Question

Sally has a mass of 45.9 kilograms. Earth has a mass of 5.98 x 1024 kilograms and an average radius of 6.38 x 106 meters. What is the force due to gravity between Sally and Earth? Include units in your answer. How much does Sally weigh? Include units in your answer. All answers must be in 3 significant digits.

Answer 1

Part I

The gravitational atractive force between Sally and the Earth is given by:

`F=G*(m_(S*)m_E)/(r^2)`

where:

G = gravitational constant =

`G=6.67*10^(-11)N.m^2kg^(-2)`

ms = mass of Sally

mE = mass of the Earth

r = distance between Sally and the Earth, namely the radius of the Earth

Putting all the information in the formula above we get:

`\begin{gathered} F=6.67*10^(-11)*(45.9*5.98*10^(24))/((6.38*10^6)^2) \\ F=(1,830.79)*(10^(13))/(40.70*10^(12)) \\ F=44.98*10 \\ F\approx450N \end{gathered}`

Part II

The weight of Sally is the intensity of gravitational force due to Earth. We calculate with the formula:

`W=m* g`

where:

m = mass of Sally

g = acceleration of gravity = 9.8 m/s²

Putting the information in the formula, we have:

`\begin{gathered} W=45.9*9.8 \\ W=449.82 \\ W\approx450N\text{ } \end{gathered}`