EXAM IV -- FINAL EXAM

All work on this exam must be your own. You may use a calculator and a 3"X5" card of equations. Clearly indicate your final answer for each question.

PART I -- EQUILIBRIUM, ELASTICITY, AND GRAVITY

Section 1: Multiple choice. No partial credit will be given for this section. Circle only one answer for each question. (2 pts each)

1) Somewhere between the Earth and the moon there is a point where an object would feel no net gravitational force from the two. How far is this point from the center of the Earth? (The mass of the moon is 1/81 the mass of the Earth.) a) 1/81 of the way to the moon.

b) 19% of the way to the moon.

c) 80/81 of the way to the moon.

d) 9/10 of the way to the moon.

2) A board is laid with its ends resting on two tables. A weight is placed in the middle of the board (with no table surface below it). Which of the following is true? a) The upper part of the board is in tension; the lower part of the board is also in tension.

b) The upper part of the board is in compression; the lower part of the board is in tension.

c) The upper part of the board is in tension; the lower part of the board is in compression.

d) The upper part of the board is in compression; the lower part of the board is also in compression.

3) Two ropes are identical except that one is three times as long as the other. Equal weights are hung from each rope. The longer rope is stretched as the shorter rope. a) 3 times as much.

b) 1/3 as much.

c) 9 times as much.

d) the same amount.

4) A ladder is set up on frictionless ice, leaning against a wall that does have friction. Which of the following is true? a) The ladder can be in equilibrium if the wall exerts no force on it. b) The ladder can be in equilibrium if the wall exerts no horizontal force on it.

c) The ladder can be in equilibrium if the wall exerts no vertical force on it.

d) The ladder cannot be in equilibrium.

5) A horizontal beam of weight W is supported by a hinge and a cable as shown. The force exerted on the beam by the hinge must have

a) A vertical component upward, and a horizontal component to the right.

b) A vertical component upward, and a horizontal component to the left.

c) A vertical component downward, and a horizontal component to the right.

a) A vertical component downward, and a horizontal component to the left.

6) Two satellites are in geosynchronous circular orbits around the earth. Which of the following is true? a) The satellites must have the same angular speed.

b) The satellites must have the same speed.

c) The satellites must be the same distance from the center of the earth.

d) All of the above.

7) Satellite A is in orbit further from the Earth than satellite B. The total mechanical energy of satellite A is ___ the total mechanical energy of satellite B. a) less than

b) the same as

c) greater than

d) not enough info is given to determine the answer.

Section 2: Problems and questions. Choose three of the following four problems. Do all sections of each problem you choose. If you attempt more than three problems, please indicate which three you wish to have graded. (20 pts each)

Partial credit will be given for this section. Show ALL WORK and JUSTIFY all answers. Be sure your answers include UNITS where appropriate.

For the following problems, you may need the value of the gravitational constant:

G = 6.673 X 10-11 N m2/kg2

8) NOTE: since we did not cover oscillations in 201 this year, you might be better off using one of the equilibrium problems in the text as an example problem.
A 44g block is hanging at equilibrium from a spring which has a spring constant of 2.7 N/mm. The block is then pulled down by 1.0 cm, released from rest, and allowed to oscillate.

a) Find the period of oscillation and maximum velocity of the block.

b) Plot the displacement of the block as a function of time, neglecting air resistance. Your plot should have a scale and units for both axes. (This is not a rough sketch).

c) Plot the velocity of the block as a function of time, neglecting air resistance. Your plot should have a scale and units for both axes. (This is not a rough sketch).

9) A 103 kg log hangs from two vertical wires. The center of mass of the log is 1/3 of the way from the left edge. The wires had identical lengths before the log was hung from them, and they have the same diameter. The Young's modulus of wire B is 7.0 X 1010N/m2, the Young's modulus of wire A is 2.0 X 1011N/m2. a) What fraction of the log's weight is supported by wire A?

b) What is the ratio Delta-LA/Delta-LB (see figure).

10) Given the following astronomical information:

Mass of Earth: ME = 5.98 X 1024 kg

Radius of Earth: rE = 6.37 X 106 m

Radius of Earth's orbit around sun: RE = 1.5 X 1011 m

Mass of Jupiter: MJ = 318ME

Radius of Jupiter: rJ = 11.2rE

Radius of Jupiter's orbit around sun: RJ = 5.20RE

The Earth and Jupiter have approximately circular orbits around the Sun. (Assume the Sun, the Earth, and Jupiter are in a line, in that order.)

a) What direction should one fire a rocket from Earth if is to go directly to Jupiter? Justify your answer.

b) When a rocket of mass 4400 kg is still on Earth, what is the gravitational force of the Earth on the rocket?

c) When a rocket of mass 4400 kg is still on Earth, what is the gravitational force of Jupiter on the rocket?

11) Given: The mass of Venus is 0.815 times the mass of the Earth, and its radius is 0.949 times the radius of the Earth. A pendulum of length 0.65 m, with a hanging bob of mass 0.22 kg is on the surface of Venus, swinging with a maximum angular displacement of 5o. a) Find the acceleration of gravity on the surface of Venus.

b) Find the maximum angular acceleration of the pendulum bob.

c) Describe two things you could do to increase the maximum acceleration of the pendulum bob.

PART II -- REVIEW

Section 1: Multiple choice. No partial credit will be given for this section. Circle only one answer for each question. (2 pts each)

12) A block of mass m is pulled at constant velocity of 1.0 m/s along a rough horizontal floor by an applied force T as shown. What is the magnitude of the frictional force?

a) m smg

b) T

c) zero

d) mg

13) The net force on an object: a) equals the negative integral with respect to distance of the potential energy function.

b) is the rate at which work is done on the object.

c) equals the time rate of change of momentum of the object.

d) has the dimensions of momentum multiplied by time.

14) Given the following sketch of an object's velocity as a function of time, what is (are) the time interval(s) during which the object's speed is increasing?

a) 0s to 2s.

b) 0s to 2s and 3.3s to 4s.

c) 2s to 4s.

d) 0s to 1s and 3.3s to 4s.

Section 2: Problems and questions. Do all of the following problems.

Partial credit will be given for this section. Show ALL WORK and JUSTIFY all answers. Be sure your answers include UNITS where appropriate. (5 pts each)

15) Three blocks, each having mass M, are connected by massless strings. Block C is pulled to the right by a force F that causes the entire system to accelerate. Neglecting friction, what is the net force on block B?

16) An object is thrown vertically down with an initial speed of 1.0 m/s. How far will it have travelled after 5.0 s?

17) A disk with a rotational inertia of 5.0 kg m2 and a radius of 0.25 m rotates about an axis perpendicular to the disk and through its center. A 2.0 N force is applied tangentially at the rim. What is the angular acceleration of the disk?

18) Two blocks are moving toward each other. One block has a mass of 1.2 kg and is initially moving at 1.7 m/s; after the collision it is moving in the same direction at 1.38 m/s. The other block has a mass of 0.45 kg, and is initially moving at 0.16 m/s. What is its final velocity (magnitude and direction)?