Gravitational Fields 28-29

Question 1

Draw a graph of the strength of the gravitational field,g, against the distance r from the centre of mass of an object.

Answer 1

Inverse square law

Question 2

What is gravitational potential energy of a mass

Answer 2

It is the work that would need to be done to move it against the force of gravity.

Question 3

What is the equation for the gravitational potential energy of a mass,m?

Answer 3

E_grav = -GMm/r

Question 4

Draw the graph of gravitional potential energy vs r to show how the gravitational potential energy varies for Earth.

• What does the gradient of the graph show?
• What is the potential energy at an infinite distance from Earth?

Answer 4

• The gradient of a tangent to the graph gives the value of the gravitional force at that point. The force is greatest at the Earth’s surface.
• Potential energy is zero at an infinite distance from the Eartch.

Question 5

What is gravitional potential at a point,V?

Answer 5

It is the potential energy per unit mass, V = E_grav/m .

Question 6

In a radial field, what is the equation for gravitiational potential at a point,V?

Answer 6

V = - GM/r

Question 7

Draw the graph of gravitational potential vs r, for a point mass r distance away.

• The gradient of the graph tells you what?
• When is the gravitational potential zero?

Answer 7

• The graident of a tangent to the graph gives the value of g at that point.
• The gravitiational potential,V, is zero at infinity.

Question 8

What are equipotentials?

Answer 8

Equipotentials show all the points in a field which has the same potential.

Question 9

What is the gravitational potential at the Earths surface?

Answer 9

63 MjKg^-1

Question 10

What is the equation that gives the linear velocity of a circular orbit of planets due to the centripetal force of gravitational force?

Answer 10

v = (GM/r)^1/2

It comes from equation F = - GMm/r² and F = mv²/r