### Fall 2007 Physics 101 Hour Exam 2(24 questions)

The grading button and a description of the scoring criteria are at the bottom of this page. Basic questions are marked by a single star *. More difficult questions are marked by two stars **. The most challenging questions are marked by three stars ***.

True-false questions are worth 2 points each, three-choice multiple choice questions are worth 3 points each, five-choice multiple choice questions are worth 6 points each. The maximum possible score is 120. The exam period was 90 minutes. The mean score was 101.1; the median was 106. Click here to see page1 page2 of the formula sheet that came with the exam.

Unless told otherwise, you should assume that the acceleration of gravity near the surface of the earth is 9.8 m/s2 downward and ignore any effects due to air resistance.

### QUESTION 1**

This and the next question concern the same situation:

A solid sphere and a solid cylinder, both with mass M and radius R, are released from rest simultaneously at the top of a ramp.

Which reaches the bottom of the ramp first?

(a)   cylinder
(b)   sphere
(c)   They arrive at the same time.

### QUESTION 2**

Which has greater kinetic energy (including rotational and translational) when arriving at the bottom of the ramp?

(a)   cylinder
(b)   sphere
(c)   They have the same kinetic energy.

### QUESTION 3**

This and the next question concern the same situation:

A box of mass m = 2.2 kg is suspended from a thin wire which is wound around a solid, cylindrical frictionless pulley with mass M = 5.6 kg and radius R = 0.2 m. The box is released from rest at a height h = 0.8 m off the ground.

What is the acceleration of the box?

(a)   1.27 m/s2
(b)   2.66 m/s2
(c)   3.05 m/s2
(d)   4.31 m/s2
(e)   5.07 m/s2

### QUESTION 4**

What is the rotational kinetic energy of the pulley when the box reaches the ground?

(a)   6.77 J
(b)   9.66 J
(c)   12.8 J
(d)   15.02 J
(e)   17.25 J

### QUESTION 5*

This and the next question concern the same situation:

Two masses are suspended from a massless rod, which is supported at a pivot point, as shown. In this figure LA = 3 m, L1 = 1 m, L2 = 2.5 m, m1 = 1 kg, and m2 = 5 kg. Note that the figure is not drawn to scale.

What mass would have to be placed at the point A to balance the rod?

(a)   0.22 kg
(b)   1.91 kg
(c)   2.86 kg
(d)   3.83 kg
(e)   4.07 kg

### QUESTION 6*

Suppose you could change the value of m1. At what value would the system be balanced, without an additional mass at point A?

(a)   5.5 kg
(b)   8.6 kg
(c)   12.5 kg
(d)   13.7 kg
(e)   14.2 kg

### QUESTION 7**

A mass m = 1.6 kg is suspended from a pulley of radius R = 0.2 m, which is connected on its axis to a crank of length L = 2 m. What force F must be applied to the end of the crank to support the mass?

(a)   1.57 N
(b)   2.08 N
(c)   3.36 N
(d)   4.78 N
(e)   5.12 N

### QUESTION 8*

A hoop with radius 1.2 m and mass 3 kg is rolling at a speed v = 2 m/s. What is its rotational kinetic energy?

(a)   4.32 J
(b)   6.00 J
(c)   17.28 J

### QUESTION 9*

This and the next question concern the same situation:

A hoop of radius R = 0.4 m and mass M = 0.4 kg is released from rest at the top of an inclined plane with height h = 0.8 m. The angle between the plane and the horizontal is 20°. The hoop rolls without slipping.

What is the ratio of the hoop's rotational kinetic energy to its translational kinetic energy?

(a)   Krot / Ktrans = 1/3
(b)   Krot / Ktrans = 1/2
(c)   Krot / Ktrans = 1
(d)   Krot / Ktrans = 3/2
(e)   Krot / Ktrans = 2

### QUESTION 10*

What is the speed of the hoop when it reaches the bottom?

(a)   2.8 m/s
(b)   3.6 m/s
(c)   4.2 m/s
(d)   5.7 m/s
(e)   6.6 m/s

### QUESTION 11*

This and the next question concern the same situation:

Two solid disks with mass m1 = 3.5 kg and m2 = 0.8 kg and radius R1 = R2 = 0.2 m both slide and rotate without friction on a vertical axis. Initially, the upper disk m1 is rotating with angular velocity ω1 and the lower disk is at rest. The upper then disk falls, sticks to the lower disk, after which they are observed rotate together at angular velocity ω2 = 23 rad/s.

What was the initial angular velocity of the upper disk, ω1?

### QUESTION 12*

What is the moment of inertia of the final ensemble?

