### Fall 2009 Physics 211 Hour Exam 3(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 101. The exam period was 90 minutes; the average score was 79.4; the median score was 84. Click here to see the formula sheet that came with the exam.

### QUESTION 1*

This and the next two questions refer to this situation:

A solid puck with radius R1 = 1 m and mass M = 1.5 kg is sitting on a frictionless table. A top view of the puck is shown in the figure. Three constant forces are applied to the puck as shown: F1 = 3 N and F2 = 5 N are applied at radius R1, while F3 = 4 N is applied at radius R2 = 0.4 m. The moment of inertia for the puck is I = MR2/2.

What is the angular acceleration of the puck?

### QUESTION 2*

The puck begins to rotate in the clockwise direction.

(T)   True
(F)   False

### QUESTION 3*

Suppose the forces are set up so that the puck has a constant angular acceleration, α = 4.0 rad/s2. How long would it take for the puck to go from rest (ω = 0 rad/s) to an angular velocity of ω = 16 rad/s?

(a)   1 s
(b)   2 s
(c)   3 s
(d)   4 s
(e)   5 s

### QUESTION 4**

This and the next two questions refer to this situation:

A block of mass m1 = 1 kg sits atop a frictionless plane and is connected to mass m2 = 2 kg through a string that goes over a pulley of mass Mpulley = 4 kg and radius Rpulley = 0.2 m. The pulley rotates about its axis without friction and the string moves over the pulley without slipping. The system starts at rest and mass m2 falls through a height H = 2 m. The moment of inertia of the pulley is I = MR2/2.

What is the velocity (v) of mass m2 immediately before it hits the ground?

(a)   v = 2.4 m/s
(b)   v = 2.8 m/s
(c)   v = 3.1 m/s
(d)   v = 4.0 m/s
(e)   v = 5.1 m/s

### QUESTION 5*

There is no net torque generated about the axis of the pulley.

(T)   True
(F)   False

### QUESTION 6**

If the pulley is replaced by another pulley of the same mass, but with a smaller radius (e.g. a thicker disk), the velocity of block m2 immediately before it hits the ground will

(a)   increase.
(b)   stay the same.
(c)   decrease.

### QUESTION 7*

This and the next two questions refer to this situation:

A girl sits fixed on a merry-go-round of mass M = 500 kg and radius R = 2 m. The merry-go-round is initially at rest and is free to rotate without friction. The girl shoots a gun in a horizontal direction tangent to the outer edge of the merry-go-round as shown in the figure. The bullet has mass m = 0.025 kg and a speed v = 700 m/s relative to the ground. The moment of inertia of the merry-go-round is I = MR2/2.

If you ignore the mass of the girl, what is the angular velocity ω of the girl and merry-go-round after the gun has been shot?

### QUESTION 8*

If we included the mass of the girl, how would the angular velocity, ω' compare to the value ω calculated in the previous problem?

(a)   ω' < ω
(b)   ω' = ω
(c)   ω' > ω

### QUESTION 9**

Both angular momentum and linear momentum are conserved in this problem.

(T)   True
(F)   False

### QUESTION 10**

This and the next two questions refer to this situation:

A plank of length L = 2 m and mass M = 3 kg sits atop two scales that are fixed to the ground. Scale 1 is at the left end of the plank and scale 2 is a distance D = 1.25 m from scale 1. A block having the same mass as the plank (3 kg) is placed 0.5 m from the left end of the plank as shown in the picture.

(a)   10.9 N
(b)   22.6 N
(c)   27.0 N
(d)   35.3 N
(e)   43.1 N

### QUESTION 11*

If the 3 kg mass were moved closer to scale 2, the reading of scale 1 would decrease by exactly the same amount that the reading on scale 2 would increase.

(T)   True
(F)   False

### QUESTION 12*

Where would the mass have to be placed in order to have scale 1 read zero?

