The exam lasts 2 hours. Please hand in this paper according to the initial letter of your last name, using the alphabetical trays, and the scantron in a separate, wooden tray. Your pledge on the scantron sheet applies to the whole exam.

1. As a car moves forward on a level road at constant velocity, the net force acting on the tires is:
   1. greater than the normal force times the coefficient of static friction.
   2. equal to the normal force times the coefficient of static friction.
   3. the normal force times the coefficient of kinetic friction.
   4. zero.
2. A 100-N block, on a 30° incline, is being held motionless by friction. The coefficient of static friction between the block and the plane is 0.60. The force due to friction is
   1. 0 N         b. 30 N         c. 50 N         d. 52 N
3. A block is launched up an incline plane. After going up the plane, it slides back down to its starting position. The coefficient of friction between the block and the plane is 0.3. The speed of the block when it reaches the starting position on the trip down
   1. is the same as the launching speed.
   2. is less than the launching speed.
   3. is more than the launching speed.
   4. cannot be compared to the launch speed with the information given.
4. If during a given physical process the only force acting on an object is friction, which of the following must be assumed in regard to the object's kinetic energy?
   1. decreases         b. increases         c. remains constant
     d. cannot tell from the information given
5. A hill is 100 m long and makes an angle of 12° with the horizontal. As a 50-kg jogger runs up the hill, how much work does gravity do on the jogger?
   1. 49 000 J         b. 10 000 J         c. -10 000 J         d. zero
6. A 2.00-kg ball has zero potential and kinetic energy. Maria drops the ball into a 10.0-m-deep well. After the ball comes to a stop in the mud, the sum of its potential and kinetic energy is:
   1. zero         b. 196 J         c. -196 J         d. 392 J
7. A force of 5.0 N is applied to a 20-kg mass on a horizontal frictionless surface. As the speed of the mass increases at a constant acceleration, the power delivered to it by the force
   1. remains the same.
   2. increases.
   3. decreases.
   4. first increases then decreases.
8. In a system with two moving objects, when a collision occurs between the objects,
   1. the total kinetic energy is always conserved.
   2. the total momentum is always conserved.
   3. the total kinetic energy and total momentum are always conserved.
   4. neither the kinetic energy nor the momentum is conserved.
9. The kinetic energy of an object is quadrupled. Its momentum will change by what factor?
   1. zero         b. two         c. eight         d. four
10. A ball with original momentum +4.0 kg·m/s hits a wall and bounces straight back without losing any kinetic energy. The change in momentum of the ball is:
    1. 0         b. 4.0 kg·m/s         c. 8.0 kg·m/s         d. -8.0 kg·m/s
11. A moderate force will break an egg. However, an egg dropped on the road usually breaks, while one dropped on the grass usually doesn't break. This is because for the egg dropped on the grass:
    1. the change in momentum is greater.
    2. the change in momentum is less.
    3. the time interval for stopping is greater.
    4. the time interval for stopping is less.
12. A lump of clay is thrown at a wall. A rubber ball of identical mass is thrown with the same speed toward the same wall. Which statement is true?
    1. The clay experiences a greater change in momentum than the ball.
    2. The ball experiences a greater change in momentum than the clay.
    3. The clay and the ball experience the same change in momentum.
    4. It is not possible to know which object has the greater change in momentum.
13. Object 1 has twice the mass of Object 2. Each of the objects has the same magnitude of momentum. Which of the following statements is true?
    1. Both objects can have the same kinetic energy.
    2. One object has 0.707 times the kinetic energy of the other.
    3. One object has twice the kinetic energy of the other.
    4. One object has 4 times the kinetic energy of the other.
14. An artificial Earth satellite in an elliptical orbit has its greatest centripetal acceleration when it is at what location?
    1. nearest the Earth                     b. farthest from the Earth        
       c. between Earth and Moon         d. between Earth and Sun
15. Which of the following best describes the property of the period of orbital revolution for an Earth satellite?
    1. greater when the orbital radius is smaller
    2. greater when the orbital radius is larger
    3. independent of the orbital radius
    4. determined mainly by the satellite's mass
16. An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N. What free fall acceleration will the 0.50-kg object experience when at the surface of Planet X?
    1. 48 m/s²         b. 20 m/s²         c. 16 m/s²         d. 40 m/s²
17. A figure skater with arms initially extended starts spinning on the ice at 3 rad/s. She then pulls her arms in close to her body. Which of the following results?
    1. a smaller rotational rate
    2. a greater rotational rate
    3. a greater angular momentum
    4. a smaller angular momentum
18. The Earth moves about the Sun in an elliptical orbit. As the Earth moves closer to the Sun, which of the following best describes the Earth Sun system's moment of inertia?
    1. decreases         b. increases         c. remains constant
        d. none of the above choices are valid
19. A solid sphere of mass 2.0 kg is at rest at the top of a ramp inclined. It rolls to the bottom without slipping. The upper end of the ramp is 1.0 m higher than the lower end. Find the sphere's total kinetic energy when it reaches the bottom.
    1. 47 J         b. 19.6 J         c. 18 J         d. 8.8 J
20. A turntable has a moment of inertia of 3.00 × 10^-2 kg·m² and spins freely on a frictionless bearing at 25.0 rev/min. A 0.300-kg ball of putty is dropped vertically on the turntable and sticks at a point 0.100 m from the center. By what factor does the angular momentum of the system change after the putty is dropped onto the turntable?
    1. 1.22         b. 1.00         c. 0.820         d. 1.50
21. The Earth's gravity exerts no torque on a satellite orbiting the Earth in an elliptical orbit. Compare the motion at the point nearest the Earth (perigee) to the motion at the point farthest from the Earth (apogee). At these two points:
    1. the tangential velocities are the same.       c. the angular velocities are the same.
    2. the angular momentum is the same.         d. the kinetic energies are the same.
22. A solid sphere rolls down an incline of height 3 m after starting from rest. In order to calculate its speed at the bottom of the incline, one needs to know
    1. the mass of the sphere.           c. the mass and the radius of the sphere.
    2. the radius of the sphere.         d. no more than is given in the problem.

