Answer 5 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. Current courses may contain different material than what is in this exam.
1. A 20 kg body is moving in the direction of the positive x-axis with a speed of 200 m/s when, owing to an internal explosion, it breaks apart into three pieces. One part, whose mass is 10 kg, moves away from the point of explosion with a speed of 100 m/s in the direction of the positive y-axis. A second fragment, with a mass of 4 kg moves in the direction of the negative x-axis with a speed of 500 m/s. (a) What is the velocity of the third fragment? (b) How much energy was released in the explosion? (10/66P)
2. A proton with mass of 1 u, moving horizontally at velocity vo collides with a proton of mass 1.00 u that is at rest before the collision. The two protons have the same speed after the collision. What is (a) the speed of each proton in terms of vo and (b) the directon of the velocity vectors after collision. (c) What is the change in kinetic energy? (where 1 u = 1.67 x 10-27 kg). (8/28)
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? (7/31+)
4. Io, a one of the Galilean satellites of Jupiter, has an orbital period of 1.77 days and an orbital diameter of 8.44 x 105 km. (a) What is the mass of Jupiter in kilograms? (b) What is the orbital period of Callisto which has an orbital radius of 1.883 x 106 km? (7/52+)
5. 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=9.80 m/s2 (7/65)
6. 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) [20 points]
7. 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, what is its speed when it is farthest from the Sun? You may assume that its angular momentum about the sun is conserved. (8/59+)
8. An electron has a momentum that is 90% greater than its classical momentum. (a) Find the speed of the electron. (b) What is its kinetic energy? (c/d) How would your results change if the particle were a proton?
9. A solid sphere, a spherical shell, a solid cylinder, and cylindrical shell all have the same mass, 1 kg. They are rolled from rest down a 1 m long ramp at an angle of 15o. How long does it take for each to roll down the ramp?
Extra Credit Conceptual Question (10 points each):
10. What are Kepler’s laws and how are they different from Newton’s.11. Explain the twin's paradox.
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