Three small, identical masses initially lie in a straight line with equal separations…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Three small, identical masses m initially lie in a straight line with equal separations d between neighboring masses. The masses interact only through Newtonian gravitation. A slow, controlled process then moves the middle mass sideways so that it forms an isosceles right triangle with the two end masses, while the end masses remain fixed in place.
The zero of gravitational potential energy is set at infinite separation. Assume no kinetic energy is generated during the slow repositioning.
(a) Write an expression for the total gravitational potential energy of the initial collinear configuration. Express your answer in terms of G,m, and d.
(b) Determine the total gravitational potential energy of the final triangular configuration once the middle mass has been displaced sideways by a distance d (so that the two equal sides of the triangle each have length 2d).
(c) Calculate the change in total gravitational potential energy ΔU=Ufinal−Uinitial in symbolic form. State clearly whether the potential energy became more negative or less negative and interpret the sign physically.
(d) Suppose the process is reversed and the middle mass is allowed to move back to the line under only gravitational forces. Describe qualitatively how energy conservation accounts for the motion you would observe.