Chapter 21 - Gravitational Fields

Question 1

What is a force field?

Answer 1

A region in which a body experiences a non-contact force.

Question 2

What are the similarities and differences between gravitational and electrostatic forces?

Answer 2

Similarities: Both have inverse-square force laws that have many characteristics in common, eg use of field lines, use of potential concept, equipotential surfaces etc.

Differences: masses always attract, but charges may attract or repel.

Question 3

What is gravity?

Answer 3

A mutual attractive force acting between all masses.

Question 4

What is gravitational potential energy, Ep?

Answer 4

The work done against the gravitational force to:

• stop the object from moving towards the centre of gravity
• move an object away from the centre of gravity.

The work done against a gravitational force that moves an object from infinity to a certain point in the gravitational field.

Question 5

Is the change in G.P.E. positive or negative when an object is moving towards the centre of the gravitational field?

Answer 5

Negative, as the work done against the gravitational force decreases.

Question 6

An objects GPE is always _____ as the gravitational force is an _______ force.

Answer 6

An objects GPE is always negative as the gravitational force is an attractive force.

Question 7

What is infinity in terms of gravity?

Answer 7

A point outside a gravitational field. A point where V = 0 and G.P.E. = 0.

Question 8

What is gravitational potential defined as an equation?

Answer 8

V = Ep/m

Note: In the context of gravity, Ep is G.P.E.

Question 9

What is the potential difference between two points in a gravitational field?

Answer 9

The work done per unit mass to move a small mass between the two points.
ΔV = V2 - V1

Work done against gravitational force to move any mass between the two points:
Ep = mΔV (← ON DATA SHEET!)

Question 10

What is an equipotential?

Answer 10

A line or surface along which the gravitational potential is constant/equal. No work is done when moving a mass along an equipotential surface.

Question 11

Explain the significance of the negative sign in the equation for gravitational potential (and G.P.E.) in a radial field.
V = -GM/r

(G.P.E., Ep = -GMm/r)

Answer 11

The gravitational potential is the work done per unit mass AGAINST the gravitational force and so is opposite to the gravitational force. The gravitational force is attractive and so is considered positive.

Question 12

What is the potential gradient?

Answer 12

The rate at which potential varies with distance (ΔV/Δr).

Question 13

What is given by the area under a graph of g against r?

Answer 13

ΔV

Question 14

What is escape velocity?

Answer 14

The minimum vertical velocity required to entirely leave a gravitational field from a point in the field.

v = √(2gr)
or
v = √(2GM/r)
as g = GM/r^2

Question 15

What is Keppler’s Third Law?

Answer 15

T^2 ∝ r^3

T^2 = kr^3
where k is a constant.

k = (4π^2)/(GM)

Keppler’s Third Law is derived from equating the equations for gravitational force and centripetal force.

Question 16

What is the equation for orbital velocity (e.g. that of a satellite)?

Answer 16

v = √(GM/r)

where r is the distance from the centre of the source of the gravitational field.

Question 17

What is a geostationary satellite?

Answer 17

A satellite which orbits the Earth with a time period of 24 hours. It has the same position relative to the Earth.

Question 18

What are uses of geostationary satellites?

Answer 18

Communications and for long-term observations of the Earth.

Question 19

What is the energy of an orbiting satellite?

Answer 19

An orbiting satellite has kinetic and potential energy - its total energy (kinetic + potential) is always constant.