## Saturday, November 20, 2010

### Circular Motion-1

A. Speed and Acceleration

1. A 2.0 kg mass swinging at the end of a 0.50 m string is traveling 3.0 m/s. What is the
a. centripetal acceleration of the mass?
b. centripetal force on the mass?

2. A person standing at the Earth's equator has what rotational speed? (R = 6.38 x 106 m)

3. A building is located 28º north of Earth's Equator. What distance does it travel as a result of the Earths rotation?

4. A planet has a radius of 6.04*106 m and free fall acceleration of 9.9 m/s2. What would be the tangential speed of a person standing at the equator, if its rotation increased to the point that the centripetal acceleration was equal to the gravitational acceleration?

B. Horizontal Circular Motion Problems

1. A stopper tied to the end of a string is swung in a horizontal circle. If the mass of the stopper is 13.0 g, and the string is 93.0 cm, and the stopper revolves at a constant speed 10 times in 11.8 s,
a. what is the tension on the string?
b. what would happen to the tension on the string if the mass was doubled and all other quantities stayed the same?
c. what would happen to the tension on the string if the period was doubled and all other quantities stayed the same?

2. A rock is whirled on the end of a string in a horizontal circle of radius R and period T. If the radius is halved while keeping the period constant, what happens to the centripetal acceleration of the rock?

3. A boy is whirling a yo yo on a string in a horizontal circle. What happens to the tension on the string when he whirls it twice as fast?

4. A 0.19 m cord passes through a hole in a table.. The cord attaches a mass m = 2.8 kg on the frictionless surface to a hanging mass M = 7.9 kg. Find the speed with which m must move in a circle in order for M to stay at rest?

5. A clock rests horizontally on a table with a pebble balanced at the end of its 1.0 cm long second hand.. What is the minimum coefficient of static friction which would allow the pebble to stay there without slipping?

6. What is the smallest radius of an unbanked (flat) track around which a motorcyclist can travel if her speed is 25 km/h and the coefficient of static friction between the tires and the road is 0.28?

7. A rock of mass 4.0*102 g is tied to one end of a string that is 2.0 m in length and swung around in a circle whose plane is parallel to the ground.

a. If the string can withstand a maximum tension of 4.5 N before breaking, what angle to the vertical does the string reach just before breaking?

b. At what speed is the rock traveling just as the string breaks?

8. A 1050 kg car travels around a turn of radius 70 m on a flat road. If the coefficient of friction between tires and road is 0.80 what is the maximum speed the car can travel without slipping? Does this result dependent on the mass of the car?

9. Two ice skaters of equal mass grab hands and spin in a circle once every four seconds. Their arms are 0.76 m long, and they each have a mass of 55.0 kg. How hard are they pulling on one another?

10. A hollow vertical cylinder with radius R spins about its vertical axis of symmetry. A stone is held to the inner cylinder wall by static friction. Express the period of rotation in terms of the radius and the coefficient of friction, μs.

11. A coin slides around a horizontal circle at height y inside a frictionless hemisphere bowl of radius R. Derive the coin’s velocity in terms of R, y and g.

12. A train travels at a constant speed around a curve of radius 225 m. A ceiling lamp at the end of a light cord swings out to an angle of 20.0º throughout the turn. What is the speed of the train?