Physics A2 · Gravitational fields. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The gravitational potential ϕ at a point is the work done per unit mass in bringing a small test mass from infinity to that point. It is a scalar, with unit J kg−1.
Potential is taken as zero at infinity. Gravity is attractive, so a mass coming in from infinity is pulled inwards and the work done on it by an outside agent is negative. This is why gravitational potential is always negative. Moving away from the mass, ϕ increases: it becomes less negative and approaches zero.
A mass m placed at the point has gravitational potential energy EP = mϕ. The work needed to move it between two points is m multiplied by the change in potential.
Students drop the minus sign or use r2. Potential uses r, not r2, and a change from −3 to −2 (in the same units) is an increase of +1. Do not use mgh for large changes in height, because g is not constant.
Answer: ϕ = −1.26 × 107 J kg−1; energy needed about 2.5 × 108 J.
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