Force-Distance Graph (OCR A Level Physics)

Force Distance Graphs for Point or Spherical Masses

• Recall that Newton's Law of Gravitation says the magnitude of the force F between a mass M and a mass m is given by the equation:

• Therefore, a force-distance graph would be a curve, because F is inversely proportional to r², or:

Work is done on the satellite of mass m to move it from A to B, because gravity is attractive. The area under the curve represents the magnitude of energy transferred

• The product of force and distance is equal to work done (or energy transferred) 

• Therefore, the area under the force-distance graph for gravitational fields is equal to the work done

  • In the case of a mass m moving further away from a mass M, the potential increases

  • Since gravity is attractive, this requires work to be done on the mass m

  • The area between two points under the force-distance curve therefore gives the change in gravitational potential energy of mass m