The footfall player has a mass equal to 100kg standing on earth surface at distance of 6.38×10^6m.calculate force of gravitational attraction between the earth and football player?

1 Answer
Apr 6, 2018

#approx 1000N#

Explanation:

Using Newton's law of universal gravitation:

#F=G(Mm)/(r^2)#

We can find the attraction force between two masses given their proximity to each other, and their respective masses.

The mass of the football player is #100kg# (let's call it #m#), and the mass of the Earth is #5.97 times 10^24# kg.(let's call it #M#).

And as the distance should be is measured from the center of the object, the distance the Earth and the player are from each other must be Earth's radius- which is the distance given in the question- #6.38 times 10^6# meters.

#G# is the gravitational constant, which has a value of #6.67408 × 10^-11 m^3 kg^-1 s^-2#

Now, let's plug everything into the equation:

#F=(6.67408 times 10^-11) times ((100) times (5.97 times 10^24))/(6.38 times 10^6)^2#

#F=978.8N approx 1000N# as the least amount of significant figures given is 1 significant figure.

This closely resembles the value of the gravitational field strength or Earth, #g#.

If we use the equation that gives gravitational field strength, or force per unit mass:

#g=(F)/m#

We can test our answer. In reality, #g=9.81 ms^-2#

With our value:

#g=978.8/100#

#g=9.788 approx 9.81#

So it more or less checks out.