What is the spring constant of the silk thread

Physics 2010 Fall 2011

Test 2

Name:

Place an X next to your Problems Lab section:

Youngkins (TR 8:00 – 10:30) Youngkins (WF 8:00 – 10:30) Frank (TR 11:20 – 1:50) Lowhorn (WF 11:30 – 2:00) Ford (TR 2:40 – 5:10) Smith (WF 9:10 – 11:40) Lowhorn (TR 6:00 – 8:30) Robertson (WF 12:40 – 3:10)

ï The following test consists of two parts. Part I contains 10 multiple choice questions worth 3 points each. Write the letter of the best answer in the boxes provided at the end of the section. Part II contains 3 problems worth a total of 70 points.

ï There is no partial credit for the multiple choice questions. To receive full credit on the problems, all reasoning must be shown (using symbols!) and your answer must have the appropriate units.

ï Start by writing down basic definitions or equations that you are using in your solution. Be sure to show your set-up.

ï Keep numbers out of your equations until as late as possible in your solutions. ï Box-in your final numerical answers. ï Be careful, be concise, but be complete. ï Ask if you don’t understand the statement of a given problem. ï Please silence and put away your cell phones, and turn any ball caps backwards.

You have 1 hour and 25 minutes to complete this exam. Budget your time accordingly!

Instructor use only:

MC 1 2 3 Total

Phys 2010 Fall 2011

Part I – Multiple Choice (3 points each)

Choose the best answer to each of the following questions. Write your answers in the spaces provided at the end of the MC questions.

1. The compact disc in a CD player is spinning at 8.40 Hz. What is the period of the CD’s rotation?

A. 8.40 s B. 0.56 s C. 16.07 s D. 0.12 s E. 9.31 s

2. A motorbike is being ridden around a circular racetrack at a constant speed of 75 mph. What can you say about the acceleration of the motorbike?

A. The acceleration is zero, because the speed of the motorbike is not changing.

B. The acceleration is not zero; it points towards the center of the racetrack.

C. The acceleration is not zero; it points away from the center of the racetrack.

D. The acceleration is not zero; its direction is tangential to the racetrack.

E. The acceleration is zero, because the motorbike’s velocity is constant.

3. A spring is hanging vertically from the ceiling. The lower end of the spring is attached to a steel block that has a mass of 0.15 kg, causing the spring’s length to increase by 5.0 cm from its equilibrium length. What is the spring constant of the spring? (Hint: draw a FBD for the steel block.)

A. 29.4 N/m

B. 0.15 N/m

C. 150 N/m

D. 88.5 N/m

E. 2.1 N/m

4. Rex and Rover, two mischievous pet dogs, are having a tug-of-war with their favorite toy, a poor old teddy-bear named “Teddy”. Rex and Rover each have hold of one of Teddy’s arms, and are pulling in opposite directions. They are evenly matched, at least for now, so that Teddy is not moving. Which of the following statements about the forces acting on Teddy is NOT true?

A. The net force acting on Teddy is zero. B. There are no forces acting on Teddy, since he’s not moving. C. The sum of the x-components of the forces acting on Teddy is zero. D. The sum of the y-components of the forces acting on Teddy is zero. E. Teddy’s acceleration is zero.

5. Frank the spider (we’ll be meeting him again in long-answer question 3) has made it to the final round of the hit spider TV game show “American Ninja Spider Warrior”. Hanging on the end of a thread of spider silk, Frank is being swung CCW in uniform circular motion, as shown in the diagram. To win the grand prize, Frank must cut his silk thread at the correct position so that he will land on the shaded platform shown in the diagram. At which position on the circle should Frank cut his thread?

A

B C

D

E

F

G H

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6. A rock is thrown horizontally with a speed of 15 m/s. It is 1.4 m above the ground when released. What is the rock’s initial y-component of velocity?

A. 0 B. 15 m/s C. 15 sin 45◦ D. 15 cos 45◦ E. 15 tan 45◦

7. The frequency of revolution of the propeller on an airplane is 38 Hz. What is the angular frequency of the propeller?

A. 12 rad/s B. 55 rad/s C. 122 rad/s D. 198 rad/s E. 239 rad/s

8. Which of the following statements about the normal force is correct?

A. It always points directly upwards.

B. It always points along the line of the rope.

C. It always points in a direction perpendicular to the surface.

D. It always has a magnitude equal to mg.

E. It always opposes the motion of the object.

9. The acceleration of a jet plane flying high above the Earth is zero. Which of the following statements is true?

A. There are no forces acting on the plane.

B. There is a force acting on the plane, but it has no effect since the acceleration is zero.

C. The sum of the forces acting on the plane adds up to zero net force.

D. Newton’s second law says the plane must be accelerating, if it is in flight.

E. The gravitational force on the plane is zero.

10. A 12.0-kg box is being pulled in a straight line at a constant speed along a rough, horizontal surface by means of a horizontal rope. The coefficient of friction between the surface and the box is 0.13. What is the magnitude of the friction force acting on the box?

A. 15.3 N B. 1.6 N C. 0 N (there is no friction force) D. 12.0 N E. 28.3 N

Write your multiple choice answers here. This is the ONLY place your answers will be graded!

1 2 3 4 5 6 7 8 9 10

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Part II – Long Answer Questions

1. (25 pts) A box of mass 55 kg is sliding with constant velocity down an incline of 38◦. The coefficient of friction between the box and the incline is µ .

55 kg

38°

(a) (5 pts) Draw a good FBD for this problem, in the space to the right of the diagram.

(b) (5 pts) What is the magnitude of the friction force acting on the box?

(c) (5 pts) What is the apparent weight of the box?

(d) (5 pts) What is the value of the coefficient of friction between the box and the incline?

(e) (5 pts) The box hits a slick patch on the incline, where there is no friction. As a result, the box starts to accelerate down the incline. What is the magnitude of the box’s acceleration?

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2. (25 pts) A catapult is used to launch a rock toward a castle. The catapult is 122 m from the wall of the castle, and the rock is 2.5 m off the ground when it leaves the catapult. The rock’s initial velocity is 36.4 m/s at an angle of 41◦, as shown in the diagram.

41° 36

.4 m

/s

(a) (10 pts) How long does it take for the rock to reach the castle wall? (For full credit, you should (i) label positions [e.g. “xi”] as appropriate on the diagram above; (ii) show your choice for the positive x and y directions; and (iii) list all appropriate kinematic quantities for the x and y directions.)

(b) (4 pts) How high above the ground is the rock when it reaches the castle wall? Label positions as appropriate on the diagram above.

(c) (5 pts) What are the x and y components of the rock’s velocity when it reaches the castle wall?

(d) (6 pts) What is the rock’s velocity when it reaches the castle wall? (Be sure to give both the magnitude and direction of the velocity.)

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3. (20 pts) The latest extreme-sport craze in the spider world is called “fan-flying”, where a spider hangs by a thread of silk from the end of a ceiling fan. Frank, who has a mass of 5.0 g, has spun himself a thread that has a length L of 15 cm, and he is flying from a ceiling fan that has a radius of 65 cm. The fan takes 1.35 s to complete one rotation. The angle θ that Frank’s thread makes to the horizontal is 30◦.

L Frank

θ

65 cm

(a) (2 pts) What is Frank’s frequency as he rotates about the fan?

(b) (5 pts) What is the radius, in meters, of Frank’s circular motion?

(c) (5 pts) What is Frank’s speed as he rotates around the fan?

(d) (5 pts) What is the tension in Frank’s thread?

(e) (3 pts) What is the magnitude and direction of Frank’s centripetal acceleration?

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