### Fall 2003 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 92. The exam period was 90 minutes; the average score was 70.2; the median score was 71. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1**

Two cylinders with identical dimensions are constrained to rotate about a vertical axis as shown.

The first has mass M and is acted on by a torque T. The second has a mass 2M and is acted on by a torque T/2. Both cylinders start from rest and after a certain amount of time have rotated through angles θ1 and θ2.

The relationship between θ1 and θ2 is:

(a)   θ1 = 4 θ2
(b)   θ1 = 2 θ2
(c)   θ1 = θ2

### QUESTION 2*

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

A cube (mass 2.50 kg, volume 0.0026 m3) and a cylinder (mass 1.25 kg, volume 0.0026 m3) are attached by strings to the bottom of a fish tank. Without the strings, both objects would float at the surface. The water in the fish tank has a density of 1000 kg/m3.

Let the buoyant force acting on the cube be FB,cube and that acting on the cylinder FB,cylinder. These buoyant forces are related by:

(a)   FB,cube  >  FB,cylinder
(b)   FB,cube  =  FB,cylinder
(c)   FB,cube  <  FB,cylinder

### QUESTION 3*

Let the tension in the string attached to the cube be Tcube and the tension in the string attached to the cylinder be Tcylinder. These tensions are related by:

(a)   Tcube  >  Tcylinder
(b)   Tcube  =  Tcylinder
(c)   Tcube  <  Tcylinder

### QUESTION 4*

What is the magnitude of the tension in the string attached to the cylinder?

(a)   8.71 N
(b)   9.26 N
(c)   12.5 N
(d)   13.2 N
(e)   21.9 N

### QUESTION 5*

A certain submarine is rated to withstand a maximum external pressure of 42 MPa. (1 MPa = 1 × 106 Pa). What is the maximum depth to which this submarine can descend? (The density of seawater is 1025 kg/m3.)

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

### QUESTION 6**

This and the following question relate to the same situation:

A solid cylinder (mass M = 0.50 kg, radius R = 2.5 cm) rolls without slipping down a plane inclined at 15° to the horizontal.

If the cylinder is released from rest, what is its speed after it travels 1.2 m down the plane?

(a)   1.4 m/s
(b)   2.0 m/s
(c)   2.5 m/s
(d)   2.9 m/s
(e)   3.4 m/s

### QUESTION 7**

If a race (both objects are released at the same time, from rest at the top of the plane) was held between this cylinder and a solid sphere of the same mass and radius,

(a)   the cylinder would reach the bottom first.
(b)   the sphere would reach the bottom first.
(c)   they would tie.

### QUESTION 8**

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

A physics grad student is playing in a park. He runs toward a stationary merry-go-round (mass M = 200 kg and radius R = 3.0 m) with a velocity of 5.0 m/s. The merry-go-round is initially at rest and is free to rotate without friction. He leaps aboard and remains at the outer edge of the merry-go-round. The moment of inertia of the merry-go-round is I = ½MR2. The student can be treated as a point mass of 75 kg. At the moment he leaps onto the merry-go-round, his velocity is exactly tangential to the merry-go-round.

What is the angular velocity (ω) of the merry-go-round after the student has jumped on?

### QUESTION 9**

The kinetic energy is conserved in this situation.

(T)   True
(F)   False

### QUESTION 10*

If the student now moves towards the center of the merry-go-round, what happens to the angular velocity of the merry-go-round?

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

### QUESTION 11*

This and the following question relate to the same situation:

Two discs of identical size, but different masses (MA = 0.45 kg, MB = 0.25 kg) are shown below. Initially, disc A is suspended directly over disc B and is rotating with constant angular speed ωA = 12 rad/sec. Disc B is at rest on a frictionless surface. Viewed from above, A is rotating counterclockwise.

Then, A’s suspension breaks and it falls onto B. Later both disks move with the same angular velocity ωf.

### QUESTION 12**

Compute the ratio of the total kinetic energy of the discs after A fell on B, KEafter, and the total kinetic energy of the discs before A fell on B, KEbefore.

(a)   KEafter / KEbefore  =  0.37
(b)   KEafter / KEbefore  =  0.50
(c)   KEafter / KEbefore  =  0.64
(d)   KEafter / KEbefore  =  1.0
(e)   KEafter / KEbefore  =  1.3

### QUESTION 13*

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

A block of mass 2.0 kg resting on a horizontal frictionless surface is attached to a spring with force constant k = 250 N/m. The other end of the spring is fixed to a wall. A force of unknown magnitude is applied to the block in the x-direction, thereby stretching the spring (see picture). The block is initially at rest. At time t = 0, the force is removed and the block starts to oscillate back and forth along the x-axis with amplitude 0.7 m.

What was the magnitude of the initial applied force?

(a)   150 N
(b)   175 N
(c)   250 N

### QUESTION 14*

How long does it take to complete one cycle?

(a)   0.56 s
(b)   0.78 s
(c)   1.32 s

### QUESTION 15**

Which function best describes the velocity of the block as a function of time where x = 0 corresponds to the relaxed spring?

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

### QUESTION 16*

What is the maximum speed of the mass?

(a)   2.5 m/s
(b)   5.3 m/s
(c)   7.8 m/s

### QUESTION 17**

If the initial force used to stretch the spring was doubled, the total mechanical energy in the system would

(a)   double.
(c)   be unchanged.

### QUESTION 18**

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

A section of pipe carries water (ρ = 1000 kg/m3). In section a, the pipe has a diameter 0.04m, and the water is flowing to the right with velocity va = 2 m/s. In region b, the pipe has a diameter 0.04 m. Region c has a slight constriction reducing the diameter to 0.03 m.

Compare va, the speed of the fluid in the pipe marked a with vb, the speed of the fluid in section b of the pipe.

(a)   va > vb
(b)   va = vb
(c)   va < vb

### QUESTION 19**

Compare Pa, the pressure of the fluid in the pipe marked a with Pb, the pressure of the fluid in section b of the pipe.

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

### QUESTION 20*

Compare va, the speed of the fluid in the pipe marked a with vc, the speed of the fluid in section c of the pipe.

(a)   va > vc
(b)   va = vc
(c)   va < vc

### QUESTION 21*

Compare Pb, the pressure of the fluid in the pipe marked b with Pc, the pressure of the fluid in section c of the pipe.

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

### QUESTION 22*

This and the following question relate to the same situation:

A grandfather clock keeps time with a simple pendulum. The pendulum is made with a 4.0 kg mass suspended at the end of a thin rod. The period of the small amplitude simple harmonic motion is 1.0 sec.

What is the length of the thin rod?

(a)   24.8 cm
(b)   29.7 cm
(c)   31.4 cm

### QUESTION 23**

If the clock was placed on an elevator accelerating up, the clock will run

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

### QUESTION 24*

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

A 0.5 m cylinder is filled to the top with water. Two identical holes are placed in the side of the cylinder. The first hole is placed in the middle of the cylinder, the second hole is 0.1 m from the bottom

Through which hole will the water flow the fastest?

(a)   hole 1
(b)   hole 2
(c)   same

### QUESTION 25**

Calculate the speed of the water flowing through hole 2.

(a)   1.5 m/s
(b)   2.1 m/s
(c)   2.8 m/s

### QUESTION 26**

As the water empties (but remains above hole 1), the speed of the water leaving hole 2

(a)   increases.
(b)   decreases.
(c)   remains the same.

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.