Download Physics Problems

Circular Motion and Gravitation Problems and Questions
Uniform Circular Motion
1. A merry-go-round takes 9.4 seconds to make one complete rotation. What is the frequency of the merry-go-round?
2. The crankshaft in an idling automobile engine turns at 1500 revolutions per minute. What is the frequency in hertz and the
period in seconds?
3. What is the tangential speed (in km/s) of the earth as it orbits the sun? The earth is 151 million kilometers from the sun.
Hint: how much time does it take for the earth to orbit the sun?
4. A carnival ride moves passengers in a circular path with a radius of 5.3 m at a tangential speed of 4.2 m/s. What is the
period of the ride?
5. Distinguish between a rotation and a revolution.
6. If you lose your grip and fall off a rapidly spinning merry-go-round, in which direction do you fly?
Centripetal Force and Centifugal Force
7. In the Olympic hammer-throw event, an athlete swings a 7.3 kg lead ball attached to a 1.2 m cable in a circular path. The
athlete swings the ball in a circle three or four times before letting it go. If the ball attains a speed of 27 m/s, how much
tension (the centripetal force) is there in the cable just before it is released?
8. A cord will break if its tension reaches 250 N. Suppose the cord is attached to a 0.45 kg ball. If the ball is swung in a
horizontal circle at the end of a 0.90 m cord, at what frequency will the cord break?
9. A 25 kg child attempts to walk from the center of a turning playground merry-go-round that makes a complete rotation in
2.2 seconds. The maximum frictional force (the centripetal force) acting between her shoes and the surface of the ride is
195 N. At what radius will she begin to slip?
10. In what direction is a centripetal force always directed?
11. What force acts as the centripetal force that allows a car to make a turn on a flat road?
12. When a car turns on a banked curve, two other centripetal forces are applied to the car (other than friction). Draw a freebody diagram to help identify these forces (each will have a centripetal component).
13. Does the force of gravity do work on the moon as it orbits the earth (assume a circular path)? Based on this, what must be
true about the tangential speed of the moon?
14. Suppose an electron follows a circular path as it orbits around the nucleus of an atom. Is a centripetal or a centrifugal force
responsible for this motion, and what fundamental force is present?
15. Suppose a small wheel-shaped space station with a period of 7.8 seconds and a radius of 15.0 meters is designed to
produce a simulated gravity. What would be the centripetal acceleration at the feet and at the head of a 2.0-meter tall
astronaut standing inside the space station?
16. Occupants in a single speed shuttle in orbit feel weightless. Describe a scheme whereby occupants in a pair of shuttles
would use a long cable to continuously experience a comfortably normal Earth-like gravity.
Answers: (1) 0.11 hz, (2) 25 hz, 0.040 s, (3) 30.1 km/s, (4) 8.0 s, (7) 4400 N, (8) 4.0 hz, (9) 0.96 m, (15) 9.8 m/s2 and 8.4 m/s2; this
difference would make the astronaut very dizzy!
Universal Gravitation
17. Calculate the force of gravity between two 1.0 kg masses that are 1.0 meter apart. Note the smallness of the value!
18. Calculate the force of gravity between the earth and the moon, and the earth and the sun. The mass of the earth is 5.98 x
1024 kg and the mass of the moon is 7.35 x 1022 kg . The radial distance of the moon’s orbit is 384,000 km (the orbital semimajor axis). The sun has a mass of 1.99 x 1030 kg and the average orbital radius of the earth is 149.6 million kilometers.
19. How much greater is the force of gravity between the earth and the sun compared to the earth and the moon? Interesting
point: despite the sun’s larger gravitational force, it is the moon that has a much greater influence on the earth’s ocean
tides!
20. Your weight (Fw = mg) is due to the force of gravity between you and the earth (Fg = GmMe/r2). Set these two equations
equal to each other and solve for g. The distance is equal to the radius of the earth which equals 6378 kilometers.
21. The sun can be considered to be a satellite of our galaxy, the Milky Way. Based on various measurements, astronomers
have determined that the sun revolves around the center of the galaxy with a radius of 2.2 x 10 17 km and the period of
rotation around the galaxy is 2.5 x 108 years (not seconds). Find the approximate mass of the Milky Way galaxy. To do this,
set the equations for centripetal force and universal gravitation equal to each other, and then solve for the mass of the
galaxy. The sun can be considered the “bob” in this problem.
22. The sun has a mass of 2.0 x 1030 kg. Assume the average mass of a star is equal to the mass of the sun. Based on this
assumption, how many stars are in the Milky Way? Hint: just use dimensional analysis.
23. Why did Newton think that a force must act on the moon? What force did he believe acted on the moon?
24. If the sun pulls with a tremendous force on the earth, why doesn’t the earth “fall into” the sun?
25. How is gravitational force and distance (or radius) proportional?
Answers: (17) 6.67 x 10-11 N, (18) 1.99 x 1020 N, 3.55 x 1022 N, (19) 178 times more, (20) 9.81 m/s2, (21) 1.0 x 1041 kg, (22) 5.0 x 1010
stars/galaxy