### Fall 2010 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 99. The exam period was 90 minutes; the average score was 76.6; the median score was 82. Click here to see the formula sheet that came with the exam.

### QUESTION 1**

This and the next question refer to this situation:

A ladder of weight 60 N leans against a frictionless wall at an angle of θ = 70° as shown in the figure. Friction between the floor and the ladder keeps it from slipping.

What is the magnitude of the force of friction Ff between the floor and the ladder?

(a)   Ff = 5 N
(b)   Ff = 11 N
(c)   Ff = 15 N
(d)   Ff = 29 N
(e)   Ff = 60 N

### QUESTION 2*

If the angle of the ladder were decreased from 70° to 50°, the force of friction required to keep the ladder from slipping would

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

### QUESTION 3***

This and the next question refer to similar situations.

Consider a student rotating on a stool with angular speed ω, holding weights in her outstretched hands. If she drops one of the weights to the ground, her angular speed will

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

### QUESTION 4*

Now consider a student rotating on a stool with angular speed ω with no weights in her hands. Suppose someone drops (vertically) a small weight into her horizontally outstretched hand. Her angular speed will

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

### QUESTION 5*

This and the next two questions refer to this situation:

A wad of gum having mass m = 0.2 kg is thrown with speed v = 8 m/s at a perpendicular bar with length d = 1.4 m and mass M. The bar is initially at rest but can rotate freely about a pivot at its center. The gum sticks to the end of the bar and the angular speed of the bar just after the collision is measured to be ω = 3 rad/s. Assume that the wad of gum is a point particle and assume that the pivot is frictionless. (You do not have to worry about gravity in this problem)

What is the magnitude of the angular momentum of the gum with respect to the pivot before it collides with the bar?

(a)   0 kg m2/s
(b)   0.48 kg m2/s
(c)   1.12 kg m2/s

### QUESTION 6**

What is the angular momentum of the gum with respect to the pivot after it collides with bar?

(a)   0.29 kg m2/s
(b)   0.48 kg m2/s
(c)   1.12 kg m2/s

### QUESTION 7*

What is the mass of the bar?

(a)   1.7 kg
(b)   2.0 kg
(c)   2.3 kg
(d)   3.1 kg
(e)   5.2 kg

### QUESTION 8*

The axle of a spinning disk of mass m is placed upon a single fixed support as shown below. The disk's angular velocity vector ω is indicated in the figure, as is the gravitational force on the disk.

Which of the figures at right accurately shows the motion of the spinning disk?

(a)
(b)
(c)

### QUESTION 9*

This and the next two questions refer to this situation:

A skater spins about a fixed point on the ice. She begins with her arms extended and an initial angular velocity ω0. She then pulls her arms in to her body. After her arms are pulled to her body, she spins with an angular velocity ωf. Throughout the time she is spinning, no external forces are acting in the horizontal plane.

How do the magnitudes of the initial and final angular velocities compare?

(a)   ω0 > ωf
(b)   ω0 = ωf
(c)   ω0 < ωf

### QUESTION 10*

Which one of the following statements is true?

(a)   The angular momentum of the skater remains constant.
(b)   The moment of inertia of the skater remains constant.
(c)   Both the angular momentum and the moment of inertia of the skater change.

### QUESTION 11*

The kinetic energy of the skater

(a)   increases because the skater does work.
(b)   decreases because the skater does work.
(c)   stays the same because the skater does no work.

### QUESTION 12*

This and the next question refer to this situation:

A uniform rod of mass M = 2 kg and length L = 1.5 m is attached to a wall with a frictionless pivot and a string as shown in the diagram above. The initial angle θ of the rod with respect to the wall is 39°. The string is then cut. The moment of inertia of a rod about an axis through one end is ML2/3.

What is the angular acceleration α of the rod immediately after the string is cut?

### QUESTION 13**

What is the angular velocity ω of the rod when it is horizontal (θ = 90°) ?

### QUESTION 14*

This and the next question refer to this situation:

A disk of radius R, mass M and moment of inertia I = MR2/2 rolls without slipping down an incline and onto a horizontal table. The disk then continues to the right and goes up a frictionless ramp. The disk starts at rest at a height h above the table, as shown.