(a)   directly over scale 2
(b)   directly over the center of mass of the plank
(c)   a distance on 0.25 m to the right of scale 2

### QUESTION 13*

This and the next question refer to this situation:

A cylinder of mass M sits on a rough incline, as shown. The cylinder is attached at its outer radius to a wall by a string that is parallel to the inclined surface. Friction between the cylinder and the incline keeps the bottom from moving. Compare the magnitude of the frictional force f acting on the cylinder to the tension in the string T.

(a)   f = T
(b)   f < T
(c)   f > T

### QUESTION 14***

The string suddenly breaks and the cylinder begins to roll without slipping down the incline. What is the magnitude of the frictional force between the incline and the cylinder as it rolls down the incline? It may be useful to remember that Icylinder = MR2/2 and that sin(30°) = ½.

(a)   Mg
(b)   Mg / 2
(c)   Mg / 4
(d)   Mg / 6
(e)   Mg / 16

### QUESTION 15*

A square is constructed of 4 point masses, each of mass m, and 4 massless rods of length L. About which axis (or axes) shown below is (are) the moment(s) of inertia the greatest?

(a)   B
(b)   A and C
(c)   B and D

### QUESTION 16*

This and the next question refer to this situation:

A uniform, massless pole 6 m long is attached to a wall by a pivot at one end. The pole is held at an angle of 30° above the horizontal by a horizontal wire attached to the pole 4.0 m from the end pivot. A load of 60 kg hangs from the upper end of the pole.

What is the tension in the wire connecting the pole to the wall?

(a)   1190 N
(b)   1270 N
(c)   1340 N
(d)   1480 N
(e)   1530 N

### QUESTION 17**

The vertical component of the force on the pole at the pivot

(a)   points up.
(b)   points down.
(c)   is zero.

### QUESTION 18*

This and the next question refer to this situation:

A turntable has a mass of 1.14 kg and a radius of 0.17 m and is initially rotating freely at 78 rpm (ωi,t = 8.168 rad/s). There are no external forces acting on the system. The moment of inertia of the turntable can be approximated by that of a disk (Idisk = MR2/2).

A point particle, initially at rest, is dropped onto the turntable and sticks to it at a distance d = 0.10 m from its center as shown in the figure. The final angular velocity of the system is 72.7 rpm (7.613 rad/s). What is the mass of the particle?

(a)   0.038 kg
(b)   0.070 kg
(c)   0.102 kg
(d)   0.116 kg
(e)   0.120 kg

### QUESTION 19*

Let the initial kinetic energy of the turntable be Ki and the final kinetic energy of the turntable and the particle be Kf . How do Ki and Kf compare?

(a)   Kf  >  Ki
(b)   Kf  =  Ki
(c)   Kf  <  Ki

### QUESTION 20**

This and the next question refer to this situation:

A plank having length L = 2 m and mass M = 3 kg is suspended from the ceiling by a wire that is attached a distance d = 0.5 m from its left end. The right end is initially held up so that the plank is horizontal, but is then released.

What is the magnitude of the acceleration of the center of mass of the plank just after the right end is released?

(a)   Acm = 2.9 m/s2
(b)   Acm = 3.5 m/s2
(c)   Acm = 4.2 m/s2
(d)   Acm = 6.6 m/s2
(e)   Acm = 11.0 m/s2

### QUESTION 21**

Just after the plank is released the tension in the wire is:

(a)   = Mg
(b)   > Mg
(c)   < Mg

### QUESTION 22*

This and the next two questions refer to this situation:

A grindstone of mass 17 kg and radius 0.6 m is initially rotating freely at 18π radians/s. An axe is brought into contact with the grindstone, which brings it to a stop in 7.3 seconds.

Assuming that the angular acceleration of the grindstone was constant as it slowed down, through what angle did the stone rotate during the 7.3 seconds it took to stop it?

### QUESTION 23*

What is the magnitude of the work done by the axe on the grindstone?

(a)   4893 J
(b)   5129 J
(c)   9753 J
(d)   10234 J
(e)   12345 J

### QUESTION 24*

Let the work done by the axe in the above problem be W1. If the grindstone started with the same angular velocity but were instead brought to rest in half the amount of time (3.65 seconds), the work done by the axe would be:

(a)   = W1
(b)   > W1
(c)   < W1

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.