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?
