AH 1.4 Gravitation Flashcards
What is meant by a gravitational field?
A gravitational field is the region in space within which a small test mass would feel the gravitational force of a planet (or other massive body).
Define the gravitational field strength of a massive body.
The gravitational field strength of a body is the gravitational force exerted by that body on a 1 kg test mass.
Sketch the gravitational field lines for an isolated point mass.
Sketch gravitational field lines around two adjacent point masses.
State in words what is meant by the gravitational potential at a point in a gravitational field.
The gravitational potential at a point in a gravitational field is
the work done by an external force in bringing a unit mass from infinity to
that point
Where is the zero of gravitational potential taken to be?
The zero of gravitational potential is taken to be at infinity.
State the equation which describes Newton’s Universal Law of Gravitation, which gives the expression for the force of attraction, F, between the two masses shown in the diagram below.
Calculate the force of attraction between Martin, mass 50 kg and Joseph, mass 55 kg if they sit 50 cm apart. Comment on the size of the force.
The Earth has a radius of 6.38 × 106 m and a mass 5.97 × 1024 kg. What is the gravitational force due to the Earth acting on a woman of mass 60.0 kg standing on the surface of the Earth?
By equating the weight equation W=mg with Newton’s Universal Law of Gravitation, show that the gravitational field strength of the Earth’s surface g, is given by
g = Gm/r2
where m= mass of the Earth and r = radius of the Earth
For a planet, state the equation for the gravitational potential Vp at a point in it’s gravitational field a distance r from it’s centre. Specify the units of gravitational potential.
Vp = -Gm/r
What does Vp stand for?
What is it’s unit?
What is the significance of the minus sign?
Vp = gravitational potential
It is masured in J kg-1
The zero of gravitational potential is set at infinity and
the closer you are to the planet, the smaller the gravitational potential.
These two factors mean gravitational potential is always negative.
Gravitational potential a property of what?
Gravitational potential a property of the field.
Must a test mass exist for the gravitational potential of a planet to exist?
No. Gravitational potential is a property of the field itself.
(It is called ‘potential’ because if a test mass WERE brought into the field, then work WOULD have to be done by the field to bring it there form infinity).
Given that gravitational potential is given by Vp= -Gm/r, sketch a graph of Vp against r around the earth, where r is the distance from the centre of the Earth and m is the mass of the Earth.
With the aid of a diagram, explain what is meant by a conservative field.
Derive the expression for escape velocity of a rocket from the surface of the Earth given below.
Work Done by rocket = Ep (at infinity) - Ep (on Earth’s surface)
» ΔEp = -GmEm / ∞ - (-GmEm / rE)
» ΔEp = 0 - (-GmEm / rE)
» ΔEp = GmEm / rE
= the minimum kinetic energy rocket must have to escape
So ½ mv2 = GmEm / rE
v2 = 2GmE / rE
v = √ 2GmE / rE
Identify the cause of the centripetal force which makes this satellite to describe uniform circular motion around the Earth, as shown below.
Give the equation for this force F, taking the mass of the Earth as mE, that of the satellite as m and the distance between the centre of the Earth and the satellite as r.
The gravitational attraction of the Earth for the satellite.
F = GMEm/r2
Find and expression for the linear speed v of a satellite orbitting the Earth by equating the gravitational force on the satellite
F = G mEm/r2
and the centripeatl force
F = mv2/r
Where
m = mass of satellite
ME = mass of Earth
r = distance between centre of Earth and satellite
G mEm/r2 = mv2/r
v2 = G mE/r
v = √G mE/r
