Circular Motion Questions

Circular Motion Questions

(FUNDAMENTALS OF PHYSICS: pp. 195 – 203)

Concept

1.  Future space stations may be designed like a giant wheel rotating about a central axis. The astronauts would live along the circumference of this structure. How would such a structure simulate gravity? (p. 195 #7)

2.  A car being driven along a mountain road proceeds through an "S" curve. The first part of the curve has twice the radius of the second (reverse) part. How does the centripetal force acting on the car in the first part compare with that acting on the car in the second part? If the car doubles its speed, what changes occur in the size of the centripetal force acting on the car as it traverses each part of the curve? (p. 195 #9)

Problems

3.  A car, traveling at 25 m/s around a circular curve, has a centripetal acceleration of 8.3 m/s2. What is the radius of the curve? (75 m – p. 126 # 37)

4.  The moon, an Earth satellite with a period of about 27.3 d and a nearly circular orbit, has a centripetal acceleration of 2.7 x 10-3 m/s2. What is the average distance from the Earth to the moon? (3.8 x 108 m – p. 126 #39)

5.  What is the centripetal acceleration due to the daily rotation of an object at the Earth’s equator if the equatorial radius is 6.4 x 106 m? (3.4 x 10-2 m/s2 – p. 126 #40)

6.  A biophysicist is able to separate very small subcellular particles, using an analytic ultracentrifuge. The physicist must determine the amount of acceleration provided by the centrifuge at various speeds and radii. (1 g of acceleration is equal to the acceleration due to gravity = 9.8 m/s2). Calculate the number of g’s of acceleration at 8.4 cm from the center of the centrifuge when it is spinning at 60000 r/min. (3.4 x 105 g ’s – p. 126 #41)

7.  A 200 g ball on the end of a string is rotated in a horizontal circle of radius 10.0 m. The ball completes 10 rotations in 5.0 s. What is the centripetal force of the string on the ball?

(3.2 x 102 N – p. 202 #53)

8.  In the Bohr model of the hydrogen atom, the electron revolves around the nucleus. If the radius of the orbit is 5.3 x 10-11 m and the electron makes 6.6 x 1015 rev/s, find

(a) the acceleration of the electron and (9.1 x 1022 m/s2 – p. 202 #54)

(b) the centripetal force acting on the electron. (This force is due to the attraction between the positively charged nucleus and the negatively charged electron.) The mass of the electron is 9.1 x 10-31 kg. (8.3 x 10-8 N – p. 202 #54)

1. A string pendulum 1.12 m long has a bob with a mass of 200 g.

(a) What is the tension in the string when the pendulum is at rest? (1.96 N – p. 203 #55)

(b) What is the tension at the bottom of the swing, if the pendulum is moving at 1.2 m/s? (2.2 N)

10.  When you whirl a ball on a cord in a vertical circle, you find a critical speed at the top for which the tension in the cord is zero. This is because the force of gravity on the object itself supplies the necessary centripetal force. How slowly can you swing a 2.5 kg ball like this so that it will just follow a circle with a radius of 1.5 m? (3.8 m/s – p. 203 #56)

11.  An object of mass 3.0 kg is whirled around in a vertical circle of radius 1.3 m with a constant velocity of 6.0 m/s. Calculate the maximum and minimum tension in the string.

(1.1 x 102 N and 54 N – p. 203 #57)

SIN QUESTIONS (Tough but do-able)

12.  Snoopy is flying his vintage war plane in a "loop the loop" path chasing the Red Baron. His instruments tell him the plane is level (at the bottom of the loop) and travelling with a speed of 180 km/h. He is sitting on a set of bathroom scales, and notes that they read four times the normal force of gravity on him. What is the radius of the loop? Answer in metres. (SIN '75)

(85 m – p. 203 #58)

13.  An Australian bushman hunts kangaroos with the following weapon, a heavy rock tied to one end of a light vine of length 2 m. He holds the other end above his head, at a point 2 m above ground level, and swings the rock in a horizontal circle. The cunning kangaroo has observed that the vine always breaks when the angle  (measured between the vine and the vertical) reaches 60°. At what minimum distance from the hunter can the kangaroo stand with no danger of a direct hit? (SIN '72) (3.0 m – p. 203 #59)

14.  A pendulum of mass 1.0 kg is suspended from the roof of a car travelling on a level road. An observer in the car notices that the pendulum string makes an angle of 10° with the vertical. What is the acceleration of the car? (1.8 m/s2 – p. 203 #60)

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