A: Uniform Circular Motion
1) (I) What is the magnitude and direction of the acceleration of a sprinter running at 10.0 m/s when rounding a curve with a radius of 256 m?
2) (I) A 615 kg racing car moving with constant speed completes one lap in 14.3 s around a circular track with a radius of 50.0 m.
a) What is the acceleration of the car?
b) What force must the track exert on the tires to produce this acceleration?
3) (II) A 2.0 kg mass is attached to a strong that is 1.0 m long and moves in a horizontal circle at a rate of 4.0 revolutions per second.
a) What is the centripetal acceleration of the mass?
b) What is the tension in the string?
4) (II) A young boy swings a 0.20 kg yo-yo horizontally above his head. The string is 51 cm long and it takes 2.0 s for the yo-yo to make one revolution.
a) What is the linear speed of the yo-yo?
b) What is the centripetal acceleration of the yo-yo?
c) What is the tension in the string?
5) (II) The same child in question # 4 swings the same yo-yo twice as fast.
a) What is the linear speed of the yo-yo?
b) What is the centripetal acceleration of the yo-yo?
c) What is the tension in the string?
6) (III) A test pilot volunteers to test the limits of a new high-performance fighter plane. The engineers say the jet is capable of flying in a horizontal circle at a speed of 105 m/s. The 80.0 kg pilot does not want his centripetal acceleration to exceed 7 g's (7 times free fall acceleration). What is the minimum radius of the circular path for the plane?
7) (II) An early objection to the idea that the earth is spinning on its axis was that the earth would turn so fast at the equator that people would be thrown into space. Show the error is this logic by calculating the centripetal force needed to hold a 100. kg person in place at the equator. The radius of the earth is about 6400 km. Compare this force with the force of gravity (weight) of the 100. kg person.
8) (II) The radius of the moon’s orbit is about 3.6 x 108 m. The moon’s period of revolution is 27.3 days. Calculate the centripetal acceleration of the moon around the earth.
9) (III) A 2.00 x 103 kg car rounds a circular turn of radius 20.0 m. If the road is flat and the coefficient of kinetic friction between the tires and the road is 0.70, how fast can the car travel around the curve without skidding?
10) (II) A dog sits 0.50 m from the center of a merry-go-round. If the dog’s centripetal acceleration is 1.5 m/s2, how long does it take the dog to go around once?
11) (II) A 13 g stopper is attached to a 93 cm string. The stopper is swung in a horizontal circle, making one revolution in 1.18 s. Find the tension in the string on the stopper.
12) (II) If the mass of the stopper in problem # 11 is doubled but all other quantities remain the same. What would be the effect on the velocity, acceleration, and tension?
13) (II) If the radius of the circle for the stopper in problem #11 is doubled but all other quantities remain the same, what would be the effect on the velocity, acceleration, and tension?
14) (II) If the period of revolution in problem #11 is half as large but all other quantities remain the same, what would be the effect on the velocity, acceleration, and the force?
1) 0.39 to center / 2) (a) 9.68 m/s2 (b) 5950 N / 3) (a) 630 m/s2 (b) 1260 N4) (a) 1.6 m/s (b) 5.0 m/s2 (c) 1.0 N / 5) (a) 3.2 m/s (b) 20. m/s2 (c) 4.0 N / 6) 161 m
7) Fc = 3.4 N; Fw = 980 N / 8) 0.0026 m/s2 / 9) 12 m/s / 10) 3.6 s
11) 0.34 N / 12) Tension doubled / 13) All doubled / 14) v is doubled, a and T are 4 times more