A

PHYSICS 218 – FINAL EXAM Tuesday, December 13, 2011

NAME: ENCIRCLE YOUR SECTION NUMBER: 513 514 515 516 Note: 513 Recitation & lab Wed 8:00 - 10:50 am 514 Recitation & lab Wed 10:20 am - 1:10 pm 515 Recitation & lab Wed 12:40 - 3:30 pm 516 Recitation & lab Wed 3:00 - 5:50 pm There are a total of 12 problems on this test:

• Problems 1 through 4 are worth 5 points each. For these four problems, points will be deducted for the wrong units or wrong number of significant digits. Other than that, no partial credit will be awarded for incorrect answers.

• Problems 5 through 12 are worth 10 points each. For these eight problems, partial credit will be awarded where appropriate.

For all 12 problems: • You must show your work and/or explain your reasoning to receive any credit for a

problem; merely stating the answer is NOT sufficient. • Write your final answer(s) in the blanks provided. • You may use the backs of the pages for scratch calculations if you wish, but only the work in the

spaces provided on the front of the pages will be graded. • For numerical values, assume that all specified digits are significant, including trailing zeros.

Also remember, an answer CAN NOT be completely correct if it has the wrong units or the wrong number of significant digits.

G O O D L U C K and H A P P Y H O L I D A Y S ! ! !

A

For problems 1 through 4, do your work in the space provided, and write your final answer in the blank. Points will be deducted for the wrong units or wrong number of significant digits. Other than that, no partial credit will be awarded for incorrect answers. 1. (5 points) As part of your daily workout, you lie on your back and push with your feet against a

platform attached to two identical, stiff springs arranged side-by-side so that they are parallel to each other. When you push the platform, you compress the springs. You do 65.0 J of work when you compress the springs by 0.150 m. How much additional work must you do to move the platform 0.150 m farther?

Work _________________________________ 2. (5 points) You are riding on a circular Ferris wheel with a radius of 12.0 m. Your speed is 4.00 m/s,

and you are speeding up at a rate of 2.00 m/s2. What is the magnitude of your acceleration? Acceleration ____________________________ 3. (5 points) A pendulum consists of a small ball attached to the end of a thin uniform rod of length L.

The ball and the rod each have mass m. The pendulum hangs from a frictionless hinge and makes small oscillations. What is its period?

Period ________________________________ 4. (5 points) A diving board 3.00 m long is supported at a point 1.00 m from the end, and a diver

weighing 480 N stands at the free end. (See figure below.) The diving board is of uniform cross section and weighs 260 N. Find the force at the support point.

Force __________________________________

A

For problems 5 through 12, do your work in the space provided, and write your final answer in the blank. For these problems, partial credit will be awarded where appropriate, based on the work that you show. 5. (10 points) In a carnival booth, you win a stuffed giraffe if you toss a quarter into a small dish. The

dish is on a shelf above the point where the quarter leaves your hand, and is a horizontal distance of 2.2 m from this point. If you toss the coin with a velocity of 6.4 m/s at an angle of 600 above the horizontal, the coin lands in the dish. You can ignore air resistance.

(a) What is the height of the shelf above the point where the quarter leaves your hand? (b) What is the vertical component of the velocity of the quarter just before it lands in the dish? Height _____________________________________________ Velocity component __________________________________

A

6. (10 points) An astronaut, whose mission is to go where no one has gone before, lands on a spherical

planet in a distant galaxy. As she stands on the surface of the planet, she releases a small rock from rest and finds that it takes the rock 0.480 s to fall 1.80 m. If the radius of the planet is 8.60 x 107 m, what is the mass of the planet?

Mass ____________________________________

A

7. (10 points) A thin, taut string tied at both ends and oscillating in its third harmonic has its shape

described by the equation: y(x,t) = (5.40 cm) sin[(0.0320 rad/cm)x] sin[(42.0 rad/s)t] .

In this expression, the origin is at the left end of the string, the x-axis is along the string, and the y-axis is perpendicular to the string.

(a) Draw a sketch which shows the standing wave pattern. (b) What is the length of this string? (c) What are the period and speed of the traveling waves that make up this standing wave? (d) What would be the equation y(x,t) for this string if it were vibrating in its fourth harmonic with

the same amplitude? Length _____________________________________ Period ______________________________________ Speed _______________________________________ y(x,t) = _______________________________________________________________________

A

8. (10 points) An object of mass 55.0 kg is initially at rest in the middle of the horizontal, frictionless

surface of an ice-covered lake. Then a force directed east and with magnitude F(t) = (15.6 N/s)t is applied.

