Spring 2001 Physics 101 Hour Exam 2
(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. When the exam was given, the mean was 85.3; the median was 87. The maximum possible score is 113. Click here to see the formula sheet that came with the exam.


QUESTION 1*

This and the following two questions concern the same physical situation.

A bowling ball is a sphere of mass M = 2.0 kg and radius R = 0.10 m. It rolls without slipping on a horizontal surface with a center-of-mass speed VCM = 3 m/s. What is the rotational speed of the ball in units of revolutions per minute (rpm)?

(a)   490
(b)   160
(c)   120
(d)   290
(e)   330


QUESTION 2**

Suppose the bowling ball with the same VCM encounters a ramp while still rolling without slipping. What is the maximum height in meters above the horizontal surface reached by the ball?

(a)   0.64
(b)   0.85
(c)   1.17
(d)   1.43
(e)   1.85


QUESTION 3**

Let your answer to the previous question be H. Suppose instead that the ramp is a frictionless surface, so that the ball slides rather than rolls. The maximum height above the horizontal surface reached by the ball will now be

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


QUESTION 4*

This and the following question concern the same physical situation.

A solid cylinder has mass M = 1.5 kg and radius R = 0.25 m. A torque of magnitude t = 0.3 N-m is applied about the rotation axis. What is the angular acceleration of the cylinder?

(a)   0.4 rad/s2
(b)   6.4 rad/s2
(c)   3.4 rad/s2
(d)   1.5 rad/s2
(e)   2.3 rad/s2


QUESTION 5*

Let your answer to the previous question be a . Suppose instead that you have a solid sphere with the same mass and radius and that the same torque is applied. The magnitude of the angular acceleration of the sphere is

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


QUESTION 6**

This and the following question concern the same physical situation.

A star is a uniform sphere of mass M and radius R. It rotates about its center with angular velocity w . The star then collapses to radius R/10 (with the mass still M). What is the angular velocity of the star after its collapse?

(a)   w / 100
(b)   w / 10
(c)   w
(d)   10 w
(e)   100 w


QUESTION 7**

What happens to the kinetic energy of the star as a result of its collapse?

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


QUESTION 8**

A tightrope walker is better able to keep his balance by holding a long stick horizontally. Of the following, the best reason for this is to

(a)   shift his center of mass.
(b)   increase his moment of inertia about a horizontal axis.
(c)   reduce the torque due to gravity.


QUESTION 9*

This and the following two questions concern the same physical situation.

A big man (mass 100 kg) is riding his bicycle south at 4 m/s. A little man (mass 50 kg) rides his bicycle north at 10 m/s. You may neglect the mass of each bicycle.

Whose momentum is larger in magnitude?

(a)   big man
(b)   little man
(c)   both are the same


QUESTION 10*

Suppose the two men on bicycles collide head-on in such a way that they get tangled up and stick together. What is their common velocity just after the collision?

(a)   4.0 m/s south
(b)   3.3 m/s south
(c)   0.33 m/s north
(d)   0.67 m/s north
(e)   3.3 m/s north


QUESTION 11*

Now suppose that instead of sticking together, the two men bounce off each other like rubber balls, that is, they suffer a perfectly elastic collision. What is their combined total kinetic energy after the collision?

(a)   0 J
(b)   1280 J
(c)   3300 J
(d)   4990 J
(e)   6670 J


QUESTION 12*

This and the following three questions concern the same physical situation.

Two hockey players, each having an identical mass of 50 kg, are gliding across the ice toward the puck. Player A is moving at 3 m/s in the +x direction. Player B is moving at 4 m/s in the +y direction.

What is the magnitude of their total momentum?

(a)   5 kg m/s
(b)   200 kg m/s
(c)   250 kg m/s
(d)   300 kg m/s
(e)   460 kg m/s


QUESTION 13*

What direction does their total momentum vector point with respect to the x axis?

(a)   along the x axis
(b)   27°
(c)   53°
(d)   109°
(e)   220°


QUESTION 14*

If the mass of each player were doubled, how would your answer to the previous question change?

(a)   The direction would be the same.
(b)   The direction would be closer to the x axis.
(c)   The direction would be closer to the y axis.


QUESTION 15**

Player A and Player B are not looking where they are going, and they both collide with Player C, also known as "Tony Zamboni". Tony is not moving before the collision and has a mass of 100 kg. They all collapse together in a heap and drift across the perfectly smooth and frictionless ice. At what speed are they moving?

(a)   0.85 m/s
(b)   1.25 m/s
(c)   1.65 m/s
(d)   2.00 m/s
(e)   2.45 m/s


QUESTION 16***

A skater is carrying a heavy box and skating at constant velocity on frictionless ice. Then the skater gently releases the box. As a result, the velocity of the skater remains constant.

(T)   True
(F)   False


QUESTION 17*

A hammer strikes a stone, which has a mass of 8 kg and is initially at rest, delivering a mean force of 2400 N during a total contact time of 8 × 10-4 s. What is the resulting speed of the stone?

(a)   0.15 m/s
(b)   0.20 m/s
(c)   0.24 m/s
(d)   0.29 m/s
(e)   0.33 m/s


QUESTION 18***

This and the following two questions concern the same physical situation.

A wheel of radius R rolls without slipping on a horizontal surface at a nonzero speed V. The instantaneous speed of the dot at the top of the wheel (see drawing) is:

(a)   V
(b)   2V
(c)   0


QUESTION 19**

In the drawing, the diamond is located closer to the center of the wheel than the dot. Which of the two points has the larger angular velocity?

(a)   the dot
(b)   the diamond
(c)   they both have the same angular velocity


QUESTION 20*

Suppose a wheel with a slightly larger radius rolls without slipping with the same angular velocity as the original wheel. The speed of this larger wheel is

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


QUESTION 21**

This and the following question concern the same physical situation.

You have your bicycle upside down for repair. The front wheel is free to rotate about its axis and is perfectly balanced except for the 0.025 kg valve stem 0.3 m from the rotation axis. The location of the stem is at an angle q with respect to the horizontal, as shown in the figure. Gravity points downward in the figure.

For which of the following values of q is the torque about the wheel’s due to weight of the stem the smallest?

(a)   0°
(b)   45°
(c)   90°


QUESTION 22**

If q = 24°, what is the resulting torque about the wheel’s axis?

(a)   0.176 Nm
(b)   0.363 Nm
(c)   0.014 Nm
(d)   0.067 Nm
(e)   0.214 Nm


QUESTION 23**

This and the following question concern the same physical situation.

A 5 m long uniform beam has a mass of 100 kg and is hanging vertically, supported by a cable which is 2 m from the right end of the beam. How far from the right end of the beam must a 50 kg box be placed in order that the beam be in static equilibrium?

(a)   0.5 m
(b)   1.0 m
(c)   1.5 m
(d)   2.0 m
(e)   3.0 m


QUESTION 24**

Let your answer to the previous problem be D. Suppose the mass of the beam is doubled. The distance from the right end that the box must be placed to balance the beam is now

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


QUESTION 25*

You switch a food blender from its high to low setting. The blade speed drops from 400 rad/s to 200 rad/s in 1.5 s. How many radians does it turn through during this time?

(a)   150
(b)   300
(c)   450
(d)   600
(e)   750