Physics 213 Final 20 Points Each December 13, 2006

Instructor: K. W. Nicholson Please circle your answers.

Note: Use 10 m/s² for the acceleration due to gravity in these problems.

1. Draw the x vs t , v vs t, and a vs t curves for the ball’s motion until it rolls off the right edge of the track.

2. George is riding in a hot air balloon that is moving upward at 20 m/s . George holds his teddy bear up to show Martha who is watching from the ground. When the balloon is 185 m above Martha's waiting arms, (humm, let's see now, in literature don't they call that foreshadowing of things to come ?), George accidentally drops Harry, (the teddy bear). Two seconds after dropping Harry, the destraught George faints and falls out of the gondola. Two seconds later, the cold wind in his face causes George to wake up. How long after he wakes up does George lands safely in Martha's waiting arms?

3. Gi-Gi, the famous Daredevil Gazelle plans to leap across Royal Gorge at a location where the distance across the canyon is 224 m. She plans to leap from a platform in order to give her enough time to reach the other side. She plans to leap at an angle of 37° above the horizontal at her maximum speed at that angle, which is 40 m/s. Assuming the wind speed is negligible, how high must her platform be in order to insure she just barely makes it to the other side (the "near miss" is always good for show business)?

1. Draw a picture and impose a reference frame on this picture. 6 pt

2. Draw motion diagrams in both vertical and horizontal directions. 4 pt

3. Mark on picture points A and B. 2 pt

4. Write down in neat column form, values for x, v_x , a_x,, y, v_y , a_y and t at each point. If you do not know the value, write down the equation for that value. 6 pts

5. Finally, for 2 points, solve the problem!

4. Elvira pushes on the box with all her might horizontally. The block acclerates up the hill 6 m/s². If the force F she applies to the box is 400 N, what is the coefficient of kinetic friction between the box and the hill ?

5. Consider the conical pendulum with an 8 kg bob on a 10 m string making an angle of 37° with the vertical. Determine the tangential speed of the bob.

6. A 30 kg solid sphere (moment of inertia for sphere = 0.4 mr² ) rolls up an incline and collides with a spring whose spring stiffness constant is 500 N/m. If the incline is as indicated in the diagram below, and the spring gets depressed 2 m, what was the block's initial speed?

7. In a land not very far away, a popular sport is to do the yellow jello slam on a skate board. A 60 kg skate boarder is zooming along at 28 m/s when she slams into the giant blob of jello. She exits the other side 4 seconds later drenched in yucky jello travelling only 12 m/s.

a. How much work is done on the drenched damsel by the yellow blob?

b. What is the average force the blob imposes on the skate boarder?

8. Fido the fat (200 kg) is sitting on a stationary merry-go-round. His mistress, a rotund 150 kg, sits on the merry-go-round a distance of 2 m from the center. When Fido begins galloping clockwise around the merry-go-round a distance of 3 m from the center at a speed of 4 m/s (relative to the earth ), the merry-go-round rotates in the opposite direction 2 rad/s, what must be it’s moment of inertia?

9. Karol is skating along and throws the 30 kg ball to Karl with a velocity of 25 m/s relative to the earth. The impulse of this effort slows her to a speed of 20 m/s. What was Karol's velocity before she threw the ball ?

10. We have here the hopefully happy, (but possibly very tragic), story of the hungry bear who's struggled up the pole and managed to traverse the beam in pursuit of a bag of really yummy smelling goodies.

Statistics: mass of the Beam is 40 kg, mass of the bear is 200 kg, mass of the goodies is 100 kg, and the lengths are as indicated in the diagram. The rope will break if tension exceeds 3700 N. Question is, does the bear reach the goodies or does the rope break before he gets there ?

Still hungry for more physics problems? Try this for 20 points bonus!

you get half credit if you can just write down a good plan.

1. 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 5 m as indicated. What is the coefficient of friction between the surface and the box ?