PROBLEMS
1. What is the period of a pendulum that swings with a small angle while inside an elevator that is accelerating upward at 2.0m/s2 if the pendulum is made of a mass on the end of a 0.50m long string?
2. What is the period of the same pendulum if the elevator is accelerating downward at the same rate?
3. What is the effective gravitational acceleration at the bottom position of a Ferris wheel if the wheel has a radius of 8.0m and has a period of 10.0s? Top position? Side position? Use a coordinate system in which up is the +y direction and the line from the center of the wheel to the side position is the +x direction. Please give all answers as vectors.
4. What lean angle corresponds to 1.0g (multiples of gravitational acceleration) of lateral acceleration? 1.2g? 0.3g?
5. How short would a day need to be on earth (assume earth remains roughly spherical even though it wouldn't) in order for everything at the equator to be weightless?
6. In Lynchburg, VA (37 degrees north latitude) how many degrees northward does a person need to lean in order to feel perfectly upright?
7. A bucket of water is placed on the floor inside a train that rides on a level and straight track. The train starts accelerating away from a station at 1.0m/s2. What angle does the surface of the water make in the bucket if the bucket does not slide and the water is not splashing around?
8. Helium balloons rise because the air below them is slightly denser than the air above them due to gravity. This also means the air pressure on the underside of the balloon is higher than the air pressure above, which results in an upward buoyant force. If such a balloon is placed in a big van with closed windows (so the air moves calmly along with the van) and the van driver jams on the brakes, which way does the balloon fly? Straight upward, forward, backward or some combination?
9. A river is flowing southward in the northern hemisphere. Is there a Coriolis deflection, and if so, in which direction?
10. A bullet is fired parallel to the ground in the northward direction from a latitude of 30 degrees south. It flies at 800m/s over a distance of 1200m. How much of a deflection is expected from the Coriolis force (and acceleration), and in which direction? Do this with kinematics and assume the deflection is small enough that it doesn't affect the time of arrival or the actual path length (1200m) to the target. Those assumptions are very accurate, by the way.
Answers
1. 1.28s
2. 1.57s
3.
4. , ,
5. 5015s (using g=10m/s/s and r=6.37x106m)
6. using g=10m/s/s
7.
8. backward and upward opposite the effective gravitation
9. Yes. Westward in the direction of v cross omega.
10. 6.5 cm