### Fall 2001 Physics 101 Hour Exam 3(26 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 ***.

This exam consists of 26 questions; 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 119. When the exam was given, the mean was 90.0; the median was 92. Click here to see the formula sheet that came with the exam.

### QUESTION 1**

This and the following two questions relate to the same situation:

A uniform solid disk of mass 4 kg and radius 0.25 m is at rest at the top of a 4 m long incline that makes an angle of 30° with the horizontal as shown in the figure.

If the disk is released and it rolls down the incline without slipping, what is the linear speed of the center of mass of the disk when it reaches the bottom of the incline?

(a)   1.81 m/s
(b)   3.62 m/s
(c)   5.11 m/s
(d)   6.26 m/s
(e)   12.46 m/s

### QUESTION 2**

Suppose that the solid disk is replaced by an annular disk (see figure), with the same outer radius (0.25 m) and mass (4 kg) and an inner radius equal to 0.15 m. Compared to your previous answer, the linear speed of the annular disk at the bottom of the incline will be

(a)   smaller.
(b)   the same.
(c)   larger.

### QUESTION 3**

Suppose the original solid disk now slides (rather than rolls) down the incline, which now has a frictionless surface. Compared with the case where it rolls without slipping, the total kinetic energy of the disk the bottom of the incline will be

(a)   smaller.
(b)   the same.
(c)   larger.

### QUESTION 4**

This and the following three questions relate to the same situation:

A student of mass 60 kg stands at the edge of the platform of a merry-go-round, which is a uniform circular disk of radius 2 m and mass 200 kg. Assume that the student can be treated as a point mass.

If the merry-go-round rotates at an angular velocity of 2 rad/s around its axis, what is the angular momentum of the system consisting of student plus merry-go-round around the axis of rotation of the platform?

(a)   200 kg-m2/s
(b)   100 kg-m2/s
(c)   60 kg-m2/s
(d)   520 kg-m2/s
(e)   1280 kg-m2/s

### QUESTION 5**

If now the student walks slowly inward toward the center of the platform, what is the angular velocity of the platform when the student is at distance of 1 m from the axis of rotation? (Assume that there is no friction and that there is no external torques on the platform).

### QUESTION 6**

With the student 1 m from the axis of the platform, how does the kinetic energy of the system compare with what it was initially?

(a)   smaller
(b)   equal
(c)   larger

### QUESTION 7**

Now the student is back at the edge of the platform, which is rotating at 2 rad/s. Which of the following actions will cause the angular velocity of the platform to slow down?

(a)   Walk to the center of the platform.
(b)   Walk along the edge of the platform in the direction of rotation of the platform.
(c)   Walk along the edge of the platform opposite to the direction of rotation of the platform.

### QUESTION 8*

The net work done in accelerating a propeller from rest to an angular velocity of 200 rad/s is 2000 J. What is the moment of inertia of the propeller?

(a)   0.20 kg-m2
(b)   0.10 kg-m2
(c)   0.005 kg-m2
(d)   0.15 kg-m2
(e)   0.25 kg-m2

### QUESTION 9*

This and the following four questions relate to the same situation:

A 2.4-kg object is attached to a horizontal spring of force constant k = 9000 N/m. The spring is stretched 0.10 m from equilibrium and released. Neglect friction.

Find the total energy.

(a)   22.5 J
(b)   9 J
(c)   5 J
(d)   90 J
(e)   45 J

### QUESTION 10*

Let Etot be your answer to the previous question. When the object passes through the equilibrium position, its kinetic energy is:

(a)   Etot / 4
(b)   Etot / 2
(c)   Etot

### QUESTION 11***

In terms of Etot, what is the kinetic energy of the object when it is half the distance (i.e., 0.05 m) from the equilibrium position?

(a)   Etot / 4
(b)   Etot / 2
(c)   3 Etot / 4
(d)   Etot
(e)   0

### QUESTION 12**

How long after it is released does it take the object to return to the equilibrium position for the first time?

