆ +1zˆ

B =1xˆ − 3yˆ − 2z

2.0 m/s in still water, and the river is flowing parallel to the shore at 0.48 m/s toward the left side of the page. At what angle with respect to the shoreline should Popeye steer his

rowboat in order to make his desired landing?

following statements are true?

I. The vectors are parallel.

II. The two vectors are perpendicular.

III. The two vectors have a zero cross product.

IV. The two vectors have a nonzero cross product

Calculate A * B

Calculate |A| and |B|

Calculate the angle in degrees between A and B

– The vehicle stopped and Bob continued to move to the right

– Seat belt and shoulder harness pushing on Floyd to the left caused him to slow down with the vehicle

– Bob’s exit = 1st law

– Floyd’s remaining in vehicle = 2nd law

horizontal component of the lift changes the direction

of the momentum while the vertical component

supports the weight of the airplane.

W = weight

L = lift

There is a net force, so the object’s momentum vector must change with time. But we have no information about the direction of the force relative to the momentum. As a result, the object could be changing speed only (force parallel to momentum or object at rest), changing direction only (force perpendicular to momentum) or both (force with components both parallel and perpendicular to momentum). Without

information about the directions of the force and momentum vectors we cannot distinguish between these possibilities.

we can conclude with certainty that

A. It is changing speed.

B. It is changing direction.

C. It is changing speed and direction.

D. None of these.

Ground pushes up on you, you push down on ground

2) Fground on you (friction)

Ground pushes forward on you, you push backward on ground

3) Fgravity on you

Earth pulls down on you, you pull up on Earth

4) Fair on you

Air pushes on you, you push on air

1) What force does —>(1) pointing upward from bike represent?

2) What force does —> (2) pointing from bike to the right represent?

3) What force does —> (3) pointing downwards from bike represent?

4) What force does —> (4) pointing to the left from the bike represent?

ALSO, what is a 3rd law partner of each one? (All act on you)

a. greater than 0

b. equal to 0

c. less than 0

a. greater than 0

b. equal to 0

c. less than 0

2) T

3) F

4) F

5) T

6) F —- sum of forces = m * a

1) Every force has one and ONLY one 3rd law pair force

2) 2 forces in each pair act in OPPOSITE directions

3) 2 forces in each pair can either both act one SAME body OR on DIFFERENT bodies

4) 2 forces in each pair may have different origin (Ex. one force due to gravity and its pair force is due to friction)

5) 2 forces of 3rd law pair ALWAYS act on different bodies

6) Given 2 bodies interact via force, accelerations of the 2 bodies have EQUAL MAGNITUDE but OPPOSITE DIRECTIONS. NO other forces act on either

antiparallel (opposite)

the moon

2) 5N; book

3) No

4) 5N; Earth; book; upward

5) 5N; table; book; downward

6) 1st and 2nd

7) 3rd

1) Downward force of magnitude 5N is exerted on book by which force

2) Upward force of magnitude of ____N is exerted on ______ by table.

3) Does downward force and upward force from 1 & 2 constitute a 3rd law pair?

4) Reaction to force by 1 is force of magnitude ____N exerted on the ____ by the _____. Direction is _______.

5) Reaction to force by 2 is force of magnitude ____N exerted on the ____ by the _____. Direction is _______.

6) Which law predicts that the forces in 1 & 2 are equal and opposite?

7) Which law predicts that forces in 2 & 5 are equal and opposite?

Fab = Fad

F(AB) = force on boat from rope running to A from B

Fab = magnitude of that force

What is the magnitude of the force provided by the 3rd rope in terms of the angle?

Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes F1 =1.0 [N], F2 =8.0 [N] and F3 = 7.0 [N], where [N] is the standard unit of force, what is the component of the net force parallel to the tilted floor?