23. As ice floats in water, about 10% of the ice floats above the surface of the water. If we float some ice in a glass of water, what will happen to the water level as the ice melts?
    1. The water level will rise by 10% of the volume of the ice that melts.
    2. The water level will rise, but not as much as the 10% indicated in answer A.
    3. The water level will remain unchanged.
    4. The water level will become lower.
24. A large stone is resting on the bottom of the swimming pool. The normal force of the bottom of the pool on the stone is equal to the:
    1. weight of the stone.
    2. weight of the water displaced.
    3. sum of the weight of the stone and the weight of the displaced water.
    4. difference between the weight of the stone and the weight of the displaced water.
25. A heavily loaded boat is floating in a pond. The boat sinks because of a leak. What happens to the surface level of the pond? (Think of a big boat in a small pond, so changes in water level become noticeable.)
    1. It stays the same.         b. It goes up.         c. It goes down.
       d. More information is needed to reach a conclusion.
26. A heavily loaded boat is floating in a pond. The boat starts to sink because of a leak but quick action plugging the leak stops the boat from going under although it is now deeper in the water. What happens to the surface level of the pond?
    1. It stays the same.         b. It goes up.         c. It goes down.
       d. More information is needed to reach a conclusion.
27. Dmitri places one end of a copper rod in a heat reservoir and the other end in a heat sink. By what factor is the rate of heat flow changed when the temperature difference between the reservoir and sink is tripled?
    1. 0.33         b. 1/9         c. 3.0         d. 9.0
28. Heat flow occurs between two bodies in thermal contact when they differ in what property?
    1. mass         b. specific heat         c. density         d. temperature
29. How does the heat energy from the sun reach us through the vacuum of space?
    1. conduction         b. radiation         c. convection
       d. none of the above choices are valid
30. The filament temperature of a light bulb is 2 000 K when the bulb delivers 40 W of power. If its emissivity remains constant, what power is delivered when the filament temperature is 2 500 K?
    1. 105 W         b. 62 W         c. 98 W         d. 50 W
31. Which of the following statements is true?
    1. A hot object contains a lot of heat.
    2. A cold object contains only a little heat.
    3. Objects do not contain heat.
    4. Statements a and b are true.
32. According to the second law of thermodynamics, which of the following applies to the heat received from a high temperature reservoir by a heat engine operating in a complete cycle?
    1. must be completely converted to work
    2. equals the entropy increase
    3. converted completely into internal energy
    4. cannot be completely converted to work
33. The maximum theoretical thermodynamic efficiency of a heat engine operating between hot and cold reservoirs is a function of which of the following?
    1. hot reservoir temperature only
    2. cold reservoir temperature only
    3. both hot and cold reservoir temperatures
    4. None of the above choices are valid.
34. A heat engine receives 6 000 J of heat from its combustion process and loses 4 000 J through the exhaust and friction. What is its efficiency?
    1. 33%         b. 40%         c. 67%         d. 73%

The items in this question refer to two identical cups, A and B.

Cup A contains 100 grams of water at 0°C and cup B contains 100 grams of water at 50°C. The contents of the two cups are mixed together in an insulated container (no heat can transfer in or out). The final temperature of the water in the container is
35.