(a) How far does the object travel in the first 5.00 s after the force is applied? (b) What is the instantaneous power delivered to the object by the force at t = 5.00 s? Distance _________________________________________ Instantaneous power ________________________________

A

9. (10 points) A small block with mass 0.0450 kg slides in a vertical circle of radius R = 0.800 m on the

inside of a circular track. There is no friction between the track and the block. At the bottom of the block’s path, the normal force that the track exerts on the block has a magnitude 3.80 N. What is the magnitude of the normal force that the track exerts on the block when it is at the top of its path?

Normal force _____________________________

A

10. (10 points) A 20.0-kg projectile is fired at an angle of 53.10 above the horizontal with a speed of 65.0

m/s. At the highest point of its trajectory, the projectile explodes into two fragments with equal mass, one of which falls vertically with zero initial speed. You can ignore air resistance and assume the terrain is level. How far from the point of firing does the other fragment strike the ground?

Distance __________________________________

A

11. (10 points) A block with mass M rests on a horizontal frictionless surface and is connected to a

horizontal spring of spring constant k. The other end of the spring is attached to a wall, as shown in the figure below. A second block with mass m rests on top of the first block. The coefficient of static friction between the blocks is μs.

(a) Draw a free-body diagram that would satisfy your Engineering professor for each of the two blocks. Assume your diagrams are for a time when the spring is stretched and the blocks are moving toward the wall.

NOTE: You must encircle your free-body diagrams and label them “Top” and “Bottom”, as appropriate, or you will receive no credit for this part.

(b) Find the maximum amplitude of oscillation such that the top block will not slip on the bottom block.

Amplitude ________________________________

A

12. (10 points) A bowling ball rolls without slipping up a ramp that slopes upward at an angle θ with

respect to the horizontal. Treat the ball as a uniform solid sphere, ignoring the finger holes. (a) Draw a free-body diagram for the bowling ball. Clearly label your coordinate system on the

diagram. (b) Explain your choice for the direction of the frictional force. Encircle your explanation, which

must use a total of no more than two lines of text. (WARNING: If you use more than two lines, I won’t read it, and you will receive ZERO CREDIT for this part.)

(c) What is the acceleration of the center of mass of the ball? (d) What minimum coefficient of static friction is needed to prevent slipping? Acceleration __________________________________ Coefficient of friction ___________________________

A

B

PHYSICS 218 – FINAL EXAM Tuesday, December 13, 2011

NAME: ENCIRCLE YOUR SECTION NUMBER: 513 514 515 516 Note: 513 Recitation & lab Wed 8:00 - 10:50 am 514 Recitation & lab Wed 10:20 am - 1:10 pm 515 Recitation & lab Wed 12:40 - 3:30 pm 516 Recitation & lab Wed 3:00 - 5:50 pm There are a total of 12 problems on this test:

• Problems 1 through 4 are worth 5 points each. For these four problems, points will be deducted for the wrong units or wrong number of significant digits. Other than that, no partial credit will be awarded for incorrect answers.

• Problems 5 through 12 are worth 10 points each. For these eight problems, partial credit will be awarded where appropriate.

For all 12 problems: • You must show your work and/or explain your reasoning to receive any credit for a

problem; merely stating the answer is NOT sufficient. • Write your final answer(s) in the blanks provided. • You may use the backs of the pages for scratch calculations if you wish, but only the work in the

spaces provided on the front of the pages will be graded. • For numerical values, assume that all specified digits are significant, including trailing zeros.

Also remember, an answer CAN NOT be completely correct if it has the wrong units or the wrong number of significant digits.

G O O D L U C K and H A P P Y H O L I D A Y S ! ! !

B

For problems 1 through 4, do your work in the space provided, and write your final answer in the blank. Points will be deducted for the wrong units or wrong number of significant digits. Other than that, no partial credit will be awarded for incorrect answers. 1. (5 points) As part of your daily workout, you lie on your back and push with your feet against a

platform attached to two identical, stiff springs arranged side-by-side so that they are parallel to each other. When you push the platform, you compress the springs. You do 85.0 J of work when you compress the springs by 0.150 m. How much additional work must you do to move the platform 0.150 m farther?

Work _________________________________ 2. (5 points) You are riding on a circular Ferris wheel with a radius of 12.0 m. Your speed is 5.00 m/s,

and you are speeding up at a rate of 3.00 m/s2. What is the magnitude of your acceleration? Acceleration ____________________________ 3. (5 points) A pendulum consists of a small ball attached to the end of a thin uniform rod of length L.

The ball and the rod each have mass m. The pendulum hangs from a frictionless hinge and makes small oscillations. What is its period?

