Question

Sally has a mass of 58.4 kilograms. Earth has a mass of 5.98 x 1024 kilograms and an average radius of 6.38 x 106 meters.a. What is the force due to gravity between Sally and Earth? Include units in your answer.b. How much does Sally weigh? Include units in your answer. All answers must be in 3 significant digits.

Answer 1

a)

In order to calculate this force, we can use the formula below:

`F=(G\cdot M\cdot m)/(d^2)`

Where G is the gravitational constant, M is the bigger mass, m is the smaller mass, and d is the distance between each one.

So, for G = 6.674*10^−11, M = 5.98*10^24 kg, m = 58.4 kg and d = 6.38*10^6 m, we have:

`\begin{gathered} F=(6.674\cdot10^(-11)\cdot5.98\cdot10^(24)\cdot58.4)/((6.38\cdot10^6)^2) \\ F=(2330.774\cdot10^(13))/(40.704\cdot10^(12)) \\ F=573\text{ N} \end{gathered}`

b)

Sally's weight is equal to the previously calculated force:

`W=F=573\text{ N}`

If we use a value of gravity of 9.81, we can get approximately the same value:

`\begin{gathered} W=m\cdot g \\ W=58.4\cdot9.81 \\ W=573\text{ N} \end{gathered}`