(a)   0.124 s
(b)   0.026 s
(c)   0.065 s
(d)   0.081 s
(e)   1.75 s

### QUESTION 13*

Suppose instead that the spring were stretched to 0.20 m from its equilibrium position and released. How would the time it takes for the object to return to the equilibrium position for the first time change?

(a)   increases
(b)   decreases
(c)   stays the same

### QUESTION 14*

A 3-kg object oscillates on a horizontal spring with an amplitude of 0.08 m. Neglect friction. Given that its maximum acceleration is 3.5 m/s2, what is the period of oscillation?

(a)   1.06 s
(b)   0.95 s
(c)   1.9
(d)   0.14 s
(e)   6.6 s

### QUESTION 15*

This and the following two questions relate to the same situation:

Consider a simple pendulum in which a point object of mass 2 kg is suspended from a string. The period of the pendulum is 5 s, and the gravitational acceleration is g = 9.8 m/s2.

What is the length of the pendulum?

(a)   3.1 m
(b)   6.2 m
(c)   9.3 m
(d)   8.3 m
(e)   15.5 m

### QUESTION 16*

Suppose the same pendulum (same mass and length) is on a planet such as Jupiter with a gravitational acceleration greater than that of Earth. The period of the pendulum will be

(a)   greater than 5 s.
(b)   less than 5 s.
(c)   equal to 5 s.

### QUESTION 17**

Now suppose the pendulum is mounted on the ceiling of an elevator on Earth. In which case is the period of the pendulum larger than 5 s?

(a)   The elevator is accelerating upward.
(b)   The elevator is accelerating downward.

### QUESTION 18*

This and the following question relate to the same situation:

A slab of ice (density = 920 kg/m3, volume = 0.725 m3) floats on a freshwater lake. What is the maximum mass that a woman can have in order that she can stand on the ice without getting her feet wet?

(a)   75 kg
(b)   64 kg
(c)   58 kg
(d)   52 kg
(e)   46 kg

### QUESTION 19*

Suppose the same slab of ice were floating on salt water, which is denser than fresh water. The answer to the preceding question would then be

(a)   greater.
(b)   less.
(c)   the same

### QUESTION 20*

This and the following three questions relate to the same situation:

Water flows at a rate of 3.11 kg/s through a hose with a diameter of 3 cm. What is the speed of the water in the hose?

(a)   1.3 m/s
(b)   1.8 m/s
(c)   2.4 m/s
(d)   7.2 m/s
(e)   4.4 m/s

### QUESTION 21**

Suppose your answer to the preceding question is V. If the hose is attached to a nozzle with a diameter of 0.750 cm, what is the speed of the water in the nozzle?

(a)   4 V
(b)   16 V
(c)   V / 4
(d)   V / 16
(e)   V

### QUESTION 22*

The number of kilograms per second flowing through the nozzle is:

(a)   greater than 3.11
(b)   less than 3.11
(c)   equal to 3.11

### QUESTION 23**

Where is the water pressure larger?

(a)   in the hose
(b)   in the nozzle
(c)   the pressure is the same in each

### QUESTION 24*

This and the following question relate to the same situation:

A piece of wood of density 706 kg/m3 is tied with a string to the bottom of a water-filled flask. The wood is completely submerged and has a volume of 8.00 × 10-4 m3. What is the tension in the string?

(a)   1.1 N
(b)   1.4 N
(c)   5.9 N
(d)   7.8 N
(e)   2.3 N

### QUESTION 25*

Suppose the wood is replaced by a material with the same volume but smaller density. The tension in the string will now be:

(a)   greater
(b)   less
(c)   the same

### QUESTION 26**

Suppose you pour water into a container until it reaches a depth of 12 cm. Then you add 6.2 cm of olive oil (density = 920 kg/m3). How much larger is the pressure at the bottom than at the top of the container, in units of Pa?

(a)   1120
(b)   1740
(c)   2350
(d)   4230
(e)   5560

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.