Gravitational Fields

Question 1

State Newton’s law of gravitation.

Answer 1

Two point masses attract each other with a force that is proportional to the product of the masses and inversely proportional to the square of their separation.

Question 2

Formula for Newton’s law of gravitation.

Answer 2

Check notes.

Question 3

What is a gravitational field?

Answer 3

Region of space where a mass experiences a force.

Question 4

Define gravitational field strength.

Answer 4

Force per unit mass acting on a mass placed at that point.

Question 5

Formulae for gravitational field strength.

Answer 5

Check notes.

Question 6

Derive the equation for the gravitational field strength of a point mass

Answer 6

Check notes.

Question 7

On the surface of the Earth, gravitational field strength is also called ________.

Answer 7

the acceleration of free fall.

Question 8

For an object in a circular orbit around a planet, what provides the centripetal force?

Answer 8

Gravitational force.

Question 9

Show that T squared is proportional to R cubed, where T is the period of orbit of Earth and R is the radius of orbit.

Answer 9

Check notes.

Question 10

What are the features of a geostationary satellite?

Answer 10

(a) its period of rotation is 24 hours (it orbits the Earth once every 24 hours)
(b) the satellite rotates from west to east
(c) its orbit is directly above the Equator

Question 11

A ‘feeling’ of weightlessness occurs when __________ .

Answer 11

the only force acting on the body is gravitational force.

Question 12

Define gravitational potential.

Answer 12

Work done per unit mass in moving a mass from infinity to the point.

Question 13

Define gravitational potential energy.

Answer 13

Work done in moving a mass from infinity to the point.

Question 14

Gravitational potential energy is always negative. Explain why.

Answer 14

The gravitational force between two masses is always attractive. Hence, to move a mass m from infinity towards another mass M, work is done by the gravitational force, ie. work done by the external force is negative, and the gravitational potential energy Ep decreases. Therefore, masses closer than infinity has negative amount of Ep (relative to ∞ ).

Question 15

Recall the formula for gravitational potential energy.

Answer 15

Check notes.
Ep = ϕ x m
ΔEp = Δ ϕ x m

Question 16

State the relationship between gravitational field strength and gravitational potential.

Answer 16

The gravitational field strength is equal to the negative of potential gradient.

Question 17

The gravitational field strength is equal to the negative of potential gradient.
What does the minus sign indicate?

Answer 17

The minus sign indicates that g is in the direction of decreasing potential.

Question 18

An object is orbiting round the Earth with speed v. How do we find an expression for v?

Answer 18

Centripetal force is provided by gravitational force.

Check notes for the rest of the working.

Question 19

Deduce the equation for kinetic energy of a satellite.

Answer 19

Centripetal force is provided by gravitational force.

Check notes.

Question 20

Deduce the equation for total energy of a satellite.

Answer 20

The total energy of the satellite is the sum of kinetic energy and potential energy of satellite.
Check notes for working.

Question 21

What is meant by the escape speed of a mass?

Answer 21

The escape speed is the minimum speed needed to project a mass m from the surface of a planet to infinity.

Question 22

How do you find the escape speed of a mass?

Answer 22

loss in kinetic energy = gain in potential energy
Ek on surface – Ek at infinity
= Ep at infinity – Ep on surface
Check notes for working.