Question

A 5 kg object is located at a distance of 9.0 x109 km from the center of a larger object whose mass is 2.0 x 1030 kg.

a. What is the size of the force acting on the smaller object

b. What is the size of the force acting on the larger object?

c. What is the acceleration of the smaller object when it is released?

d. What is the acceleration of the larger object when it is released?

Answer 1

a. The force acting on the smaller object:

$F=G\frac{m_1m_2}{R^2}=6.67\cdot 10^{-11}\frac{5\cdot 2\cdot 10^{30}}{(9\cdot 10^{12})^2}=8.2\cdot 10^{-6} \space N.$

b. The force acting on the larger object is the same:

$F=8.2\cdot 10^{-6} \space N.$

c. The acceleration of the smaller object when it is released:

$a_1=\frac{F}{m_1}=\frac{8.2\cdot 10^{-6}}{5}=1.64\cdot 10^{-6}\space m/s^2.$

d. The acceleration of the larger object when it is released:

$a_2=\frac{F}{m_2}=\frac{8.2\cdot 10^{-6}}{2\cdot 10^{30}}=4.1\cdot 10^{-36}\space m/s^2.$