### Fall 2005 Physics 101 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 105; the average score was 78.6; the median score was 84. 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 three questions relate to the same situation:

A small solid cylinder of mass M and radius R is released from rest at the top of a hill. The height of the hill is H . The cylinder rolls without slipping down the hill. Assume no energy is lost to friction.

When the cylinder is part of the way down the hill, the magnitude of its acceleration is a. What is the magnitude of the torque about an axis through the center of the cylinder due to the static friction between the cylinder and the surface?

(a)   MR2a
(b)   MRa/2
(c)   MRa
(d)   MR2a
(e)   MRa/4

### QUESTION 2*

The total kinetic energy (translational plus rotational) of the cylinder at the bottom of the hill is

(a)   greater than MgH.
(b)   equal to MgH.
(c)   less than MgH.

### QUESTION 3*

You are now given that M = 2 kg, R = 0.25 m, and H = 20 m. What is the speed of the cylinder at the bottom of the hill?

(a)   12.4 m/s
(b)   18.1 m/s
(c)   16.2 m/s
(d)   24.3 m/s
(e)   32.5 m/s

### QUESTION 4*

Let your answer to the previous problem be V. Suppose instead that the 'solid cylinder' is replaced by a 'hollow cylinder' with the same radius and mass. The speed of the hollow cylinder at the bottom of the hill is

(a)   greater than V.
(b)   equal to V.
(c)   less than V.

### QUESTION 5*

This and the following two 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)   60 kg-m2/s
(b)   100 kg-m2/s
(c)   200 kg-m2/s
(d)   520 kg-m2/s
(e)   1280 kg-m2/s

### QUESTION 6*

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 7*

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 8*

This and the following question relate to the same situation:

Disk A has moment of inertia 10 kg-m2 and initial angular velocity ω = 20 rad/s about its axis. Disk B has moment of inertia 30 kg-m2 and is initially at rest. Disk A is then dropped onto Disk B so that they stick together and their axes line up. What is the angular velocity of the combined disks about their mutual axis?

### QUESTION 9**

Compare the kinetic energies of the disks before and after the collisions.

(a)   Kbefore < Kafter
(b)   Kbefore = Kafter
(c)   Kbefore > Kafter

### QUESTION 10**

Two fluids are placed in a U shaped pipe. Fluid A is water ρA = 1000 kg/m3 and rises 0.7 m above the bottom of the left pipe. Fluid B rises 0.6 m above fluid A in the right tube as shown in the figure.

Calculate the density of fluid B.

(a)   ρB = 500 kg/m3
(b)   ρB = 666 kg/m3
(c)   ρB = 1000 kg/m3
(d)   ρB = 1500 kg/m3
(e)   ρB = 2000 kg/m3

### QUESTION 11*

This and the following question relate to the same situation:

While waiting to get into the elevator that goes to the observation floor in the Sears Tower in Chicago, you suspend your keys from a thread and set the resulting pendulum oscillating. It completes exactly 90 cycles in 1 minute. Assume that the angle through which the pendulum swings is small.

What is the length of the thread?

(a)   7 cm
(b)   11 cm
(c)   15 cm
(d)   19 cm
(e)   23 cm

### QUESTION 12*

You are now in the elevator that is accelerating upward. If you would now repeat the experiment of the previous problem, you would find that the pendulum completes

(a)   more than 90 cycles in 1 minute.
(b)   exactly 90 cycles in 1 minute.
(c)   less than 90 cycles in 1 minute.

### QUESTION 13**

A strong wind (30 m/s ρ = 1.29 kg/m3) blows across a flat roof of a house that is 7 m long and 8 m wide. Calculate the net force on the roof due to the air.

(a)   33000 N
(b)   38000 N
(c)   42000 N

### QUESTION 14*

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

A block of mass 1.5 kg is suspended from the ceiling by a spring with spring constant k= 15 N/m. A force of 20 N is applied to the block in the +y-direction, thereby compressing the spring (see picture). The block is initially at rest. At time t = 0, the force is removed and the block starts to oscillate down and up.

What is the amplitude of the oscillation?

(a)   0.5 m
(b)   0.7 m
(c)   1.0 m
(d)   1.3 m
(e)   2.0 m

### QUESTION 15*

About how many cycles does the block undergo in a time of 10 seconds?

(a)   2
(b)   5
(c)   8

### QUESTION 16*

Which function best describes the acceleration of the block as a function of time where t = 0 corresponds to just after the external force is removed?

(a)   a(t) = -A ω2 sin(ωt)
(b)   a(t) = -A ω2 cos(ωt)
(c)   a(t) = -A ω2 tan(ωt)

### QUESTION 17*

Let the period of the oscillation in the above experiment be T0. If you repeat the experiment, but you use an initial force which is twice as big (i.e. F = 40 N) to compress the spring. The new period of oscillation, Tnew, will be:

(a)   Tnew = T0
(b)   Tnew = 2 T0
(c)   Tnew = T0 / 2

### QUESTION 18**

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

A funnel of water is connected to pipes as shown in the figure. The top of the funnel is sufficiently large that the speed downwards of the water (ρ = 1000 kg/m3) at the top of the funnel is nearly zero. The water is observed to be moving at 2.0 m/s through the pipe at point B and the water is observed to exit pipe C at a speed of 2.8 m/s. Note that the pressure at point C is the atmospheric pressure.

Compare the pressure at point A in the funnel with the pressure at point C in the horizontal pipe. Assume that the speed at point A is 0.5 m/s.

(a)   PA > PC
(b)   PA = PC
(c)   PA < PC

### QUESTION 19***

Calculate the difference between the pressure at point B, 2 m below the surface of water, and atmospheric pressure.

(a)   PB - PAtm = 1.6 × 104 N/m2
(b)   PB - PAtm = 1.8 × 104 N/m2
(c)   PB - PAtm = 2.0 × 104 N/m2
(d)   PB - PAtm = 2.2 × 104 N/m2
(e)   PB - PAtm = 2.4 × 104 N/m2

### QUESTION 20*

The radius of the pipe at point B is 0.15 m. What is the radius of the pipe at point C?

(a)   rc = 0.110 m
(b)   rc = 0.127 m
(c)   rc = 0.178 m

### QUESTION 21**

Calculate h, the difference in height between point B and point C.

(a)   1.2 m
(b)   1.4 m
(c)   1.6 m

### QUESTION 22**

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

A plastic cube with length 0.3 m on each side is floating in a pool of water (ρ = 1000 kg/m3). A cylinder with volume 0.005 m3 is supported by a string attached to the upper cube. The tension T in the string attaching the two objects is 24.5 N. The system is at equilibrium with the cube submerged a distance h = 0.2 m.

Calculate the mass of the submerged cylinder.

(a)   2.5 kg
(b)   5.0 kg
(c)   7.5 kg
(d)   10.0 kg
(e)   15.0 kg

### QUESTION 23**

What is the mass of the plastic cube?

(a)   13.0 kg
(b)   15.5 kg
(c)   18 kg
(d)   20.5 kg
(e)   23.0 kg

### QUESTION 24**

If the cylinder is placed on top of the plastic cube. The cube would

(a)   sink lower in the water (h increases).
(b)   stay at the same level (h remains the same).
(c)   float higher in the water (h decreases).

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.