(a)   0.064 kg m2
(b)   0.075 kg m2
(c)   0.086 kg m2

### QUESTION 13*

This and the following four questions concern the same situation:

A girl on a sled slides from the top of a hill of height h0 (point A) starting from rest. The girl and the sled have a combined mass of 30 kg. The sled (with the girl) slides down on a frictionless hill to point B. Then it slides up another hill to point C and down again to point D which is at the same height as point B. The sled's speed at point B at the bottom of the hill is v0 = 19.8 m/s.

What is the height of point A, h0, that the sled started from?

(a)   16 m
(b)   18 m
(c)   20 m

### QUESTION 14*

What is the sled's speed v1 when the sled reaches point C at the top of the next hill, whose height h1=10 m?

(a)   5 m/s
(b)   8 m/s
(c)   12 m/s
(d)   14 m/s
(e)   16 m/s

### QUESTION 15*

After the sled with the girl comes to point D at the bottom of the hill, it encounters a horizontal surface with friction between point D and E. The friction force slows the sled to a stop after L = 16 m. How much work does the friction force do as it stops the sled?

(a)   -5240 J
(b)   -5520 J
(c)   -5880 J

### QUESTION 16*

What is the kinetic friction coefficient, μk, between the sled and the surface?

(a)   0.75
(b)   1.00
(c)   1.25
(d)   1.50
(e)   1.75

### QUESTION 17*

The girl who is sledding does not want to walk all the way up the first hill. To what minimum height does she have to climb for the sled to start from rest and still reach point C (at h1 = 10 m)?

(a)   7 m
(b)   10 m
(c)   20 m

### QUESTION 18*

This and the following question concern the same situation:

A block of mass M1= 3 kg slides without friction down a ramp, starting from rest at height h1. At the bottom, it runs into another block of mass M2 = 8 kg which is at rest before the collision. The two blocks stick together and slide up the second ramp (see the drawing below). They reach a maximum height h2 before sliding back down. (Note: the drawing is not to scale.) Immediately after sticking together, the two blocks move with the velocity v = 6 m/s.

What was the velocity of the 3 kg block immediately before the collision?

(a)   5 m/s
(b)   13 m/s
(c)   19 m/s
(d)   22 m/s
(e)   33 m/s

### QUESTION 19*

What was the maximum height, h2, on ramp 2?

(a)   1.66 m
(b)   1.84 m
(c)   2.10 m
(d)   2.45 m
(e)   2.75 m

### QUESTION 20*

This and the following question concern the same situation:

An object of mass 8 kg moves horizontally in a straight line at speed v0 on a frictionless surface. A force F = 100 N slows it down to 11 m/s in 2 seconds.

What was the starting speed v0?

(a)   12 m/s
(b)   16 m/s
(c)   31 m/s
(d)   36 m/s
(e)   38 m/s

### QUESTION 21*

What was the work done by the force F ?

(a)   -2100 J
(b)   -3500 J
(c)   -4700 J
(d)   -5100 J
(e)   -5900 J

### QUESTION 22*

This and the following two questions concern the same situation:

Three objects collide. Two of them have equal mass m1 = m2 = 5 kg and equal and opposite velocities in the x-direction, v1 = -v2 = 5 m/s. The third object, whose mass m3 = 2 kg, has velocity 10 m/s in the +y direction (see the figure below.) After the objects collide, they stick together and move with a final velocity vtotal .

What is the magnitude of the momentum after the collision?

(a)   20 kg m/s
(b)   70 kg m/s
(c)   120 kg m/s

### QUESTION 23*

What is the magnitude of the velocity of the combined mass after the collision, vtotal ?

(a)   1.15 m/s
(b)   1.30 m/s
(c)   1.67 m/s
(d)   1.90 m/s
(e)   2.00 m/s

### QUESTION 24*

The direction of the final velocity vtotal is:

(a)   along the +x direction
(b)   along the -x direction
(c)   along the +y direction
(d)   along the -y direction
(e)   vtotal has components in both the x and y directions.

Scoring of True-False (T,F) Questions:
• If you mark the correct answer, you get 2 points.
• If you mark the wrong answer or if you mark neither answer, you get 0 points.
Scoring of Multiple Choice I (a,b,c) Questions:
• If you mark the correct answer, you get 3 points.
• If you mark a wrong answer or if you mark none of the answers, you get 0 points.
Scoring of Multiple Choice II (a,b,c,d,e) Questions:
• If you mark one answer and it is the correct answer, you get 6 points.
• If you mark two answers and one of them is the correct answer, you get 3 points.
• If you mark three answers and one of them is the correct answer, you get 2 points.
• If you do not mark the correct answer, or if you mark more than three answers, or if you mark none of the answers, you get 0 points.