A small spacecraft of mass is moved radially outward from an orbit of radius to a…

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A small spacecraft of mass

200\,\text{kg}

is moved radially outward from an orbit of radius

r_{1}=7.0\times10^{6}\,\text{m}

to a higher orbit of radius

r_{2}=1.4\times10^{7}\,\text{m}

around a planet. In the interval considered, the only significant interaction is an attractive radial force of magnitude

F(r)=\dfrac{2.0\times10^{7}}{r^{2}}\,\text{N}

, where

r

is the distance from the planet’s centre. Assume the motion is along the same radial line. (i) Starting from the definition of work, derive an expression for the work done by the force when the spacecraft is taken from

r_{1}

r_{2}

. (ii) Evaluate the work for the given numerical data, stating its sign clearly. (iii) Explain physically why the work has the sign obtained in part (ii).

Related theory

Conservative & Non-Conservative Forces
Variable Forces & Graphical Methods
Work
Work, energy and power
Work done by a variable force

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