Answer 80 points worth (4 problems) of the following questions (20 points per problem unless a different number are specified) for full credit on this exam. Show all your work. Circle the answer to each part of each problem you work. Work an additional problem as an extra-credit problem for an additional 20 points. Problems on this exam may not be over the same material as the current course since a different text was used at that time!
1. A kid holding a baseball bat stands at rest in a small boat. The total mass of the boat, kid, and bat is 250 kg. Someone on shore throws a 0.25 kg softball at the boat. It flies straight down the length of the boat, reaching the batter at 20 m/s. He hits it with the bat and the ball sails back the way it came at 20 m/s. What is the speed of the boat immediately after the ball is hit? (7/32)2. A uniform ladder, with length 10 m and weight of 400 N, rests on the ground and against a frictionless wall with the foot of the ladder 8 m from the base of the wall. On the ladder is a person weighing 800 N at 2 m from the bottom of the ladder. Draw a free-body diagram of the forces. Calculate the force exerted on the wall by the ladder. Find the minimum coefficient of static friction between the ladder and the ground for the ladder to remain stationary. (10/22-p296)
3. A 2000 kg car rounds a circular turn of radius 20 m. If the road is flat and the coefficient of friction between the tires and road is 0.70, (a) how fast can the car go around the corner without skidding? (b) How fast can the car go if the mass of the car is 1000 kg? (c) What color is the car? Why? (7/31+)
4. An ancient coin, which has a mass of 0.0100 kg displaces 0.952 g of water. What is its specific gravity? (9/63) [10 points]
5. (a) At what pressure does a granite rock occupy a volume 1% less than at atmospheric pressure? (Bulk modulus of granite = 50 GPa) (b) If the density of granite is 2700 kg/m3, to what depth does the pressure in (a) correspond? [10 points]
6. Because the Earth spins on it’s axis of rotation, a point on the equator experiences a centripetal acceleration of 0.0340 m/s2 while a point at the poles experiences no centripetal acceleration. (a) Show that at the equator the gravitational force on an object (the true weight) must exceed the object’s apparent weight. (b) What are the apparent weights at the equator and at the poles of a 75.0 kg person? (Assume the Earth is a uniform sphere, and take g = 9.800 m/s2) (7/65)
7. A cylindrical 5 kg pulley with a radius of 0.7 m is used to lower a 3.0 kg bucket into a well. The bucket starts from rest and falls for 4.0 s. (a) What is the linear velocity of the falling bucket at 4.0 s? (b) What is the angular velocity of the cylinder at 4.0 s? (c) What is the angular acceleration of the cylinder? (d) What is the linear acceleration of the bucket? (8/31)8. Comet Hale-Bopp moves about the Sun in an elliptical orbit, with its closest approach to the Sun being 1.1 AU and its greatest distance being 1000 AU. If the comet’s speed at closest approach is 54 km/s, (a) what is its speed when it is farthest from the Sun? (b) What is the period of the comet? (c) What is the orbit's semi-major axis? (8/59+) [15 points]
9. A non-uniform bar of weight W is suspended at rest in a horizontal position by two mass-less cords. One cord makes the angle t = 36.9o with the vertical; the other makes the angle p=53.1o with the vertical. If the length L of the bar is 6.10 m, compute the distance x from the left-hand end of the bar to its center of gravity. (13/35P)
Quantities you may need to use on this test – if you need others ask me!!g is the acceleration of gravity (9.8 m/s2), G = 6.67 x 10-11 m3/kg s2