Spring 2007 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 ***.

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 111. The exam period was 90 minutes. The mean score was 80.2; the median was 81. Click here to see page1 page2 of the formula sheet that came with the exam.

Unless told otherwise, you should assume that the acceleration of gravity near the surface of the earth is 9.8 m/s2 downward and ignore any effects due to air resistance.


QUESTION 1*

This and the following two questions concern the same situation:

A mass (m = 2 kg), initially at rest, slides down a ramp with height h, emerging with velocity v = 9 m/s. The mass slides up a second ramp of height 2 m and then passes through a loop-the-loop of radius R = 0.6 m. Assume the entire surface is frictionless and g = 9.8 m/s2.

What is the height h?

(a)   2.05 m
(b)   4.13 m
(c)   6.67 m
(d)   7.45 m
(e)   8.27 m


QUESTION 2*

What is the velocity of the mass after it reaches the point P1?

(a)   3.72 m/s
(b)   4.65 m/s
(c)   5.02 m/s
(d)   6.47 m/s
(e)   7.55 m/s


QUESTION 3***

When the mass reaches the highest point, indicated by point P2, what is the normal force exerted on it by the loop?

(a)   68 N
(b)   41 N
(c)   22 N
(d)   11 N
(e)   The mass does not have enough energy to reach P2.


QUESTION 4***

You are inside a carnival ride that consists of a cylindrical shaped room of radius R = 5 m rotating on an axis. The wall has coefficient of static friction μs = 0.4. What is the minimum angular frequency it must rotate so that you stick to the wall when the floor drops out?

(a)   8.16 rad/s
(b)   6.04 rad/s
(c)   3.76 rad/s
(d)   2.21 rad/s
(e)   1.08 rad/s


QUESTION 5*

Three books, each having mass m = 0.5 kg, lie on three shelves of height h1 = 0.5 m, h2 = 1 m, and h3 = 1.5 m, as shown. What is the total change in gravitational potential energy if all three books fall onto the floor?

(a)   14.7 J
(b)   19.2 J
(c)   24.6 J
(d)   31.0 J
(e)   39.5 J


QUESTION 6*

This and the two question concern the same situation:

A box of mass M = 5 kg is pushed at constant speed a distance 5 m across a floor with coefficient of kinetic friction μK = 0.2. The force F is acting horizontally, as shown.

How much work was done by the force F ?

(a)   32 J
(b)   49 J
(c)   106 J


QUESTION 7**

Which one of the following statements is true?

(a)   The total mechanical energy of the box increased.
(b)   The total mechanical energy of the box decreased.
(c)   The total mechanical energy of the box was unchanged.


QUESTION 8*

This and the two question concern the same situation:

A block with mass m = 3 kg, initially at rest, is released at the top of a frictionless inclined plane of height h = 1.8 m. The angle θ = 15°.

What is the block's velocity when it reaches the bottom?

(a)   3.36 m/s
(b)   4.68 m/s
(c)   5.94 m/s


QUESTION 9***

Suppose the plane had a coefficient of kinetic friction of μK = 0.2. How much energy would be dissipated by friction by the time the block reached the bottom of the plane?

(a)   26.2 J
(b)   39.5 J
(c)   52.9 J
(d)   62.4 J
(e)   78.1 J


QUESTION 10*

A rocket floating in space, initially at rest, fires its engine with a thrust of 20 N for a total of 4 sec. What is the momentum of the rocket when its engine stops firing?

(a)   20 kg m/s
(b)   60 kg m/s
(c)   80 kg m/s


QUESTION 11*

An astronaut of mass 80 kg is at rest floating in outer space. He throws a baseball with mass 0.3 kg at a speed 40 m/s. What is his speed afterward?

(a)   0.15 m/s
(b)   0.28 m/s
(c)   5.1 m/s
(d)   23 m/s
(e)   40 m/s


QUESTION 12*

A mass m1 = 4 kg is sliding to the right at v1 = 8 m/s, as shown. It collides with mass m2 = 20 kg, which is initially at rest. The two masses stick together. What is the velocity of the ensemble after the collision?

