Fall 2006 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 102. The exam period was 90 minutes. The mean score was 67.6; the median was 69. 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 sled starts downhill from rest, from the height h =100 meters above the finish line. The total mass of the sled and people is M = 200 kg.

What is the final speed of the sled, vF, when it arrives (with the people) at the finish line?

(a)   vF = 40.1 m/s
(b)   vF = 44.3 m/s
(c)   vF = 50.6 m/s


QUESTION 2*

Immediately after the finish line the surface has friction to help sleds stop. The sled stops 225 m after the finish line. What is the coefficient of kinetic friction, μ, between the sled and the surface?

(a)   μ = 0.21
(b)   μ = 0.44
(c)   μ = 1.20


QUESTION 3*

On their next run, they sled gets pushed so it has an initial velocity v0 = 5.55 m/s when it is 100 m above the finish line. What is the final speed of the sled at the finish line, vF2, for this run?

(a)   vF2 = 44.1 m/s
(b)   vF2 = 44.3 m/s
(c)   vF2 = 44.6 m/s
(d)   vF2 = 44.8 m/s
(e)   vF2 = 45.0 m/s


QUESTION 4**

This and the following question concern the same situation:

A block of mass M1= 2 kg slides without friction down the ramp, starting from rest at height h1= 16 m. At the bottom, it runs into another block of mass M2 = 6 kg which is at rest before the collision. The two blocks stick together and slide up the second ramp (see the drawing below). They reach a maximum height h2 before sliding back down. (Note: the drawing is not to scale.)

How much kinetic energy, ΔKE = KEinitial - KEfinal, was lost in the collision?

(a)   ΔKE = 0 J
(b)   ΔKE = 45 J
(c)   ΔKE = 125.J
(d)   ΔKE = 235 J
(e)   ΔKE = 270 J


QUESTION 5**

What is the maximum height, h2, on ramp 2?

(a)   h2 = 1.0 m
(b)   h2 = 3.0 m
(c)   h2 = 4.0 m
(d)   h2 = 16.0 m
(e)   h2 = 27.0 m


QUESTION 6**

This and the following two questions concern the same situation:

An object of mass M = 50 kg slides on a frictionless horizontal surface with velocity v0 = 50 m/s to the right. It explodes into two pieces of masses M1 = 20 kg and M2 = 30 kg which continue to slide on the frictionless horizontal surface. The 20 kg piece goes off at 60° with velocity v1 = 100 m/s as shown in the drawing. (Note everything happens on a horizontal surface, so you do not need to worry about gravity.)

Calculate v2y, the y component of the velocity of the 30 kg piece?

(a)   v2y = -50.0 m/s
(b)   v2y = -57.7 m/s
(c)   v2y = -66.6 m/s


QUESTION 7**

What is the angle β (see figure) of the velocity of the 30 kg piece?

(a)   β = 45°
(b)   β = 49°
(c)   β = 60°


QUESTION 8**

What is the total final kinetic energy, KEf, of the two pieces M1 and M2?

(a)   KEf = 0.0 J
(b)   KEf = 62.6 kJ
(c)   KEf = 125.0 kJ
(d)   KEf = 187.5 kJ
(e)   KEf = 250.0 kJ


QUESTION 9*

This and the following question concern the same situation:

A car with mass M = 3000 kg is traveling 50 m/s when its brakes are applied bringing it to a stop in 85 meters on a flat horizontal road.

How much work, W1, does it take to stop the car?

(a)   W1 = -3500 kJ
(b)   W1 = -3750 kJ
(c)   W1 = -6000 kJ


QUESTION 10*

Consider another car traveling with the same speed that has twice the mass and stops in half the distance on the same road. The work needed to stop this car, compared to the first one, is

(a)   0.5 W1
(b)   W1
(c)   2 W1


QUESTION 11*

This and the following question concern the same situation:

An object of mass M = 10 kg is moving horizontally in a straight line at a speed of 15 m/s on a frictionless surface. A force of 50 N slows down the object to 12 m/s.

How long was the force applied?

