OCR A Level Physics

Revision Notes

5.9.3 Force-Distance Graph

Test Yourself

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:

F equals fraction numerator G M m over denominator r squared end fraction

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

F proportional to 1 over r squared



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

Exam Tip

You should be able to interpret areas under curves by thinking about what the product of the quantities on the axes would represent. Since, in this case, force × distance = work done, then it follows that the area under the curve represents the change in energy between two points. Specifically, this would be a change in gravitational potential energy!

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