Summary of Gravitational Concepts

Concept
Definition
Equation in a Uniform Force Field
General Equation
Force

(vector)
Masses are attracted to the earth.

All masses attract. The magnitude of the force is proportional to mass of each and inversely proportional to the distance between the centre of the masses. The proportionality constant is G
F=mg
F=Gm1m2/r2
Gravitational Field Strength

(vector)

also gravitational field, gravitational field strength
Only one mass is required for a gravitational force field. (This is only significant if the mass is large, like a planet.) The force field strength depicts how much force would be applied, if a mass was to be placed in a region around the large mass. (The potential for a force on a mass?)
g=F/m

(also true in general case)
g=Gm/r2

(also true in uniform case)
Gravitational Potential Energy

(scalar)
Stored energy associated with the height of a mass in a gravitational field.
Eg=mgh

(note you must either define a point where h=0, therefore Eg=0 or treat this as, DEg=mgDh )
Eg=-Gm1m2/r

This is always negative and Eg at infinity is zero)
Gravitational Potential

(scalar)
Only one mass is required for gravitational potential. It is a property of a particular location away from a mass which describes the magnitude of its potential to have gravitational potential energy.
Vg=gh
Vg=-Gm1/r

Questions (Radius of Earth = 6.38 x 103 km , Mass of Earth 5.97 x 1024 kg, ignore any rotation of the earth, aerodynamic friction etc.)

A 3.00 kg object is fired straight up from earth with such a velocity that it travels 3.62 x 103 km straight up before the force of gravity on the earth brings it to a complete stop.

  1. What is the gravitational potential at the position where the object stops?
  2. What is the gravitational field strength of the earth at the position where it stops?
  3. What is its gravitational potential energy of the mass when it stops?
  4. What is the rate of its acceleration at the time when it stops? (don't just state it, prove it)
  5. What gravitational potential energy will it loose in its first 10 m going back toward earth?
  6. Calculate its velocity at that point 10 m from its stopping point, both by using kinematics and by using energy analysis.
  7. What is its change in gravitational potential in its first 10 m back to earth?
  8. What force is acting on it when it stops?
  9. What was its velocity when it left the ground?
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