(a)   0.667 m/s
(b)   1.33 m/s
(c)   2.5 m/s


QUESTION 13**

A large mass fragments into three smaller masses m1 = 2 kg, m2 = 4 kg, m3 = 0.5 kg. All masses move in a plane with velocities |v1| = 2 m/s, |v2|= 0.5 m/s, |v3| = 3 m/s in the directions indicated. What was the x component of the velocity of the original object before it fragmented?

(a)   Vx = -4.3 m/s
(b)   Vx = -0.67 m/s
(c)   Vx = 0.13 m/s
(d)   Vx = 0.67 m/s
(e)   Vx = 4.3 m/s


QUESTION 14**

A two kilogram block is suspended from the end of a 1 meter rod that is fixed by a pivot at an angle of 45° as show in the figure. Compare the torque about the pivot produced by the weight of the block in case A when the block is suspend 0.5 m from the end, to case B when the block is suspended 0.75 from the end.

(a)   τA > τB
(b)   τA = τB
(c)   τA < τB


QUESTION 15*

An ice skater spinning with his arms extended has a moment of inertia of 4 kg-m2 and is rotating with an angular frequency of 8 radians/second. He then pulls his arms in reducing his moment of inertia to 1.25 kg-m2. What is his new angular velocity?

(a)   26 radians/second
(b)   56 radians/second
(c)   82 radians/second


QUESTION 16*

This and the following question concern the same situation:

A 4 kg, 3 kg and 2 kg mass are attached to a massless meter stick as shown in the figure.

Calculate the distance from the left edge of the meter stick to the center of mass of these 3 masses.

(a)   x = 0.51 m
(b)   x = 0.61 m
(c)   x = 0.71 m


QUESTION 17**

Calculate the moment of inertia for this system about its geometric center (x = 0.5 m).

(a)   I = 0.48 kg m2
(b)   I = 2.25 kg m2
(c)   I = 3.73 kg m2


QUESTION 18*

This and the following three questions concern the same situation:

A solid cylinder with radius 0.85 meters is pulled across a horizontal floor, such that it rolls without slipping. The cylinder starts from rest and is observed to accelerate at a constant rate of 2.8 m/s2 to the right. The moment of inertia of the cylinder is 3.25 kg m2.

Calculate the mass of the cylinder.

(a)   M = 7 kg
(b)   M = 8 kg
(c)   M = 9 kg


QUESTION 19**

Calculate the frictional force f on the cylinder due to the floor.

(a)   f = 9.1 N
(b)   f = 11.4 N
(c)   f = 12.6 N
(d)   f = 18.1 N
(e)   f = 23.1 N


QUESTION 20**

Calculate the magnitude F of the force pulling to the right.

(a)   F = 25.1 N
(b)   F = 31.4 N
(c)   F = 37.8 N


QUESTION 21**

Calculate the total kinetic energy of the block after it has been pulled 3 meters.

(a)   Ktot = 68.2 J
(b)   Ktot = 75.3 J
(c)   Ktot = 94.4 J
(d)   Ktot = 113 J
(e)   Ktot = 143 J


QUESTION 22**

This and the following question concern the same situation:

A 60 cm massless rod is suspended from the ceiling by two wires as shown. A 1.5 kg mass is suspended from the left edge of the rod, and a 2.0 kg mass is suspended from the right end of the rod.

Calculate TL the tension in the left string.

(a)   1.5 N
(b)   2.5 N
(c)   3.5 N
(d)   4.5 N
(e)   5.5 N


QUESTION 23**

What is the largest mass you could replace the 1.5 kg mass with before the rod would tip?

(a)   2.0 kg
(b)   2.8 kg
(c)   3.8 kg


QUESTION 24*

This and the following question concern the same situation:

Two masses are suspended over a massive pulley (I = 0.192 kg m2, R = 0.4 m, M = 3 kg). The 3.5 kg mass is released from rest 0.8 meters above the ground.

Assuming a uniform mass distribution, which shape best describes the pulley?

(a)   spherical
(b)   cylindrical
(c)   hoop


QUESTION 25***

What is the speed of the 3.5 kg just before it reaches the ground?

(a)   1.48 m/s
(b)   2.13 m/s
(c)   3.24 m/s
(d)   3.95 m/s
(e)   4.60 m/s