Pre-Final Problems

1. Consider a 7-m long pendulum (a Foucault pendulum, typically used to demonstrate the revolution of the Earth). Find its period on Earth, and on the Moon.

2. How long must a pendulum be such that its period is 0.5 seconds?

3. A spring-mass oscillator has a period of 0.8 seconds. What are the first 3 times where the oscillator will have its maximum speed?

4. What is the acceleration due to gravity at a point above the surface of the Earth equal to the radius of the Earth?

5. Mercury orbits the Sun once every 88 days. What is the size of its orbit (semi-major axis) and what is its average speed around the Sun (in km/hr)?

6. What is the angular velocity of a 33 1/3 album? If it takes 0.5 seconds to accelerate up to this speed, what is the angular acceleration and how many turns does it take to get up to this speed?

*7. Two masses (2 kg and 8 kg) are 5-m apart. Where is the center of mass located (as measured from the 2 kg mass)? Hint: consider one distance as x and the other distance as (5-x), then solve for x.

8. A meter stick is set up such that the fulcrum is located at the 25-cm mark. If a 100-g mass is at the 15-cm mark, what is the mass of the meter stick (assuming that it is at the 50-cm mark).