Question

As shown in the diagram below, a 5.0 kg space rock is located 2.5 x 107 m from the center of the Earth. The mass of the Earth is 6.0 x 1024 kg.ADetermine the force of gravity acting on the space rock, due to the Earth. Calculate the magnitude and state the direction.BCalculate the acceleration the rock would experience.

Answer 1

Given data

*The given mass of the space rock is m = 5.0 kg

*The given mass of the Earth is M = 6.0 × 10^24 kg

*The separation distance is r = 2.5 × 10^7 m

*The value of the gravitational constant is G = 6.67 × 10^-11 N.m^2/kg^2

(A)

The formula for the force of gravity acting on the space rock, due to the Earth is given as

`F=(GmM)/(r^2)`

Substitute the known values in the above expression as

`\begin{gathered} F=((6.67*10^(-11))(5.0)(6.0*10^(24)))/((2.5*10^7)^2) \\ =3.2\text{ N} \end{gathered}`

Hence, the force of gravity acting on the space rock, due to the Earth is F = 3.2 N

(B)

The expression for the acceleration of the rock would experience is given as

`\begin{gathered} F=ma \\ a=(F)/(m) \end{gathered}`

Substitute the known values in the above expression as

`\begin{gathered} a=(3.2)/(5) \\ =0.64m/s^2 \end{gathered}`

Hence, the acceleration the rock would experience is a = 0.64 m/s^2