3.7.2 - Gravitational fields

Question 1

How do you calculate the escape velocity of an object

Answer 1

(1/2)(m)(v^2)=(GMm)/r
=2root (2GM/r)

Question 2

What did Newton realise?

Answer 2

That when an apple falls from a tree, it falls because of gravity, and this centripetal force must be the same force that keeps the moon in orbit around the Earth (gravity)

Question 3

What is Newton’s universal law of attraction?

Answer 3

All masses attract all other masses.
F=(Gm1m2)/r^2

Question 4

What does the capital G stand for?

Answer 4

The gravitational constant, 6.67x10^-11 Nm^2kg^-2

Question 5

What was Cavendish’s experiment?

Answer 5

To find the value for ‘G’ 100 years after Newton published his theory

Question 6

Why are gravitational forces so small?

Answer 6

Because the gravitational constant, G, is so tiny

Question 7

How is a gravitational force represented by a diagram? What do they tell us?

Answer 7

Drawing straight field lines directed towards the object’s centre of mass
They tell us that gravitational fields are non-uniform since the closer together the lines, the stronger the field, and the arrows show the direction of the force which would act on a mass in that field.

Question 8

What is the strength of the field?

Answer 8

the force that would act on a unit mass (1kg) at that point OR the acceleration due to gravity

Question 9

What law does g follow outside the Earth?

Answer 9

The inverse square law: 2xEarth’s radius = 1/4 the field strength (it will never reach 0, until at a distance of infinity)

Question 10

Why is gravitational potential/ energy negative?

Answer 10

At infinity, the GP is zero. Since the gravitational pull is negative, work must be done to pull an object away from the centre of an object’s gravitational field. The negative indicates that a mass within the gravitational field would require energy to escape the field and reach infinity.

Question 11

What is the difference between gravitational potential and gravitational potential energy?

Answer 11

gravitational potential is the work done per unit mass at a certain point to move an object from infinity to that point; a property of the field, independent of the moving object’s mass.
GPE is the energy required/ work done to move a specific mass from infinity to a specific point.

Question 12

What is the relationship between V (gravitational potential) and r (distance)?

Answer 12

inversely proportional

Question 13

Why can GPE=mgh not be used here?

Answer 13

Because g is not constant and an average cannot be used since it does not progress linearly

Question 14

How do you calculate the gain in GPE of an object?

Answer 14

GPE= M x change in V
GPE= m[(-GM/r1) + (-GM/r2)]

Question 15

Why is a satellite in orbit’s total energy negative?

Answer 15

Because otherwise it would have escaped

Question 16

What is the relationship between V and g?

Answer 16

V=-GM/r
g=GM/r^2
so, g=dV/dr (derivation)

Question 17

Why do equipotential get further apart as we move away from the object?

Answer 17

If you do a certain amount of work moving away from the Earth, because the field gets weaker and weaker, you will be able to travel further for the same amount of work.

Question 18

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

Answer 18

The change in V (gravitational potential)

Question 19

What is the gradient of graph of V against r?

Answer 19

the gravitational field strength

Question 20

What happens to a satellite if it is launched with a high enough speed?

Answer 20

It would begin orbiting the object, following the curvature. This means that it is just continually falling

Question 21

What is a close orbit?

Answer 21

Close to the Earth’s surface, just above the atmosphere (about 100km), often above the poles

Question 22

What is a geostationary orbit? What are these used for?

Answer 22

one which is above the same point on the Earth all the time and has to be above the equator
communications

Question 23

How do you figure out the velocity of a geostationary orbit?

Answer 23

Derivation: T^2=(4pi^2/GM)r^3
Put T as 24 hours to find out the radius, and can use this to find the velocity