## Friday, 5 September 2014

### CIRCULAR MOTION AND GRAVITATION PROBLEMS

Circular Motion and Gravitation

1. Give three examples of objects moving in circular paths.

2. For each of your examples state what provides the centripetal force.

3. In which direction does the centripetal force act?

4. Explain why it is possible for an object travelling in a circle at a constant speed to have an acceleration.

5. Calculate the centripetal force and acceleration for a 4kg mass moving at 30ms-1 in a circle of radius 2m.

6. If the radius is reduced to 1m what is the new centripetal force?

7. If a stone tied to a string is swung in a circle and then the string is allowed to wind itself round your finger at the centre of the circle explain what happens to the velocity of the stone and the centripetal force in the string.

8. An astronaut is spun in a vertical centrifuge with a radius of 3m. What must his velocity be so that his maximum acceleration is 8g? (Take g = 9.8 ms-2)

9. The formula for the gravitational attraction between two objects is
F = GMm/r2

What do the various symbols mean?
What are the units for G?

10. What is the force between a mass of 2kg and one of 20 kg if the distance between them is: (a)         2m          (b) 2cm (c) 2km
(G = 6.67x10-11 Nm2kg-2)

11. How does the theory of gravitation help to explain the tides?

12. What is a synchronous satellite?
How high above the Earth’s surface must the orbit of such a satellite be? (Radius of the Earth = 6 400 km). Take the period of the Moon to be 27.3 days and the distance of the Moon from the Earth 3.84x108 m.

13. ‘Objects weigh less on the Moon than on the Earth. The radius of the Moon is 0.27 times that of the Earth and its mass is 0.012 times that of the Earth.’
Comment on these results.

14. How close must two people each of mass 50kg be so that the gravitational attraction between them is 0.000 001 N? (G = 6.67x10-11 Nm2kg-2)
15. What would be the value of the gravitational intensity 5 Earth radii from the surface of the Earth? g at the surface = 9.8 Nkg-1

16. A satellite takes 2hrs to orbit a planet at a height of 600km. If the radius of the planet is 5400 km what is the orbital velocity of the satellite?

17. When a satellite (mass m) orbits a planet (mass M) with orbit radius R and orbit time T the centripetal force to keep it in orbit is provided by gravitational attraction. If the orbit velocity is v write down (a) the formula relating v and R with T
(b) the formula for centripetal force
(c) the formula for gravitational attraction

Using these results work out a formula for the ratio R3 /T2

18. The value of this ratio for one of Jupiter’s moons is about 1/1000 of its value for the Earth in orbit round the Sun.
What can you deduce from this?