Question

Calculate the gravitational force between a baseball and earth. A baseball has a radius of 0.075 m and a mass of 0.145 kg. Earth has a mass of 5.9742•10^24 kg and a radius of 6.3710•10^6 m. Assume the baseball is resting on earths surface.

Answer 1

Answer: 1.424 N

Step-by-step explanation:

According to Newton's Universal Law of Gravitation:

`F_(g)=G((m_(b))(m_(E)))/(d^2)` (1)

Where:

`F_(g)` is the gravitational force between the ball and Earth

`G=6.674(10)^(-11)(m^(3))/(kgs^(2))` the Universal Gravitational Constant

`m_(b)=0.145 kg` is the mass of the ball

`m_(E)=5.9742 (10)^(24) kg` is the mass of the Earth

`d=r_(b)+r_(E)` is the distance between the ball and the Earth, being
`r_(b)=0.075 m` the radius of the ball and
`r_(E)=6.3710(10)^(6) m` the radius of the Earth

So, rewritting (1):

`F_(g)=G((m_(b))(m_(E)))/((r_(b)+r_(E))^2)` (2)

`F_(g)=6.674(10)^(-11)(m^(3))/(kgs^(2))((0.145 kg)(5.9742 (10)^(24) kg))/((0.075 m+6.3710(10)^(6) m)^2)` (3)

Finally:

`F_(g)=1.424 N` (4)