The steel segment is 1.50 [mm] in diameter, and the brass segment has twice this diameter. When a weight W is hung from the ceiling by this wire, the steel segment stretches by 1.10 [mm]. Find the weight W.

makes an angle of 28º with the direction the ship is being towed. What is the magnitude of the drag force due to the water on the ship?

(A) The force the seat belt and shoulder harness exert on Madeleine and the force Madeleine exerts on the seat belt and shoulder harness.

(B) The downward force that Madeleine exerts on her seat and the upward force applied to her by the seat.

(C) Madeleine’s weight downward and the upward normal force applied to her by the seat.

(D) The downward force that the car exerts on the road and the upward normal force that the road exerts on the car.

(E) All of the above are action reaction forces.

combined mass of the child and sled is 10 [kg].

What graph best describes the child’s horizontal position as a function of time? Note that the horizontal direction is along the x axis, with movement to the right as positive.

(1) The force of the horse pulling on the cart

(2) The force of the cart pulling on the horse

(3) The force of the horse pushing on the road

(4) The force of the road pushing on the horse

Which two forces form an “action-reaction” pair that obeys Newton’s Third Law?

A) 1 and 4

B) 1 and 3

C) 2 and 4

D) 3 and 4

E) 2 and 3

Which statement is true?

A) The particle is farthest from its starting point at D.

B) The acceleration is greatest at B.

C) The particle is moving in the opposite direction at C than it is at A.

D) The particle is closer to its starting point at C than it is at B.

E) The particle is momentarily at rest at B.

between the sled and the ice?

A) The Enterprise gains an equal amount of momentum each second

B) The Enterprise gains an equal amount of kinetic energy each second

C) The Enterprise gains an equal amount of momentum for each kilometer through which it travels

D) The Enterprise gains an amount of kinetic energy equal to the amount of impulse provided by the engines

E) The Enterprise gains an amount of momentum equal to the amount of work done by the impulse engines

A) A horse pulls a cart to the right, the cart pulls the horse to the left.

B) A book pushes down on a table, the table pushes up on the book.

C) The Physics Team pulls the History Team to the right, the History Team pulls the Physics team to the left.

D) Your weight pulling down on you and the floor pushing up on your feet.

E) Your foot pushing on the floor and the floor pushing on your foot as you walk.

between the block and the surface which will allow this to occur?

Fy = +30N – 20N – FN = 0 <-- direction determines signs Fn = 10N downwards

GF of Earth on book (-) <---> GF of book on Earth (+)

GF of Earth on table (-) <---> GF of table on Earth (+)

NF of floor on table (+) <---> NF of table on floor (-)

T = [2 (m1 * m2)/ m1 + m2] * g —– system will move but tension is same throughout but with a different value than before

w = 100kg * 10 m/s

w = 1000 N/2

g = 10 m/s

100 = 4T

SumF(y) = 2T – (Mwash + Mplat) * g = 0

T = w/8

MA = w/(w/8)

2) T = 1/2 Mg

3) T = 0

1) T of vine at point where it connects to tree. Express in terms of M and g

2) What is T 1/2 way down the vine?

3) What is T at the bottom of the vine?

2) T = 72.0 N (T = 2W)

1) Tension in rope

2) Tension in chain

W = 9.26 x 10^2

T = W

T = Vy

2T * sin(theta) = Vy

solve for T

W = 9.26 x 10^2/2 = 463 N

sin^-1(W/Tmax)

F = mg * sin(theta)

—> F = mg * sin(theta)

Fman = 288 N

—> F = mg * sin(theta) / cos(theta)

[N], and makes an angle with the ceiling? What is the angle?

the mass of the crate. If a second cable is substituted which has twice the length and twice the diameter of the original cable, the new cable stretches by an amount of what?

the diagram. Ignoring the mass of the cable, the tension in the cable is what?

What is the tension in the thread labeled 2?

between the block and the surface which will allow this to occur?

L2 = L1

Tv * L2 – mg * L1 = 0

Tv = (L1/L2) * mg

Tv = mg when L1 = L2

What value of L2 will vertical component of tension equal the weight of beam?

