GRAVITY: A FORCE OF ATTRACTION THAT EXISTS BETWEEN TWO MASSES; only significant when the masses are very large (planets).
Weight depends on the acceleration due to gravity
Weight of an object varies, depending on position within gravitational fields in the universe.
F=ma w=mg w=weight force mg=mass x acceleration due to gravity = W = weight
NEWTON’S LAW OF UNIVERSAL GRAVITATION
G= Gravitational field constant (6.67 x 10-11 Nm2kg-2)
F= force due to gravity = weight m1 & m2= mass of the two objects (one or both are usually planets) r= the distance between the centres of the two objects (distance apart + radii)
Can also be used to find acceleration due to gravity, as F=mg.
Assuming m1= planet mass and m2 = satellite mass…
F = m2g and using Law of Universal Gravitation m2g = [pic] so… g = Gm1/r2 remembering m1 is the mass of the planet.
Note: The mass of a large body such as a planet can also be shown as M, so g = GM/r2
GRAVITATIONAL FIELD: A FIELD WHERE ANY MASS WILL EXPERIENCE A FORCE DUE TO THE GRAVITATIONAL ATTRACTION OF ANOTHER MASS.
VARIATIONS IN THE VALUE OF g g = acceleration due to gravity
Varies on earth, depending on geographical location: • Variations in the thickness of the earth’s crust/lithosphere due to factors such as tectonic plate boundaries and dense mineral deposits. • Earth is not a perfect sphere; flattened at the poles. Value of g is greater at the poles since they are closer to the centre of the earth, due to the inverse square law and the Law of Universal Gravitation. • Earth’s rotation creates centrifuge effect; reduce value of g. effect is greatest at equator, no effect at poles. • ALTITUDE: As altitude increases, value of g decreases, due to g = Gm1/r2, inverse square law. NOTE: although value of g decreases with an increase in altitude, it only drops to zero when the altitude has an infinite value: outside a gravitational field. g varies depending on mass and radius of the central body (planet), as shown by g = GM/r2 value of g is different for each planet.
WEIGHT: THE FORCE ON A MASS DUE TO THE GRAVITATIONAL FIELD OF A LARGE BODY (such as the Earth)
Force due to the gravitational attraction in a gravitational field.
Any object within a gravitational field has gravitational potential energy, depending on the mass and position within the field.
GRAVITATIONAL POTENTIAL ENERGY (measured in Joules, J)
GRAVITATIONAL POTENTIAL ENERGY: THE ENERGY OF A MASS DUE TO ITS POSITION WITHIN A GRAVITATIONAL FIELD.
GRAVITATIONAL POTENTIAL ENERGY: THE WORK DONE TO MOVE AN OBJECT FROM INFINITY TO A POINT WITHIN A GRAVITATIONAL FIELD.
Due to the inverse square law relationship in the Law of Universal Gravitation, the force due to gravity will drop to zero only at an infinite distance from the centre of the body.
For this reason, infinity is chosen as the level of zero potential energy.
The negative value of Ep increases with distance up to a maximum value of zero at an infinite distance.
Work must be done to move a mass against the gravitational field (increasing the distance), and the work done is converted to gravitational potential energy.
THE GRAVITATIONAL POTENTIAL ENERGY, EP AT A POINT IN A GRAVITATIONAL FIELD IS EQUAL TO THE WORK DONE TO MOVE AN OBJECT FROM THE ZERO ENERGY LEVEL AT INFINITY TO THE POINT.
Even at the earth’s surface there is still gravitational potential energy, as the point is not at the centre of the body.
This can be shown mathematically:
Ep = -GMm/r
Ep = Gravitational potential energy
-G= Negative gravitational constant. It is negative because of the reasons shown above, where the maximum value of Ep is 0 Joules.
M = mass of planet m = mass of object r = distance between the centres of the two bodies (radii plus distance apart)
LOOK AT PRAC BOOK FOR PENDULUM PRACTICAL REGARDING ACCELERATION DUE TO GRAVITY