Fall 2008 Physics 211 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 101. The exam period was 90 minutes; the average score was 73.3; the median score was 77. Click here to see the formula sheet that came with the exam.


QUESTION 1*

This and the next two questions refer to this situation:

A wheel of mass M and radius R = 0.1700 m rests on a horizontal surface against a vertical step of height h = 0.0100 m. A point below the center of the wheel is a distance x = 0.0575 m from the vertical step. The wheel is to be raised over the step by a horizontal force F applied to the axle of the wheel as shown in the figure. Let Fmin be the minimum force needed to raise the wheel over the step. The figure is not to scale.

What is the magnitude of the torque that the force Fmin exerts about the point of contact between the wheel and the step?

(a)   (0.0200 meters) Fmin
(b)   (0.0575 meters) Fmin
(c)   (0.1600 meters) Fmin
(d)   (0.3200 meters) Fmin
(e)   (0.3765 meters) Fmin


QUESTION 2*

In terms of the weight of the wheel, Mg, what is the magnitude of the torque that gravity exerts about the point of contact between the wheel and the step?

(a)   (0.0575 meters) Mg
(b)   (0.1149 meters) Mg
(c)   (0.2251 meters) Mg
(d)   (0.3200 meters) Mg
(e)   (0.3765 meters) Mg


QUESTION 3*

In terms of the weight of the wheel, Mg, what is the minimum force needed to raise the wheel?

(a)   0.3379 × Mg
(b)   0.3594 × Mg
(c)   0.5882 × Mg


QUESTION 4**

A ladder of mass M = 20.0 kg and length L = 10.0 m rests against a frictionless vertical wall and on a frictionless horizontal surface. A rope, holding the ladder in static equilibrium, is attached to the bottom of the ladder and fixed to the vertical wall at the horizontal surface. The ladder makes an angle θ = 60° with respect to the horizontal. Find the tension, T, in the rope.

(a)   T = 42.5 N
(b)   T = 56.6 N
(c)   T = 73.5 N
(d)   T = 127 N
(e)   T = 147 N


QUESTION 5*

A dumbbell is made of a rod of length L = 1 m with two masses M1 = 5 kg and M2 = 2 kg attached at each end. Consider the rod as massless and the masses M1 and M2 as point masses. What is the moment of inertia, ICM, about an axis that is perpendicular to the rod and passing through the center-of-mass of the dumbbell?

(a)   ICM = 2.86 kg-m2
(b)   ICM = 1.43 kg-m2
(c)   ICM = 0.71 kg-m2


QUESTION 6*

This and the next question refer to this situation:

A beam of mass M and length L is held in the horizontal by two ideal massless ropes that are attached to the ends of the beam. At some time the rope on the left end of the beam breaks.

Before the rope on the left end of the beam breaks, i.e. while the beam is still supported by the two ropes, what is the tension in the rope on the left?

(a)   (1/12) Mg
(b)   (1/4) Mg
(c)   (1/3) Mg
(d)   (1/2) Mg
(e)   (3/4) Mg


QUESTION 7*

Immediately after the rope on the left end of the beam breaks, what is the magnitude of the angular acceleration, α, of the beam

(a)   α = g / 12L
(b)   α = g / 4L
(c)   α = 3g / 2L
(d)   α = g / 2L
(e)   α = 3g / 4L


QUESTION 8**

This and the next question refer to this situation:

Two blocks are suspended over a pulley with a string of negligible mass as shown below. One block has mass m1 = 1 kg, the other one has a mass of m2 = 2 kg. The pulley is a uniform solid cylinder. The string does not slip on the pulley and the center of mass of the pulley remains stationary. The downward acceleration a of mass m2 is measured to be a = g / 4 .

What is the mass M of the pulley?

(a)   M = 1.0 kg
(b)   M = 1.5 kg
(c)   M = 1.7 kg
(d)   M = 2.0 kg
(e)   M = 2.3 kg


QUESTION 9**

If you replaced the pulley by a hollow cylinder of the same mass and radius, the downward acceleration of mass m2 would be

(a)   smaller than g/4.
(b)   equal to g/4.
(c)   larger than g/4.


QUESTION 10*

This and the next question refer to this situation:

A spool of mass M = 1 kg sits on a frictionless horizontal surface. A thread wound around the spool is pulled with a force T = 4 N as shown below. The total moment of inertia about the center of mass of the spool is I = 0.8 kg·m2, its outer radius is R = 1 m and its inner radius is r = 0.5 m. The spool starts from rest.

The magnitude of the angular acceleration α of the spool is:

(a)   α = T (r+R) / (I+Mr2)
(b)   α = T R / I
(c)   α = T r / I


QUESTION 11**

When the center-of-mass of the spool has traveled 2 m the net work done on the spool is 8 J.