Tv * L2 – mg * L1 = 0

Tv = T sin(theta)

T = (mg * L1)/(L2 sin(theta))

sumtorc = +M * 4 cm – H * 14 cm – w * 30 cm = 0

solve for M

torc = rF(perp)

sumtorc = +M * 4cm*cos(60) – H * 14cm*cos(60) –

W * 30cm*cos(60)

solve for M

find torcs

1) 1/4w(L-x) – 3/4w(x) = 0

solve for (L-x)

plug and chug

2) find Wperson

Wright[L] – Wperson[x] – Wboard[L/2] = 0

x = L [(Wr-Wb/2)/(Wp)]

(show both ways to solve this)

Center (x) = sum (mx)/m

= (5)(0) + (15)(1)/5 +15

2) standing

1) Will Bill impart larger FORCE on mattress if he stands vertically or lying down?

2) Which situation will springs compress more?

2) 0

3) 150 N

4) 150 N

1) Find net upward force needed to begin to open it, if upward force is applied at center

2) Find total force on door by hinges if upward force is applied at center

3) Find net upward force needed to begin opening if force is applied at edge opposite of hinge

4) Find total force on door by hinges if upward force is applied at edge opposite of hinges

upper arm exert on the lower arm to hold a 7.5 [kg] shot put?

[N], and makes an angle with the ceiling. What is the angle?

The steel segment is 1.50 [mm] in diameter, and the brass segment has twice this diameter. When a weight W is hung from the ceiling by this wire, the steel segment stretches by 1.10 [mm]. Find the weight W.

the sign is suspended from the end of the pole, the tension in the horizontal rope is 150 [N]. What is the mass of the sign? The rope has negligible mass relative to the mass of the sign.

that the wall at P experiences? Note that the gap distance between the sign and the wall is negligible relative to the size of the sign.

pivot point? Assume that the teeter-totter is well balanced (the center-of-mass of the plank is located at the pivot point).

(A) Young should be seated 1.5 times farther from the pivot point than Newton

(B) Newton should be seated 1.5 times farther from the pivot point than Young

(C) Newton should be seated 0.67 times closer to the pivot point than Young

(D) None of the above

(E) A and C

reads 300 [N] how much does the right scale read (ie – what is Wright)?

Which of the following statements are true?

I. Hooke’s Law reasonably describes the behavior of the rubber in region B.

II. The rubber is on average stiffer in region A than in region B.

III. The average stiffness of the rubber in region B is less than in region C.

IV. The rubber is stiffer near the origin than in region B.

top of each other and place the same weight on top of them, what distance will the three stacked springs compress to support the weight? You may neglect the mass of the springs.

angle in degrees between u and v.

A. What is the mass of the person?

B. Draw and label all the forces which act on the board not already shown

in the diagram.

C. How far from the left hand end of the platform is the center of gravity of the person?

to the trunk. The diameter of the branch is 0.5 m where it attaches to the trunk. To resist the torque this weight generates, the branch is pushed away from the trunk below its

center and pulled toward it above its center. We can model this as in the picture below. What is the magnitude of the force labeled Ftop?

the wall and LCG-FF below her front feet, while the distance between her front and back feet is LBF-FF.

a) What is the magnitude and direction of the total

vertical force applied on her feet by the wall.

b) What is the magnitude and direction of the total

force exerted by all of her feet on the wall?

c) What is the magnitude and direction of the

horizontal force exerted by the wall on her back feet (the

ones on the bottom)?

d) Explain briefly what is special about gecko feet that enables them to walk up walls.

the area they present to the wind. How would you expect this changing shape to affect drag on the leaf? Will this drag force still increase as v2 ? Will it increase more rapidly, more slowly? Describe what you expect to have happen and why in a few sentences.

Consider just the right leg, one of the two on which the kangaroo stands. What is the magnitude of the normal force FN which acts on this one leg?