Physics 201/211: Final Exam

3:30PM Monday, December 16, 1996

NAME (printed):

Student Number (SSN):

Recitation Section Number :

Seat Number :

INSTRUCTIONS:

• Wait for the oral instruction to begin.
• Show all your work in order to qualify for partial credit. Write legibly!
• Assist the graders by placing a box around your final answer.
• You may only use your calculator for simple arithmetic operations.
• HELPFUL ADVICE (Part I): All the parts of the problems will be graded independently. This means that if you can't do part a), for example, then you can just pick an answer for that part in order to go on and do part b). If you do this, please write a note to the grader to this effect.
• HELPFUL ADVICE (Part II): Try to earn as many points as you can! If you find that you cannot do a problem, try to explain what physics principle you think should be applied in solving it and how that principle might influence the answer. You will receive partial credit for correct qualitative reasoning, even if the problem does ask for a numerical answer!
• Note the formula sheet appended to the end of the test.

This final examination is worth 100 points. Good Luck!

: Multiple Choice. Circle the most suitable answer for each of the questions enumerated below. There is no partial credit for this section. Each question is worth 5 points.

{1. A diver is swimming along a coral reef at a constant depth of 7.0 m. What is the pressure exerted on him by the water? Note that the density of sea water is  .

a)

.

b)

.

c)

.

d)

.

2. A bucket of water is pulled upward 3.0 m by a force F. If F is 200 N, then what is the work done by F during the process?

a)

300 J.

b)

-300 J.

c)

600 J.

d)

-600 J.

3. A well-used gang plank was standard equipment on the pirate ships of yore. The gang plank is set flush with the deck and extends 4.00 m beyond the edge, as shown in the figure. The gang plank has a mass of 23.0 kg and a length of 9.00 m. A curious cat of mass 3.00 kg meanders out onto the gang plank and begins to walk toward its outer edge. Will curiousity kill the cat? Assume that the cat can't swim!

a)

Yes.

b)

No.

4. You are one of a group of firefighters holding a trampoline for an anxious person wanting to escape a burning building. The person (of mass 65.0 kg) stands on a ledge 9.00 m above the surface of the trampoline, and the trampoline is being held at a height of 1.35 m above the ground. The trampoline can be thought of as a spring with a spring constant of 6250 N/m. The person escapes the burning building by falling onto the trampoline. After his first bounce he rises to a height of 4.55 m above the original height of the trampoline. How much work was done by nonconservative forces in his first bounce?

a)

J.

b)

J.

c)

J.

d)

J.

5. A car initially moves with a velocity of 8.0 m/s. The driver slams on his brakes, so that the car is brought to a stop with a constant acceleration over a distance of 10.0 m. What is the coefficient of kinetic friction between the tires and the road?

a)

0.15

b)

0.33

c)

0.45

d)

0.62

6. A kid with a mass of 31.0 kg sits on the edge of a small merry-go-round rotating with a angular velocity of 0.45 rad/s. The merry-go-round is a solid disk with a mass of 75.0 kg and a radius of 6.5 m. The kid falls off. What is the final angular velocity of the merry-go-round then? You can ignore any external torques.

a)

0.96 rad/s

b)

0.45 rad/s

c)

0.77 rad/s

d)

0.35 rad/s

: Problems and Short Answer. Show your work completely to obtain at least partial credit. Read each problem carefully! Each problem is worth 14 points.

{7. A solid cylinder of mass M and radius  rolls on a track with a vertical loop, as indicated in the figure. The cylinder is released from rest at a height h, and R denotes the radius of the vertical loop. If  and  , what is the minimum h required so that the cylinder will not leave the track? Assume that the cylinder rolls without slipping. (7 points)

b) Suppose you replaced the cylinder with a hoop of mass M and radius  . Would the minimum h required to stay on the track be larger, smaller, or just the same? Why? A numerical estimate is not required. (7 points)

(Hint: How does your answer from a) depend on the object's shape?)

8. A painter sitting in a bucket pulls herself up with the help of the rope and pulley apparatus shown in the figure. The pulley, which is a solid disk, has a mass of 25.0 kg and a radius of 0.83 m. The combined mass of the painter and bucket is 75.0 kg. You can assume that the rope turns the pulley without slipping. The rope slips from her grasp, so that momentarily  . What is her acceleration a at that moment? (14 points)

{9. A ladder with a mass of 8.0 kg and a length of 3.0 m has one end on a carpeted floor and the other end on a painted wall. Its tilt is  , as shown in the figure. You can assume that the painted wall is a frictionless surface, but the carpeted floor has a coefficient of static friction  . At an angle of  , the ladder begins to slip. What, then, is  ? (14 points)

{10. A mass m rotates in a circle of radius R on a frictionless air table, and is held in this orbit by a string connected to a dangling mass M through a central hole as shown in the figure. You can neglect the mass of string. If m=0.250 kg, M=0.750 kg, and R=0.300 m, then what is the initial angular velocity? (7 points)

{b) You pull on the dangling mass, so that the radius of its circular orbit decreases. If the radius of the final orbit is R=0.175 m, then what is the final angular velocity of the whirling mass? Note that there are no external torques acting on the system. (7 points)

{11. Consider the system shown in the figure. A compressed spring with spring constant k launches an originally stationary block of mass m on a frictionless surface. If k is  N/m, and the spring is compressed from its equilibrium length by .120 m, then what is the velocity of the block at point A? Note that m is .350 kg. (4 points)

true in

b) The mass m makes a elastic, head-on collision with a mass M perched at the edge of the table. What are the velocities of M and m just after the collision? Note that M is .850 kg. (6 points)

c) How far from the edge of the table -- in the horizontal direction -- does M land? Note that the height h of the table is 1.65 m. (4 points)

(Hint: Note that M will have no initial vertical component to its velocity, so that  .)
 

Mon Feb 3 19:44:23 EST 1997