Spring 2004 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 ***.

This exam consists of 25 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 87. The exam period was 90 minutes; the average score was 68.4; the median score was 70. 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 block of mass m1 = 3 kg is attached by a rope passed over a pulley to another block of mass m3 = 8 kg, as shown in the figure below. The first block slides on a frictionless table surface. The pulley is a uniform cylinder of mass m2 and radius 12 cm ( I = ½ M R2 ). The suspended block accelerates downward with an acceleration a = 6.7 m/s2.

Compute T2

(a)   T2 = 10.9 N
(b)   T2 = 24.8 N
(c)   T2 = 39.7 N
(d)   T2 = 43.5 N
(e)   T2 = 58.4 N


QUESTION 2**

Compute the mass of the pulley m2.

(a)   0.5 kg
(b)   0.8 kg
(c)   1.1 kg
(d)   1.4 kg
(e)   1.7 kg


QUESTION 3***

If we were to replace the pulley by a uniform cylinder of the same mass m2, but with a 24-cm radius, the acceleration of the block m3 would be

(a)   smaller than 6.7 m/s2.
(b)   equal to 6.7 m/s2.
(c)   larger than 6.7 m/s2.


QUESTION 4*

What would be the relation between T1 and T2 if the pulley was massless (m2 = 0)?

(a)   T1 > T2
(b)   T1 = T2
(c)   T1 < T2


QUESTION 5*

This and the following question relate to the same situation:

A uniform disc of mass M = 20 kg and radius R = 60 cm is rotating about an axis through the center as shown in the figure, with an angular velocity ω = 120 rad/s. A block of mass m = 3 kg falls vertically on the top surface of the disc at a distance r = 35 cm from the axis of rotation and sticks to the surface.

What is the angular velocity of the disc and the block after the block has fallen on the disc?

(a)   69 rad/s
(b)   83 rad/s
(c)   109 rad/s


QUESTION 6*

Let ωf be the answer to the previous question. If the 3 kg block were to land on the disc at a distance r = 55 cm from the axis of rotation, the angular velocity of the disc with the block would be

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


QUESTION 7*

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

A sphere of radius R = 30 cm is initially rotating at an angular speed of 250 revolutions per minute (rpm). A tangential force is applied to the sphere. As a result, the sphere slows down with a constant angular acceleration of 3 rad/s2.

How long does it take for the sphere to stop?

(a)   8.7 s
(b)   12.1 s
(c)   15.9 s


QUESTION 8*

How many revolutions does it take the sphere to stop?

(a)   10.3 revolutions
(b)   18.1 revolutions
(c)   23.4 revolutions


QUESTION 9**

Let n be the answer to the previous question. If we were to use a sphere with a radius of 60 cm, but the initial angular speed and the angular acceleration stayed the same, the sphere would stop after

(a)   less than n revolutions.
(b)   n revolutions.
(c)   more than n revolutions.


QUESTION 10*

This and the following question relate to the same situation:

To lift a small sunken ship from the bottom of the ocean two ballasts of equal volumes are attached to the ship. The ballast are filled with air. The mass of the ship is 50,000 kg and the mass of each ballast is 50 kg. The density of ocean water is 1027 kg/m3. The density of air is 1.25 kg/m3.

What is the minimum volume V each ballast should be in order to lift the ship to the surface of the ocean?

(a)   V = 13.3 m3
(b)   V = 24.4 m3
(c)   V = 36.6 m3
(d)   V = 47.7 m3
(e)   V = 51.1 m3


QUESTION 11**

Keeping the same balasts, how would the magnitude of the buoyancy force FB (not the net force) change if we filled the ballasts with helium rather than air? (The density of helium is 0.164 kg/m3.)

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


QUESTION 12*

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

A block of unknown mass M is attached to the ceiling by a spring with force constant k = 130 N/m. A force of 200 N is applied to the block compressing the spring from its equilibrium position. At time t = 0, the force is removed and the block starts to oscillate up and down with angular frequency ω = 1.4 s-1.

What is the maximum compression of the spring during these oscillations?

(a)   0.72 m
(b)   1.23 m
(c)   1.54 m


QUESTION 13*

What is the mass of the block?

(a)   M = 38 kg
(b)   M = 66 kg
(c)   M = 92 kg


QUESTION 14**

Which function best describes the position of the block as a function of time where y = 0 corresponds to the equilibrium position?

(a)   y(t) = -ymax sin(ωt)
(b)   y(t) = -ymax cos(ωt)
(c)   y(t) = +ymax cos(ωt)


QUESTION 15*

What is the maximum kinetic energy of the mass?

(a)   154 J
(b)   189 J
(c)   237 J


QUESTION 16*

The experiment is repeated on the moon (g = 1.6 m/s2) using the same mass, spring and initial displacement force. The angular frequency of the oscillations ω is:

(a)   ω > 1.4 s-1
(b)   ω = 1.4 s-1
(c)   ω < 1.4 s-1


QUESTION 17*

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

A large container with height 0.5 m is filled with water ( ρ = 1000 kg/m3 ). A pipe is attached to the reservoir and is plugged at the far end as shown in the figure so the water is not flowing. In regions a, and b the pipe has a diameter 0.04 m. Region c has a slight constriction reducing the diameter to 0.03 m.

Calculate ΔP, the pressure difference between the top of the container, and the bottom of the container.

(a)   ΔP = 2300 N/m2
(b)   ΔP = 3900 N/m2
(c)   ΔP = 4900 N/m2


QUESTION 18**

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

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


QUESTION 19**

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

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


QUESTION 20*

Calculate the speed of the water in region c.

(a)   vc = 1.5 m/s
(b)   vc = 2 m/s
(c)   vc = 3.6 m/s


QUESTION 21*

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

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


QUESTION 22*

This and the following question relate to the same situation:

A grandfather clock keeps time with a simple pendulum. Unfortunately the clock is running fast, (e.g. the period of the motion is 0.9 sec).

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

(a)   increase the length of the pendulum
(b)   decrease the length of the pendulum
(c)   increase the amplitude of the pendulum’s swing


QUESTION 23*

If the clock is brought to the moon (g = 1.6 m/s2) it 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 hydraulic lift consists of a narrow piston (diameter 0.25 m) connected to a large piston (diameter 1.5 m). A 500 Kg mass is placed on the large platform as shown in the diagram.

Calculate F the minimum force which must be applied to the small piston necessary to lift the 500 Kg block.

(a)   85 N
(b)   136 N
(c)   269 N
(d)   490 N
(e)   770 N


QUESTION 25**

Calculate the height h that the 500 Kg block will go up, when the force pushes the narrow piston down a distance of 1 meter.

(a)   h = 2.8 cm
(b)   h = 47.3 cm
(c)   h = 100 cm