MkV

1)A block of wood with mass M =1.1 kg rests on a frictionless surface. The block is attached to thewall through a spring with force constant k=130 N/m2. A bullet of mass m

B = 1.0 g and a velocity of

V =300 m/s is fired and is embedded in the block, as shown below.

a) What is the amplitude of the resulting oscillation (2 pts)

b) What fraction of the initial kinetic energy of the bullet is stored in the oscillating system? (2 pts)

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Quiz #6 PHYSICS 101 Nov. 8, 2000

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a) Positive velocity and positive acceleration. b) Positive velocity and negative acceleration. c) Positive velocity and zero acceleration. d) Negative velocity and positive acceleration. e) Negative velocity and negative acceleration. f) Negative velocity and zero acceleration. g) Zero velocity and zero acceleration. h) The sign of the velocity is indeterminant. i) The sign of the acceleration is indeterminant.

x

t

2) A mass attached to a spring oscillates back and forth as indicated in the position vs. time plotbelow. At the point indicated by the dot the mass has: (circle all that are correct, 2 pts)

3)A 55 kg stoplight hanging over the center of a street is held by two equal steel cables fastened topoles on either side of the street.

a) If the cables make an angle of 20 degrees with respect to the horizontal, by what fraction are thecables stretched because of the weight of the light? The cross sectional area of each cable is 2x10-5 m2 and Young’s modulus for this steel is 2x1011 N/m2. (2 pts)

b) If the ultimate strength of the steel is 5x108 N/m2, what is the maximum mass the two cables cansupport without breaking? (2 pts)

20 deg

1)A spring stretches by 0.016 m when a 2.6 kg object is suspended, at rest, from its end. How muchmass should be attached to the spring so that its frequency of vibration is f=3.2 Hz? (5 pts)

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Quiz #6 PHYSICS 101 Nov 7, 2001

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2)A block of wood with mass M=2.1 kg rests on a frictionless surface. The block is attached to thewall through a massless spring with force constant k=46,000 N/m. A bullet of mass m=2 grams andvelocity V0=310 m/s is fired and embeds itself in the block as shown below. The block is initially atrest with the spring at its natural length. What is the amplitude of the resulting oscillation? (5 pts)

2.1 kg m=2 gm, V0=310 m/s k=46,000 N/m

Physics 101 Quiz #6November 6, 2002 Name

20 Minutes. Box your answers.

A mass m = 50. g is attached to a spring of unknown Hooke’s constant, k, and itmoves in one dimension. At time t = 0, the mass is at its equilibrium position butmoving forward with velocity v0 = 1.0 m/s. The mass executes harmonic motion withperiod 0.80 s. You may ignore any friction and damping.

1. [1 point] What is the angular frequency of the motion, ω? (If you cannot get ananswer, assume ω = 5.0 rad/s for the next part).

2. [2 points] What is the spring constant? Express your answer in mks units.

3. [2 points] How much work is done by the mass on the spring in the first 0.20 s?

4. [1 point] What is the amplitude of the oscillations?

Continued on the other side....

5. [4 points] A spring of Hooke constant k = 1200 N/m and negligible mass iscompressed by 1.0 m from its natural length. A block of mass m = 10 kg is placedagainst the spring, and then released from rest on a frictionless inclined plane of angleθ = 20.◦. Starting from its initial position, how far up the hill does the mass travel?The mass is not attached to the spring; at the moment the spring regains its naturallength, the mass loses contact with the spring.

Before release:

m

θ=20ο

k

fixed

1 m

After release:

θ=20ο

k

fixed

d=?

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Quiz 7 Physics 101. November 7, 2003

A block, A, of mass M=2.0 kg is connected to a spring with constant k =100 N/m. Asecond block, B, also of mass M, sits on the table such that the two block are justtouching when the spring is completely relaxed. There is no friction.

1. The spring (with A attached) is compressed a distance ∆x=0.1 m. What force isrequired to accomplish this? [1 point]

2. The spring is released. What is the velocity of block A as it strikes block B? [2points].

3. There is Velcro on both blocks, so they stick together. What is the furthest to theright that the spring extends (relative to its uncompressed length)? [3 points]

A

x0-∆x

A B

4. What is the period of oscillation of the two blocks attached to the spring? [2 points]

5. The three graphs below show the position, velocity and acceleration of the blocks,starting just after the two blocks first meet. The three graphs are not in order, andthe magnitudes are all set to 1. Label them x, v, and a. [2 points]

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Quiz 6 Physics 101. November 5, 2004

A mass m = 2.0 kg is attached to a spring as shown. There is no friction between the

mass and floor. When displaced, the mass oscillates with a period of T= 1.0 sec.

1. What is the spring constant, k? [2 points]

2. What force, F, is needed to displace the mass 10 cm to the right? (If you couldn’t

answer (1), use k=50 N/m from here on). [2 points]

3. After it is displaced 10 cm, it is released. What is the maximum kinetic energy of

the block? [2 points]

4. Where is the maximum KE achieved? (Refer to initial, uncompressed position as x

= 0). [1 point]

m

x

k

5. Where is the maximum acceleration achieved? [1 points]

Now a second spring with the same k is attached alongside the first spring as shown.

6. What is the new angular frequency of oscillation, !? [2 points]

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m

x

k

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QUIZ 6 Physics 101, Fall 2005

Throughout, please box your answers! You have 20 minutes to complete the quiz.

Problem 1: Blocks and Spring

We study the collision between two identi-cal blocks of mass m = 1kg, sliding on africtionless surface. The first block has aninitial velocity v1,i = 10m/s. The secondblock, initially at rest, is connected to aspring with elastic constant k = 104 N/m.The spring is compressed during the colli-sion. The collision is elastic.

v1,i

1 2

a. (2 pts) At a certain point during the collision, the two blocks move with the same velocity

v and the compression of the spring is maximal. What is v? Box your answers.

b. (2 pts) At the the same point during the collision (i.e. when the two blocks move withthe same velocity v and the compression of the spring is maximal), what is the compression

x of the spring? Box your answers.

c. (1 pts) Now consider the status of the system AFTER the collision is over. The twoblocks are not anymor in contact and they will move with different velocities v1,f and v2,f .

What are the two final velocities of the blocks, v1,f and v2,f? Box your answers.

QUIZ 6 Physics 101

Problem 2: Pendulum

A pendulum is composed by a rigid, massless rod oflength d = 1m. On the rod are attached two identical,massive blocks (labelled as “1” and “2” in the figure) ofmass m = 1kg. Block “1” is placed in the middle of therod, block “2” is placed at the free swinging end of therod. The pendulum is pivoting at one end of the rod, asshown in the figure.

Pivot

1

2

a. (2 pts) What is the momentum of inertia I of the pendulum (calculated with respect to

the pivot)? Box your answers.

b. (3 pts) What is the period of the pendulum? Box your answers.

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