Question

A football player’s weight could be in the range of 1,500 N. Explain why the gravitational forces in your lab experiment are way smaller, despite the fact that the two masses are measured in billion kg.

In other words, the gravitational force between two 1 billion kg bodies 2 km apart is 16.7 N:

One football player's weight could easily be in the range on 1500 N, almost 100 times larger. Explain why the football player's weight is so large, and the gravitational force between two 1 billion kg bodies is so small.

SHOW YOUR WORK, explain your answers.

Formulas:

Weight:

Gravitational force:

Gravitational constant: G = 6.674×10⁻¹¹ N ⋅ m² / kg²

Answer 1

We have from the Newtons law of gravitation,For every 2 masses and seperated by distance ,there will be expierience a force of attraction between the bodies called gravitaional force.

Magnitude of the gravitational force between the bodies,

Where the gravitational force is directly proportional to the product of the masses and inversely proportional to the square of distance between them.

Here proportionality constant or G is called gravitational constant,

The gravitational force is a weakest force in nature.

So,The as given the value of the gravitational constant is very low.Which indicates that the magnitude of the gravitational force is very low or negligeble for the smaller bodies and for the bodies seperated by a large distance.Also the considerable value of gravitational force is occurs only in between the massive objects or the objects seperated by smaller distance.Or the gravitational force taken into consideration only for the considerably larger or heavier masses like planets,comets...seperatd by smaller distance.

We have the wieght of the body on the earth surface is the gravitational force of attraction exerted by the earth on the body.Here the gravitational force of attraction expierienced between the body and the massive earth is the wieght of the body.

ie,Wieght or the gravitational force between earth and body of mass m on surface is,

Where, is the acceleration due to gravity of earth

Where is the mass of earth and   is the radius of the earth.

Now for the case of the wieght of the football player as,

So,The mass of the player,

Here we have,mass of earth, radius of earth,

So,

ie,

For the case of gravitational force between two 1 billion kg masses seperated by 2km apart,Where the masses of the 2 bodies,

And the distance between the bodies,

So,Gravitational force between them,

Here we have

Also we have,gravitational force,  

So,Here since the ratio value of first case(wieght of football player) is very much larger than (approx.100times) that of the 2nd case of the force of attraction between the billion kg masses.So,beased on the direct proportionality relationship of the ratio to the force,the wieght of the football player (1500N) is very much higher than than the force of attraction in 2nd case(16.7N).

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