# 5.9.3 Force-Distance Graph

## 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

#### 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! ### Get unlimited access

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