Period ________________________________ 4. (5 points) A diving board 3.00 m long is supported at a point 1.00 m from the end, and a diver

weighing 520 N stands at the free end. (See figure below.) The diving board is of uniform cross section and weighs 240 N. Find the force at the support point.

Force __________________________________

B

For problems 5 through 12, do your work in the space provided, and write your final answer in the blank. For these problems, partial credit will be awarded where appropriate, based on the work that you show. 5. (10 points) In a carnival booth, you win a stuffed giraffe if you toss a quarter into a small dish. The

dish is on a shelf above the point where the quarter leaves your hand, and is a horizontal distance of 2.6 m from this point. If you toss the coin with a velocity of 6.4 m/s at an angle of 600 above the horizontal, the coin lands in the dish. You can ignore air resistance.

(a) What is the height of the shelf above the point where the quarter leaves your hand? (b) What is the vertical component of the velocity of the quarter just before it lands in the dish? Height _____________________________________________ Velocity component __________________________________

B

6. (10 points) An astronaut, whose mission is to go where no one has gone before, lands on a spherical

planet in a distant galaxy. As she stands on the surface of the planet, she releases a small rock from rest and finds that it takes the rock 0.520 s to fall 1.80 m. If the radius of the planet is 8.60 x 107 m, what is the mass of the planet?

Mass ____________________________________

B

7. (10 points) A thin, taut string tied at both ends and oscillating in its third harmonic has its shape

described by the equation: y(x,t) = (5.40 cm) sin[(0.0340 rad/cm)x] sin[(48.0 rad/s)t] .

In this expression, the origin is at the left end of the string, the x-axis is along the string, and the y-axis is perpendicular to the string.

(a) Draw a sketch which shows the standing wave pattern. (b) What is the length of this string? (c) What are the period and speed of the traveling waves that make up this standing wave? (d) What would be the equation y(x,t) for this string if it were vibrating in its fourth harmonic with

the same amplitude? Length _____________________________________ Period ______________________________________ Speed _______________________________________ y(x,t) = _______________________________________________________________________

B

8. (10 points) An object of mass 55.0 kg is initially at rest in the middle of the horizontal, frictionless

surface of an ice-covered lake. Then a force directed east and with magnitude F(t) = (16.6 N/s)t is applied.

(a) How far does the object travel in the first 5.00 s after the force is applied? (b) What is the instantaneous power delivered to the object by the force at t = 5.00 s? Distance _________________________________________ Instantaneous power ________________________________

B

9. (10 points) A small block with mass 0.0450 kg slides in a vertical circle of radius R = 0.800 m on the

inside of a circular track. There is no friction between the track and the block. At the bottom of the block’s path, the normal force that the track exerts on the block has a magnitude 4.20 N. What is the magnitude of the normal force that the track exerts on the block when it is at the top of its path?

Normal force _____________________________

B

10. (10 points) A 20.0-kg projectile is fired at an angle of 53.10 above the horizontal with a speed of 75.0

m/s. At the highest point of its trajectory, the projectile explodes into two fragments with equal mass, one of which falls vertically with zero initial speed. You can ignore air resistance and assume the terrain is level. How far from the point of firing does the other fragment strike the ground?

Distance __________________________________

B

11. (10 points) A block with mass M rests on a horizontal frictionless surface and is connected to a

horizontal spring of spring constant k. The other end of the spring is attached to a wall, as shown in the figure below. A second block with mass m rests on top of the first block. The coefficient of static friction between the blocks is μs.

(a) Draw a free-body diagram that would satisfy your Engineering professor for each of the two blocks. Assume your diagrams are for a time when the spring is stretched and the blocks are moving toward the wall.

NOTE: You must encircle your free-body diagrams and label them “Top” and “Bottom”, as appropriate, or you will receive no credit for this part.

(b) Find the maximum amplitude of oscillation such that the top block will not slip on the bottom block.

Amplitude ________________________________

B

12. (10 points) A bowling ball rolls without slipping up a ramp that slopes upward at an angle θ with

respect to the horizontal. Treat the ball as a uniform solid sphere, ignoring the finger holes. (a) Draw a free-body diagram for the bowling ball. Clearly label your coordinate system on the

diagram. (b) Explain your choice for the direction of the frictional force. Encircle your explanation, which

must use a total of no more than two lines of text. (WARNING: If you use more than two lines, I won’t read it, and you will receive ZERO CREDIT for this part.)

(c) What is the acceleration of the center of mass of the ball? (d) What minimum coefficient of static friction is needed to prevent slipping? Acceleration __________________________________ Coefficient of friction ___________________________

B