Physics 213 Final 15 Points Each December 17, 2003
Instructor: K. W. Nicholson Please circle your answers.

1. An object moves in such a way as to produce the velocity vs. time graph at the top of the page.
a) At which of the lettered times is the object the furthest from the origin?

b) At which of the lettered times is the object moving the fastest?

c) Is the object moving away from or toward the origin between times A and B?

d) Sketch the graph of this object's acceleration vs. time.

2. A rocket blasts off and accelerates upward at 5 m/s2 for 8 seconds. The engine runs out of gas and the rocket continues to drift upward and finally stops. How high does it travel before returning to earth?

1. Draw a picture and impose a reference frame on this picture. 3 pt
2. Draw motion diagrams in both vertical and horizontal directions. 3 pt
3. Mark on picture points A and B. 1 pt
4. Write down in neat column form, values for x, vx , ax,, y, vy , ay and t at each point. If you do not know the value, write down the equation for that value. 4 pts
5. Finally, for 4 points, solve the problem!

3. Gigi the dare devil gazelle leaps from the ground at an angle of 53° above the horizontal and a speed of 50 m/s. She strikes the wall 80 meters way. A is where she takes off, B is where she strikes the wall. How high above the floor must the basket be placed on the wall to catch her?

4. The pulley is massless and friction free, the inclined plane has a coefficient of kinetic friction = 0.3.
Find the magnitude and direction of the acceleration of the system. You must draw FBD's for both blocks to receive any credit.

5. The maximum speed an automobile can travel around a curve of radius 250 m on a flat highway without skidding is 40 m/s. What is the coefficient of static friction between the roadway and the tires? (you must draw a FBD to get any credit.)

6. A solid sphere rolls along the ground at 12 m/s as it approaches an incline. If it doesn't reach the top of the incline, how far up the incline does it go ? If it does reach the top, with what speed does it strike the block? (moment of inertia of a solid sphere is (2/5) m r2.

5 Pt Bonus: If the incline were friction free, would the ball go a longer or shorter or the same distance up the incline? Eplain why.

7. 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.

8. 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 ?

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

10. Definitions: Aft thrust engines propel a craft forward, forward thrust engines propel a craft backwards .
A 106 kg space ship is moving forward at 300 m/s. A forward thrust engine employed for 30 seconds applies a force of magnitude 3x106 N to the space ship.

a. What is the final speed of the space ship ?
b. How much energy was used in this manuver ?
c. What is the power output of the engine (assuming 100 % efficient)?

11. The horizontal string at top is tied to a meterstick clamp at 1 m mark 60 cm above the pivot point, which is at the 0 mark on the meterstick. 100 g hangs from meterstick clamp 2. The mass of the meterstick is 150 g, and it's center of mass is at the 50 cm point. How far from the pivot point must meterstick clamp #2 be positoned so that the tension in the string is 2.5 N ?


12. In the figure below, the 50 kg mass is attached to a Hooke's Law Spring and slides on a friction free surface. After being removed a distance A from it's equilibrium position, it is released. It begins to oscillate with an period of 4 s. It's speed when it returns to the equilibrium position is 5 m/s.

What is the initial distance A it is stretched?

13. An block, 10 cm x 15 cm x 6 cm high of mass 200 g is carefully placed at the intersection between flluids A and B as indicated in the figure below. If the density of fluid A is 8 g/cm3 and the density of fluid B is 4 g/cm3 , what is the distance d ?