Which one of the choices at right is an expression for the speed of the center of mass of the disk when it reaches the bottom of the ramp?

(a)
(b)
(c)
(d)
(e)

### QUESTION 15**

What is the maximum height above the table that the disk reaches on the frictionless ramp?

(a)   less than h
(b)   h
(c)   greater than h

### QUESTION 16*

This and the next question refer to this situation:

A disk has mass M = 1.0 kg and radius, R = 0.1 m is free to rotate about a fixed axle through its center. Since the axle is fixed, the center of mass of the disk does not move. The disk is initially not rotating. A student wraps a string 12 times around the perimeter of the disk and then pulls the string with a constant force of F = 1.0 N, as shown in the figure below.

The student pulls on the string until it is completely unwound, and the string does not slip on the disk as it is pulled. After the string has unwound, what is the angular speed ω of the disk?

### QUESTION 17*

Now suppose the student repeats the experiment, this time wrapping the string around the perimeter of the disk 6 times and pulling the string with a constant force of F = 2.0 N. As before, the disk is initially not rotating. How does the angular speed of the disk after the string unwinds, ω', compare to ω found in the previous question?

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

### QUESTION 18*

This and the next question refer to this situation:

A spool lies on a frictionless horizontal table. A string wound around the hub of the spool is pulled horizontally with a force F = 15 N. The moment of inertia of the spool about a vertical axis through its center of mass is I = 0.8 kg·m2, its outer radius is R = 0.75 m and its inner radius is r = 0.25 m. The spool starts from rest and the center of mass of the spool is observed to accelerate at a rate of 2.1 m/s2. (Note, you should not assume the moment of inertia for the spool is given by MR2/2.)

What is the mass M of the disk?

(a)   2.75 kg
(b)   5.28 kg
(c)   7.14 kg

### QUESTION 19*

What is the angular acceleration α of the disk?

### QUESTION 20**

This and the next question refer to this situation:

A Physics 211 student is out shoveling snow in the driveway. At one point he holds the shovel horizontally with 5 kg of snow in the shovel's scoop and pauses without moving it. The left hand is at the left end of the shovel, the right hand is 0.7 m to the right, and the center of mass of the snow is 0.5 meters further to the right as shown in the figure below. Gravity acts in the -y direction.

Assuming the shovel is massless, what is the y-component Fy of the force that his left hand exerts on the shovel?

(a)   Fy = -35 N
(b)   Fy = -10 N
(c)   Fy = 0 N
(d)   Fy = 10 N
(e)   Fy = 35 N

### QUESTION 21**

Now suppose that the handle of the shovel has a mass of 1 kg, uniformly distributed along its 1.2 meter length. Taking into account the mass of the handle, the magnitude of the force of the student's left hand on the end of the shovel's handle will

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

### QUESTION 22**

This and the next question refer to this situation:

Two blocks are suspended over a pulley by a string of negligible mass as shown below. The block on the left has a mass of m1, and the block on the right has mass m2. The pulley is a uniform solid cylinder with mass M and radius R. The block on the right has a downward acceleration equal to 1/3 the acceleration due to gravity. The tension in the string supporting the mass on the left is T1 = 170 N and the tension in the string supporting the mass on the right is T2 = 255 N. The string does not slip on the pulley.

What is the mass m2 of the block on the right?

(a)   m2 = 43 kg
(b)   m2 = 39 kg
(c)   m2 = 26 kg

### QUESTION 23**

What is the mass M of the pulley?

(a)   M = 14 kg
(b)   M = 27 kg
(c)   M = 39 kg
(d)   M = 46 kg
(e)   M = 52 kg

### QUESTION 24*

A judge's gavel has a mass of 0.7 kg and has a moment of inertia of 0.10 kg m2 around an axis through its center of mass, perpendicular to the paper in the drawing above. The distance between the center of mass of the gavel and the end of the handle is 30 cm. What is the moment of inertia of the gavel around an axis through the end of the handle, perpendicular to the paper?

(a)   0.05 kg m2
(b)   0.10 kg m2
(c)   0.16 kg m2
(d)   0.20 kg m2
(e)   0.31 kg m2

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.