Answer to Question #163454 in Physics for callie james

Question

Bob whose mass is 65 kg is standing near Sandra whose mass is 35 kg.  The force of gravitational attraction  between them is 5.42 x 10-8 N.  How far apart are Bob and Sandra? How far apart should they stand to have a quarter of that force.

Answer 1

a) From the law of universal gravitation, we have:

$$F=\dfrac{Gm_1m_2}{r^2},$$ $$r=\sqrt{\dfrac{Gm_1m_2}{F}},$$ $$r=\sqrt{\dfrac{6.67\cdot10^{-11}\ \dfrac{Nm^2}{kg^2}\cdot65\ kg\cdot35\ kg}{5.42\cdot10^{-8}\ N}}=1.67\ m.$$

b)

$$r=\sqrt{\dfrac{Gm_1m_2}{\dfrac{1}{4}F}}=2\sqrt{\dfrac{Gm_1m_2}{F}}=2r=2\cdot1.67\ m=3.34\ m.$$