PHY141 Midterm Exam 1

9:40-10:55am, Tuesday Oct 1, 2019

Rules

• You may use only a writing instrument while taking this test. You may not consultany calculators, computers, books, nor each other.

• Answer the multiple-choice questions (problems 1 – 5) by clearly circling the correctnumber on this exam. For each multiple-choice question, select only one answer.Questions with more than one answer or unclearly selected answers will be consideredincorrect.

• Problems 6 and 7 can be answered in the empty sheets inside this exam or in a bluebook. The answers need to be well motivated and expressed in terms of the variablesused in the problem. You may receive partial credit, but only when we can clearlyread and understand your solution. Answers that are not explained or motivated willnot receive credit.

• Not every problem is worth the same amount of points.

• Your name must be printed clearly on this exam and on your bluebooks.

Name:

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Useful equations

The momentum principle

F =dp

dtGravitational force

F = −GMm

r2r or −mgz

Gravitational potential energy

U = −GMm

ror mgz

Uniform circular motion

a = −v2

rr = −rΩ2r

v = rΩ

T = 2π/Ω

Work

W =

∫F · dx

Relativistic momentum and energy

p = γmv E = γmc2 γ =1√

1 − v2/c2

Hooke’s law for a springF = −kx

Friction forces:

Ffr,static ≤ µsFnormal

Ffr,kinetic = µkFnormal

Potential energy and force

F = −dUdx

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Problem 1: (15 points)

A ball kicked into the air moves along the path shown above; it is at point A and thenlater at point B.

(a) Which arrow best indicates the direction of the ball’s instantaneous velocity at pointB?

A. B. C. D. E.

(b) Which arrow best indicates the direction of the ball’s average velocity from pointA to point B?

A. B. C. D. E.

(c) Which arrow best indicates the direction of the change in the ball’s momentum frompoint A to point B?

A. B. C. D. E.

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Problem 2: (10 points)

A 10 g bullet is moving at a velocity of 200 m/s. The bullet hits a block of cement andis stopped in 10 milliseconds.

a) What force in Newtons (N) was applied to the bullet?

A. 2 × 10−3 N B. 2 × 10−2 N C. 2 N D. 20 N E. 200 N

b) What is the work required to stop the bullet?

A. −2 × 10−2 J B. −2 J C. 4 J D. −200 J E. 400 J

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Problem 3: (10 points)

As shown in the diagram, a block of mass m is suspended from a wire, with a compressedspring pushing it away from the wall. The angle θ is that between wire and spring. Thespring constant is k. The length of the wire is L.

θ

wir

e

spring

a) Which of the following diagrams correctly shows all the forces on the block due to objectsin the surroundings?

A. B. C. D. E.

b) The tension T on the wire is

A. mgsin θ B. mg

cos θ C. mg D. mg tan θ E. kL cos θ

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Problem 4: (10 points)

We consider a shell of mass Mc and radius Rs. Inside it is a ball or core of mass mc

and radius rc. The region between shell and core is empty.The core radius is one quarter of the shell radius; rc = Rs/4.We consider the acceleration on a small point masses on the surface of the shell and

on the surface of the core. The gravitational acceleration on the surface of the shell is thesame as the gravitational acceleration on the surface of the ball.

The mass mc is

A. 116Ms B. 1

15Ms C. 14Ms D. 4Ms E. 15Ms

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Problem 5: (10 points)

A block with mass m is on a frictionless surface and connected via two springs to a fixedpost.

The period of the block’s oscillation back and forth is

A. 2π√

3km B. 2π

√3k2m C. 2π

√3m2k D. 2π

√2m3k E. 2π

√m3k

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Problem 6: (20 points)

Two blocks with masses m1 = 1 kg and m2 = 2 kg, shown in the figure, are free to move.The coefficient of static friction between the blocks is µ = 0.5 but the surface beneath m2

is frictionless. You can approximate the gravitational acceleration g as 10 m/s2.

What is the minimum force F required to hold m1 against m2 without it slipping?Please give the units of your answer.

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Problem 7: (25 points)

A ball of mass m is tethered to a vertical post with a string of length L. The post hasheight H above the ground. The ball is undergoing uniform circular motion. The anglebetween the string holding the ball and the post is constant and is θ. The gravitationalacceleration is g.

Figure 1: A Tether ball

a) What is the ball’s velocity?

b) What is the rotation period?

c) The string breaks and the ball falls to the ground. What is the ball’s horizontalvelocity component when it hits the ground?

d) What is the ball’s vertical velocity component when it hits the ground?

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