Physics 101 Exam 1 NAME 2/7 1. In the situation below, a...

Physics 101 Exam 1 NAME ______________________ 2/7

1. In the situation below, a person pulls a string attached to block A, which is in turn attached to another, heavier block B via a second string. (a) Which block has the larger acceleration? (b) How does the force of string 1 on block A compare with the force of string 2 on block B? Explain your answers.


2. A child slides down a slide that is inclined at an angle θ with respect to the ground. At the bottom, her speed is half what it would have been if the slide had been frictionless. What is the ratio of the acceleration she actually experienced to the acceleration she would have experienced on a frictionless slide? Derive an expression for the coefficient of kinetic friction, µk, between the slide and the child in terms on the angle, θ.

θ


2. Two blocks sitting on a frictionless table are pushed from the left by a horizontal force, as shown below.

(a) Draw a free-body diagram for each of the blocks. (b) Express, in terms of the quantities given in the figure, the force of contact between the two blocks. (c) What is the acceleration of the blocks?

Suppose now that, instead of a force on the left block, a force of equal magnitude but opposite direction is applied to the block on the right.

(d) What is the force of contact between the two blocks in this case? (e) What is the acceleration of the blocks? (f) Do your answers to parts b through e make sense? Explain.

m1m2

F

m1m2

F


4. A block is heading up a ramp with an initial speed of 4 m/s. The ramp is inclined at an angle of 37o with respect to the horizontal table. The coefficient of kinetic friction between the block and the ramp is µk = 0.25. How far up the ramp will it go? How much time elapses as the block travels up the ramp and back down to its starting point? [sin(37o) = 0.6, cos(37o) = 0.8]


2. Identical constant forces push two identical masses A and B continuously from a starting line to a finish line. If A is initially at rest and B is initially moving to the right, which mass has the larger change in momentum? Which mass has the larger change in kinetic energy? Explain your answers.

start finish

A

B

v0 = 0

v0 �= 0


4. Two blocks of mass m and 3m, resting on a frictionless table, are connected by a stretched spring and then released. (a) Is there a net external force on the system? (b) Determine the ratio of their velocities. (c) What is the ratio of their kinetic energies? (d) Describe the motion of the center of mass of the system.

Physics 101 Exam 2 NAME ______________________ 1/8 Physics 101 Exam 2 NAME ______________________ 2/8 Physics 101 Exam 2 NAME ______________________ 3/8 Physics 101 Exam 2 NAME ______________________ 4/8 Physics 101 Exam 2 NAME ______________________ 5/8

Physics 101-1, Fall 2004Exam 2

Instructor: Michael W. Noel

This is an 80 minute, closed-book exam. On the final two pages of this exam several useful relationships are provided. You may separate these pages for easy reference.

This exam consists of 8 pages. Please make sure you have all of them and write your name at the top of each page.

When providing a sketch, please be as neat, accurate, and quantitative as possible. A sloppy sketch indicates misunderstanding and will receive a reduced grade.

Do all five questions on the exam. Do all work directly on this examination. Please show all of your work clearly in the space provided. If you run out of room, you may use the back of the page preceding the question you are working on. Scratch work done in blue books will not be graded and should not be turned in. Be sure to answer ALL parts of each question.

Some problems will take longer than others, but all will be weighted equally when grading.

1. Two 20-kg sleds are placed a short distance apart, one directly behind the other, on a frozen (frictionless) pond. A 4-kg cat, standing on one sled, jumps across to the other and then immediately back to the first. Both jumps are made at a horizontal speed of 3 m/s relative to the ice. Find the final speeds of the two sleds.

2. A 50-kg bungee jumper jumps from a bridge. She is tied to a bungee cord that is 10 m long when unstretched and has a spring constant of 50 N/m. How far below the bridge is she when she reaches her maximum speed? What is her maximum speed?

3. A woman of mass m stands at the edge of a solid cylindrical platform of mass M. The platform initially rotates at angular velocity ω0 about a vertical axis through its center. What will happen if she begins walking around the perimeter of the platform, opposite the direction of rotation? Suppose she walks just fast enough that she is now stationary relative to the ground. What will the angular velocity of the platform be now?

4. A thin hoop, a solid cylinder, and a sphere roll down an incline. In what order do they reach the bottom of the incline if they all start from rest at the same time (explain your answer)? What is the ratio of the speed of the hoop at the bottom of the ramp to the speed of the cylinder at the bottom of the ramp, vhoop / vcylinder?


5. A massless spring with spring constant k is placed between a block of mass m and a block of mass 3m. Initially the blocks are at rest on a frictionless surface and they are held together so that the spring between them is compressed by an amount D from its equilibrium length. the blocks are then released and the spring pushes them off in opposite directions. Find the final speeds of the two blocks.


Potentially useful relationships:

v = v0 + at

x = x0 + v0t +1

2at2

v2 = v20 + 2a(x − x0)

aR =v2

r

T =1

f

v =2πr

T

g = 10 m/s2

for at2 + bt + c = 0, t =−b ±

√b2 − 4ac

2a

Ffr = µkFN

Ffr ≤ µsFN

sin2 θ + cos2 θ = 1

sin θ

cos θ= tan θ

W =

b

a

F·dl

K =1

2mv2

Fs = −kx

W = F · d

U = mgy

U =1

2kx2

Wnet = ∆K

K2 + U2 = K1 + U1

∆K + ∆U = WNC

p = mv

ΣF = ma =dp

dt

J =

tf

ti

Fdt = ∆p

p1 + p2 = p1 + p

2

v 1 − v 2 = v 2 − v

1

v = Rω

atan = Rα

ar = ω2R

τ = R⊥F

Στ = Iα =dL

dt

I = ΣmiR2i

L = Iω

K =1

2Iω2

ω = ω0 + αt

θ = ω0t +1

2αt2

ω2 = ω20 + 2αθ

θ =s

R

ω = 2πf

Physics 101 Exam 1 NAME 2/7 1. In the situation below, a...

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