Physics 213 Test 3 Nov 18, 2005

1. Determine the rotational mass of the system of masses in the figure if the system is pivoted about an axis perpendicular to the plane containing the masses and thru one of the corner masses.

2. A 60 kg kid on a 200 kg bumper car is moving to the east at 80 m/s. She has a head-on perfectly inelastic collision with another identical car that is moving west at 30 m/s and containing two large adults of equal mass. The cars collide and stick together and travel east at a speed of 5 m/s, how much do each of the adults weigh in newtons?

3. How much work is required to increase the speed of a 40 kg object from 30 m/s to 50 m/s if:

For wimps: the object is a block sliding on a friction free horizontal plane.

For the brave and reckless: the object is a solid disk of radius 2 m rollling on a horizontal plane. (5 pts Bonus!)

4. A solid sphere of mass 30 kg and radius 3 m rolls along the ground at 10 m/s as it approaches an incline. (moment of inertia of a solid sphere is .4 m r²⁾.

a. If it doesn't reach the top of the incline, how far up the incline does it go ?

b. If so, with what speed does it strike the block?

5. If a 5 kg object has a change in momentum of 60 kg m/s in a time interval of 12 seconds, what applied force is required to accomplish this?

6. A merry go round is traveling clockwise 4 rad/s. Fido the fat (200 kg) is sitting on a merry-go-round a distance of 4 m from the center. His mistress (300 kg) is standing 3 m from the center. Fido begins galloping clockwise around the merry-go-round a distance of 4 m from the center at a speed of 6 m/s relative to the earth. His mistress begins to trot counter clockwise 2 rad/s relative to the earth. If this stops the the merry-go-round, what must be it’s moment of inertia?

7. A 3 m rod pivots about one end. A force of 20 newtons is applied to the other end at at the angle indicated in the figure below. What is the torque produced by this force?

8. We have here a massless wire hoop system, with 16 masses m attached as shown. It begins from the top of the incline that is 5 m high with initial speed v₀ = 20 m/s, how fast is it going when it reaches the bottom?

9. Definitions: Aft thrust engines propel a craft forward, forward thrust engines propel a craft backwards .

A 10⁶ kg space ship is moving forward at 600 m/s. A forward thrust engine employed for 30 seconds slows the ship to 400 m/s.

a. What is the force applied by the forward thrust engine?

b. How much energy was used in this manuver ?

c. What is the power output of the engine (assuming 100 % efficient)?

10. The 30 kg ball attached to a 2 m rope is released from the position indicated. Upon impact with the box, a special mechanism releases the ball from the cable on impact. The ball sticks to the box and the two slide forward 50 m as indicated. What is the coefficient of friction between the surface and the box ?

11. An automobile tire is inflated with air originally at 10° C and normal atmosphereic pressure. During the process, the air is compressed to 28% of its original volume and the temperature is increased to 40° C. What is the final tire pressure?

12. A brass ring of diameter 10 cm at 20°C is heated and slipped over an alumimum rod of diameter 10.01 cm at 20°C. Assuming the average coefficients of linear expansion are constant, to what temperature must this combination be cooled to separate them?
15 point bonus

A 200 kg refrigerator falls off a truck. The refrigerator is moving at 18 m/s straight toward an unsuspecting damsel 60 m away. Fred races to the rescue and applies a force of 300 N to the refrigerator for 4 s trying to stop it before tripping and falling down . The road surface is friction free at first. Alas, poor Fred gets crushed, causing a friction force between the roadway and the refrigerator with coeficient of kinetic friction of 0.4 .

Does the damsel get hit, and if so, with what speed does the refrigerator hit the damsel?