(T)   True
(F)   False


QUESTION 12**

This and the next question refer to this situation:

A solid sphere of mass M and radius R is released from rest on an inclined plane with an angle of θ. The coefficient of static friction for the sphere on the plane is μs. Assuming that the sphere rolls without slipping down the plane and that the static frictional force is at its maximum value, which of the following is the correct equation for the acceleration of the center of mass of the sphere?

(a)   a = g sinθ
(b)   a = μsg cosθ
(c)   a = g sinθ - μsg cosθ


QUESTION 13***

What is the smallest value of μs needed to ensure that it rolls without slipping?

(a)   tanθ
(b)   (2/5) sinθ
(c)   (1/5) cosθ
(d)   (2/7) tanθ
(e)   (Mg/R) sinθ


QUESTION 14***

This and the next two questions refer to this situation:

A thin hoop of mass M and radius R rolls without slipping up a plane inclined at an angle θ with the horizontal. The initial velocity of the cylinder is V.

The frictional force exerted by the plane on the cylinder is

(a)   pointing along the same direction as V.
(b)   pointing opposite to the direction of V.
(c)   zero.


QUESTION 15*

What is the maximum height, H, above the horizontal, the hoop can reach?

(a)   H = V2 / g
(b)   H = 2V2 / 3g
(c)   H = 3V2 / 4g


QUESTION 16**

If the surface of the incline were frictionless, keeping the angle of the incline and the initial velocity of the hoop the same, the maximum height, H', reached by the hoop would be

(a)   H' > H
(b)   H' = H
(c)   H' < H


QUESTION 17**

This and the next question refer to this situation:

A projectile of mass m = 0.2 kg is flying at the constant velocity V = 10 m/s in the x direction and at a distance of d = 0.4 m from the x-axis towards a solid disk of mass M = 1 kg that is rotating counterclockwise about the fixed axis with the angular velocity ω = 10 rad/s. The projectile strikes the disk and sticks at point A. The radius of the disk is 0.5 m.

What is the angular velocity of the disk, ω1, after the projectile hits the disk?

(a)   ω1 = 12.3 rad/s
(b)   ω1 = 9.0 rad/s
(c)   ω1 = 6.8 rad/s
(d)   ω1 = 10.0 rad/s
(e)   ω1 = 11.7 rad/s


QUESTION 18*

Decreasing of the distance d of the projectile's trajectory from the x-axis will result in

(a)   increasing the final angular velocity ω1.
(b)   decreasing the final angular velocity ω1.
(c)   no effect on final angular velocity.


QUESTION 19**

This and the next question refer to this situation:

The following questions are based on experimental results obtained from P211 Lab #6. A student measures the position versus time of an object of mass m = 0.132 kg rolling without slipping down an incline. From the measured data she produces the graphs shown below.

Based upon the information provided, what shape did she assume for the rolling object?

(a)   solid cylinder
(b)   hollow cylinder
(c)   solid sphere
(d)   hollow sphere
(e)   There is not enough information to answer this question.


QUESTION 20*

What is the magnitude of the translational velocity at the moment t = 1.5 s when the object reaches the end of the track?

(a)   3.2 m/s
(b)   2.1 m/s
(c)   1.6 m/s


QUESTION 21**

This and the next question refer to this situation:

Two wheels A and B are connected by an ideal massless non-stretchable and non-slipping belt. The radius RA is three times of radius RB.

What would be the ratio of moments of inertia IA / IB if both wheels have the same angular momentum?

(a)   IA / IB = 1/3
(b)   IA / IB = 1
(c)   IA / IB = 3


QUESTION 22**

What would be the ratio of moment of inertia IA / IB if both wheels have the same rotational kinetic energy?

(a)   IA / IB = 9
(b)   IA / IB = 1
(c)   IA / IB = 3


QUESTION 23**

This and the next question refer to this situation:

A woman whose mass is 70 kg stands at the rim of a horizontal turntable that has a moment of inertia 300 kg m2 and radius of 2 m. The system is initially at rest and is free to rotate about frictionless vertical axle through the center of the turntable. The woman begins to walk clockwise around the rim at a speed 1.5 m/s relative to the earth.

In what direction and with what angular speed does the turntable rotate?

(a)   0.36 rad/s counterclockwise
(b)   0.42 rad/s clockwise
(c)   0.70 rad/s counterclockwise
(d)   0.42 rad/s counterclockwise
(e)   0.70 rad/s clockwise


QUESTION 24**

How much work does the woman do to set the system (woman plus turntable) in motion?

(a)   44.1 J
(b)   78.75 J
(c)   152.25 J