(a)   0.3 s
(b)   0.6 s
(c)   0.9 s


QUESTION 12*

The work done by the force on the object is

(a)   -405 J
(b)   -252 J
(c)   0 J
(d)   +252 J
(e)   +405 J


QUESTION 13*

This and the following two questions concern the same situation:

A massless beam is placed on a fulcrum as shown in the figure (not to scale) below. A 3 kg box is placed 1.25 m to the left of the fulcrum. A force of 15 N is applied at an unknown distance x to the right of the fulcrum (see the figure), so the beam is balanced.

What is the force of the fulcrum on the beam?

(a)   15 N
(b)   29 N
(c)   44 N


QUESTION 14*

What is the distance x from the fulcrum to the right end of the plank where the force F is applied?

(a)   x = 1.25 m
(b)   x = 2.0 m
(c)   x = 2.45 m


QUESTION 15**

Calculate the torque about the pivot due to the 3 kg block, when the plank makes an angle of 25° with respect to horizontal. (Be careful: all three answers can be obtained using numbers given in the problem).

(a)   38 Nm
(b)   33 Nm
(c)   16 Nm


QUESTION 16*

This and the following three questions concern the same situation:

A solid sphere rolls downs a ramp of height h. The sphere has a radius of 0.38 m and a moment of inertia of 0.14 kg m2 and its acceleration as it rolls down the ramp is 0.4 m/s2. When it reaches the bottom of the ramp, the sphere is traveling at 7 m/s.

What is the mass of the sphere?

(a)   m = 2.42 kg
(b)   m = 3.62 kg
(c)   m = 4.37 kg


QUESTION 17**

What is the height of the ramp?

(a)   h = 2.5 m
(b)   h = 3.0 m
(c)   h = 3.5 m
(d)   h = 4.0 m
(e)   h = 4.5 m


QUESTION 18***

What is the magnitude of the frictional force of the ramp on the sphere?

(a)   0
(b)   0.29 N
(c)   0.39 N
(d)   0.98 N
(e)   1.3 N


QUESTION 19**

If another sphere is rolled down the ramp with the same mass, but twice the radius, itís speed at the bottom of the ramp will be?

(a)   < 7 m/s
(b)   = 7 m/s
(c)   > 7 m/s


QUESTION 20*

This and the following three questions concern the same situation:

A 65 kg person is standing 0.5 meters from the center of a merry-go-round that is spinning with angular frequency ω = 1.7 radians/second. When no one is on it, the merry-go-round has moment of inertia of 150 kg m2.

What is the speed of the person standing 0.5 m from the center of the merry-go-round?

(a)   v = 0.85 m/s
(b)   v = 1.35 m/s
(c)   v = 2.17 m/s


QUESTION 21**

What is the minimum force required to keep the person from slipping off the merry-go-round?

(a)   94 N
(b)   235 N
(c)   637 N


QUESTION 22***

The person walks toward the edge and stands 1.5 meters from the center of the merry-go-round. What is the angular velocity of the merry-go-round when the person is 1.5 meters from the center?

(a)   ω = 0.95 rad/s
(b)   ω = 1.4 rad/s
(c)   ω = 1.7 rad/s
(d)   ω = 2.3 rad/s
(e)   ω = 3.4 rad/s


QUESTION 23**

Compare KE0.5 the kinetic energy of the person when he is 0.5 meters from the center with KE1.5 the kinetic energy of the person when he is 1.5 meters from the center. (Note this is just the kinetic energy of the person, and does not include the kinetic energy of the merry-go-round).

(a)   KE0.5 < KE1.5
(b)   KE0.5 = KE1.5
(c)   KE0.5 > KE1.5


QUESTION 24**

This and the following question concern the same situation:

Two identical blocks with mass M are connected by a string that runs over a disk pulley (I = 1/2 MR2) that also has mass M as shown. The top block is on a horizontal frictionless table. The blocks are released from rest.

How fast are the blocks moving after the vertical block has dropped 0.4 meters?

(a)   1.53 m/s
(b)   1.77 m/s
(c)   1.98 m/s
(d)   2.87 m/s
(e)   3.21 m/s


QUESTION 25***

If the experiment was repeated with an identical setup but the disk pulley was replaced with another disk pulley that had twice the radius and 1/2 the mass, the block would fall ______________ the original experiment.

(a)   faster than
(b)   the same rate as
(c)   slower than