Gravitational Fields

Question 1

Define gravitational field

Answer 1

-a region where a mass experiences a force

Question 2

Define gravitational field strength

Answer 2

The gravitational force per unit mass g=F/m

Question 3

Recall Newton’s law of gravity

Answer 3

-The attractive gravitational force that acts between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
-The force that acts between two masses,m1 and m2, whose centres are separated by a distance of r is given by: F = Gm1m2/r^2

Question 4

Explain what an inverse square law relationship between force and distance means and how to prove it using data

Answer 4

-The inverse square law relationship means that force is proportional to 1/r^2
-ways to prove this:
1. Plot a graph of F against 1/r^2-should be a straight line through the origin
2. Plot a graph of ln F against ln r - should be a straight line with gradient -2
3. From the data, calculate three separate values of Fr^2 - all of these should equal the same constant k
4. From the data, determine the values of r when F doubles(do this at least 3 times). Identify whether r has decreased by a factor of 4.

Question 5

Describe what gravitational field lines show

Answer 5

-The field lines show the direction that a mass in a gravitational field would experience a force

Question 6

Describe what is meant by a uniform field

Answer 6

-A uniform field is one in which the gravitational field strength is constant everywhere
-The field lines are parallel in a uniform field

Question 7

Describe what is meant by a radial field

Answer 7

-A radial field is one in which the field obeys an inverse square law
-The gravitational field strength decreases with the inverse square of the distance from the centre of the mass

Question 8

Derive the equation for gravitational field strength a distance r away from a body of mass M

Answer 8

-g=F/m
-F=GMm/r^2
-g=-GMm/r^2m
-g=-GM/r^2

Question 9

Explain why the mass of the orbiting body(eg Earth around the Sun or Moon around the Earth)has no effect on the gravitational field strength-link to the equation

Answer 9

-g=-GM/r^2 gravitational field strength equation- the gravitational force per unit mass
-M is the mass of the gravitational field creator
-In the gravitational field strength definition, it is the force per unit of mass so the mass of the orbiting body is irrelevant as it does not appear in the equation.

Question 10

Define centripetal force and explain where it comes from in gravitational fields

Answer 10

-The centripetal force is the resultant force that acts towards the centre of a circle when an object moves in a circle
-In gravitational fields, the centripetal force is provided by the gravitational force.

Question 11

Explain why fast-moving distant objects(e,g. distant comets) will not move in a circular motion around the Earth

Answer 11

-The gravitational force is low when an object is far away from the earth, as F=GMm/r^2 so when r is high F is low
-The required centripetal force for circular motion, is high F = mv^2/r as v is high
-Therefore the gravitational force is not high enough to provide the required centripetal force F=mv^2/r for circular motion

Question 12

Explain why the mass of the orbiting body has no effect on its orbital velocity

Answer 12

-The orbital velocity of an orbiting body is v=√GM/r
-Therefore the velocity only depends on the distance, r from the centre of the field creating mass, the mass M of the field creating mass and gravitational constant G

Question 13

Explain what happens to the orbital velocity as an object’s radius of orbit increases

Answer 13

-The orbital velocity decreases as the radius r increases
-Orbital velocity is proportional to the inverse square root of the radius of orbit

Question 14

Describe how a change in radius affects the time period

Answer 14

-T=√(4π^2r^3)/(GM)
-As the radius increases the time period increases
-The time period squared is proportional to the radius cubed

Question 15

Describe key differences and similarities between electric field gravitational fields

Answer 15

-Gravitational fields are regions in which a mass experiences a force due to its mass. Electric fields are regions in which a charge experiences a force due to its charge
-Both types of fields have an infinite range.
-In each type of field the force varies as an inverse square
-the force between masses is always attractive whereas the force between charges can be attractive or repulsive Or electric fields can cancel or reinforce but gravitational fields always reinforce one another
-The force between (unit) charges at a given separation is much stronger than the force between(unit) masses at the same separation

Question 16

Define gravitational potential

Answer 16

The work done per unit mass against the field to move a point mass from infinity to a point in a gravitational field

Question 17

State the equation for the gravitational potential at a distance r from a mass M

Answer 17

-The gravitational potential at a distance r from a mass M is given by: V=-GM/R

Question 18

Explain why the gravitational potential is negative for gravitational fields

Answer 18

-The value is negative because the potential at infinity is zero and as we move towards the mass, the potential or energy decreases.
-The gravitational field is attractive so work is done by the field in moving the mass, meaning energy is given out.

Question 19

State the units of gravitational potential

Answer 19

-Gravitational Potential is measured in Joules per kilogram,Jkg^-1

Question 20

Is gravitational potential a scalar or a vector?

Answer 20

-Scalar