1. lower than 0°C
2. 0°C
3. 25°C
4. 50°C
5. see next set of answers
36.
1. between 0°C and 25°C
2. between 25°C and 50°C
3. higher than 50°C
4. can't tell from the information given
5. see previous set of answers

Cup A again contains 100 grams of water at 0°C but cup B now contains 200 grams of water at 50°C. The contents of the two cups are mixed together in an insulated container (no heat can transfer in or out). The final temperature of the water in the container is
37.
1. lower than 0°C
2. 0°C
3. 25°C
4. 50°C
5. see next set of answers
38.
1. between 0°C and 25°C
2. between 25°C and 50°C
3. higher than 50°C
4. can't tell from the information given
5. see previous set of answers

39, 40. Cup A contains 100 grams of water and is initially at 10°C in a refrigerator. Cup A is heated until its temperature is 20°C. Cup B contains 50 grams of water initially at 70°C in an oven. Cup B is heated until its temperature is 90°C. Which cup had more heat energy transferred to it?
1. cup A
2. cup B
3. both the same
4. can't tell from the information given

41, 42. For the situation in problem 39,40, which had more heat energy transferred to it, one gram of water in cup A or one gram of water in cup B?
1. the gram in cup A
2. the gram in cup B
3. both the same
4. can't tell from the information given

A bowling ball rolls into a stationary bowling pin, which is much lighter than the ball.

1. During the collision, is the force exerted by the ball on the pin greater than, less than, or equal to the force exerted by the pin on the ball? Briefly explain.
   

   
   

   The forces are the same. This follows from Newton's third law.
   

   
   

2. During the collision, is the bowling ball's change in speed greater than, less than, or equal to the pin's change in speed. Briefly explain.
   

   
   The bowling ball's change in speed is less. Because the forces in A. are the same magnitude (and act for the same time), the changes in momenta are also the same. Since Dp = m Dv, the larger mass experiences the smaller Dv.
   

   
   

3. During the collision, is the bowling ball's change in momentum greater than, less than, or equal to the pin's change in momentum. Briefly explain.
   

   
   They are equal (and opposite) as explained in B., and also noted in D.
   

   
   

4. A student makes the following argument about part C:
   In the collision, the pin's momentum changes more than the ball's momentum, because the ball's motion hardly changes, while the pin's motion changes a lot; it bounces off the ball really fast.
   How could you help this student reconcile his intuitive ideas about the "changes in motion" with the fact that the ball's momentum and the pin's momentum change by the same amount?
   

   
   "Momentum" has a precise meaning (mv), so that a heavy object may change its momenum considerably even if its speed changes only a little.
   Also, our perception of motion is not "linear": The change in an object starting from rest, reaching speed v in some time, is more noticable more than that of an object already moving, and picking up additional speed v (or slowing down by v) during that same time.

A. Draw a free body diagram (FBD) of the ball on earth, and when at the top of the rotating Ferris wheel. Assume the rubber string has zero unstretched length, so the force it exerts at the top is about 10% less than the force it exerts when the wheel is not rotating. On your diagram draw these forces in accurate proportion. Label each force.

The statioary picture should show mg down and an equal force (F_s) from the rubber string up
the rotating picture is similar, but the upward force is smaller by about 10%.

B. The "stationary" picture corresponds to normal earth gravity (g = 9.8 m/s²; assume that does not vary between bottom and top of the Ferris wheel). What is therefore the acceleration of the ball, due to the rotation of the Ferris wheel, in the "rotating" picture?

From the rotating FBD, ma = mg - F_s = mg - 0.9×mg = 0.1 mg   so a = 0.1 g = 0.98 m/s².
(actually it's (4.5 - 4)g/4.5 = 1.09 m/s²)

C. The Ferris wheel completes one revolution in 20 s. What is its radius?

since a = w² we have

Because of the 1/r² law we have   g_h (at height h above surface radius r) = (^r/_r+h)²   which solves to

*from an actual eyewitness report

V. A 10 m high tree is felled. We model it as a uniform cylinder rotating about a hinge at its lower end. Its moment of inertia about that point is ML²/3.

1. What is the torque exerted by gravity on the tree just before it hits the ground (in terms of M, L, g)?
   

   The force Mg can be considered as applied at the center of the tree, L/2 away from the hinge. Therefore
   

   t = Mg(L/2)
   

   
   

   
   

   
   

2. What is the tree's angular acceleration a just before it hits the ground (numerically, use L = 10 m, g = 9.8 m/s²)?
   

   t = I a             a = t/I =

   MgL/2 ML²/3

   = 3g / 2L = 1.47 radians/s²

   
   

   
   

   
   

3. With what speed does the tip of the tree hit the ground? Assume that the tree started from a nearly vertical position with negligible speed (numerically).
   

   
   Becsause the question asks for a speed, energy conservation is called for. The initial energy is potential, of the center of mass at h = L/2 (= 5 m), so V = Mgh = MgL/2. Just before hitting the ground, V = 0, and kinetic energy = ½Iw², so
   

   MgL/2 = ¹/₂ (^ML²/₃) w² = ¹/₆Mv²

   since the speed v of the top of the tree is v = Lw. Cancel M, solve for v² = 3gL = 294 (m/s)²   hence   v = 17 m/s.