### Spring 2005 Physics 101 Hour Exam 3(25 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 96; the average score was 79.1; the median score was 82. The exam period was 90 minutes. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1*

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

A string is tied around a uniform disc of mass 7 kg and radius 0.3 m. The disc is held by a small rod that goes through its center. A vertical tension T is applied to the string. The angular acceleration of the disc is 20 rad/s2.

Calculate the torque on the disc exerted by the tension T.

(a)   5.2 N m
(b)   6.3 N m
(c)   7.4 N m

### QUESTION 2*

If the disc was initially at rest, how much time does it take for the disc to make 25 revolutions?

(a)   1.0 s
(b)   2.0 s
(c)   3.0 s
(d)   4.0 s
(e)   5.0 s

### QUESTION 3*

If the disc was initially at rest, what is its angular speed after 25 revolutions?

### QUESTION 4**

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

A composite disk of total mass 7 kg and radius 0.8 m is pulled on a horizontal surface by a string that is tied to its center. There is friction between the disk and the surface. The disk rolls without slipping. The acceleration of the disk is a = 4 m/s2 and the friction force is F = 23 N.

Calculate the moment of inertia of the disk.

(a)   2.54 kg m2
(b)   3.68 kg m2
(c)   4.77 kg m2
(d)   5.83 kg m2
(e)   6.49 kg m2

### QUESTION 5*

Calculate the force T exerted on the disk by the string that goes through its center.

(a)   21 N
(b)   35 N
(c)   44 N
(d)   51 N
(e)   72 N

### QUESTION 6***

Let T be the answer to the previous question. If the friction coefficient between the disk and the surface were increased, for the acceleration to stay the same, the tension in the string should be

(a)   smaller than T.
(b)   equal to T.
(c)   larger than T.

### QUESTION 7*

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

A string is attached to a cube of wood of volume V = 0.1 m3 that is placed in fresh water with density 1000 kg/m3, as shown in the figure below. The density of the wood is 750 kg/m3.

Calculate the tension in the string.

(a)   131 N
(b)   245 N
(c)   377 N
(d)   465 N
(e)   526 N

### QUESTION 8*

Let T be the answer to the previous question. If the fresh water were replaced by seawater of density 1030 kg/m3, the tension in the string would be

(a)   smaller than T.
(b)   equal to T.
(c)   larger than T.

### QUESTION 9*

If you placed this cube of wood in a bucket of fresh water, the cube would float. The submerged portion of the volume of the cube of wood would be

(a)   Vs = 0.030 m3
(b)   Vs = 0.050 m3
(c)   Vs = 0.075 m3

### QUESTION 10*

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

Martha stands at the edge of the platform of a merry-go-round that is a uniform circular disk of radius 2 m and mass 250 kg. Martha can be treated as a point mass.

If the merry-go-round rotates at an angular velocity of 3 rad/s around its axis, and the angular momentum of the system consisting of Martha and the merry-go-round is equal to 2160 kg-m2/s, what is the mass of Martha?

(a)   39 kg
(b)   47 kg
(c)   55 kg
(d)   66 kg
(e)   72 kg

### QUESTION 11*

If now Martha walks slowly inward to the center of the platform, what is the angular velocity of the platform when Martha is on the axis of rotation? (Assume that there is no friction and that there are no external torques on the platform).

### QUESTION 12**

Let KEinitial be the kinetic energy of the system consisting of Martha and the merry-go-round when Martha was standing at the edge of the platform, and KEfinal be the kinetic energy of the system consisting of Martha and the merry-go-round when Martha was standing on the axis of rotation. Which one of the following statements is correct?

(a)   KEinitial  <  KEfinal
(b)   KEinitial  =  KEfinal
(c)   KEinitial  >  KEfinal

### QUESTION 13*

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

A 1.7 kg block is attached to the floor by a spring with force constant k = 23.1 N/m. At time t = 0, the block is observed to be at position y = 0 and traveling up with a velocity of 11.1 m/s.

What is the maximum force the spring exerts on the block?

(a)   70 N
(b)   123 N
(c)   154 N

### QUESTION 14*

What is the period for 1 complete oscillation?

(a)   1.7 s
(b)   2.9 s
(c)   5.4 s

### QUESTION 15**

Which function best describes the velocity of the block as a function of time?

(a)   v(t)  =  -vmax sin(ωt)
(b)   v(t)  =  -vmax cos(ωt)
(c)   v(t)  =  +vmax cos(ωt)

### QUESTION 16**

What is the kinetic energy of the mass when it is at the position y = 1.5 m?

(a)   105 J
(b)   79 J
(c)   53 J

### QUESTION 17*

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

Water (ρ = 1000 kg/m3 ) is flowing through a hose with radius 2.8 cm. There is a slight constriction in the hose in region b, such that the effective radius is only 2.1 cm. Water flows from left to right, region c is raised 0.4 meters above the ground, and the water is observed to flow out of region c with a velocity of 5 m/s.

How much time will it take to fill a tub of volume 0.8 m3?

(a)   29 s
(b)   53 s
(c)   65 s

### QUESTION 18*

Calculate vb the speed of the water in region b.

(a)   vb = 2.8 m/s
(b)   vb = 6.5 m/s
(c)   vb = 8.9 m/s

### QUESTION 19*

Compare Pa the pressure in region a with Pb the pressure in region b.

(a)   Pa > Pb
(b)   Pa = Pb
(c)   Pa < Pb

### QUESTION 20*

Calculate Pa – Pc the pressure difference between regions a and c.

(a)   Pa – Pc = 2300 N/m2
(b)   Pa – Pc = 3900 N/m2
(c)   Pa – Pc = 4900 N/m2

### QUESTION 21*

Compare Pc the pressure in region c with Pb the pressure in region b.

(a)   Pc > Pb
(b)   Pc = Pb
(c)   Pc < Pb

### QUESTION 22*

A hydraulic lift consists of a circular narrow piston (unknown diameter) connected to a large circular piston (diameter 1.5 m). A 500 kg mass is placed on the large platform and is balanced by a 20 kg mass placed on the small cylinder as shown in the diagram. What is the diameter of the small cylinder?

(a)   d = 6 cm
(b)   d = 25 cm
(c)   d = 30 cm

### QUESTION 23*

How deep under the sea level should you dive so that the pressure on you is twice the atmospheric pressure? (Atmospheric pressure=1.01 105 Pa; Density of seawater = 1030 kg/m3).

(a)   10 m
(b)   30 m
(c)   50 m
(d)   70 m
(e)   90 m

### QUESTION 24*

This and the following question relate to the same situation:

A grandfather clock keeps time with a simple pendulum. Unfortunately the clock is running slow, (e.g. the period motion is 1.1 sec).

Which of the following changes could improve the clock’s performance?

(a)   Increase the mass of the pendulum.
(b)   Decrease the length of the pendulum.
(c)   Increase the amplitude of the pendulum’s swing.

### QUESTION 25**

If the clock is placed on an elevator that is accelerating upward, it will run

(a)   slower.
(b)   at the same rate.
(c)   faster.

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.