Question

What is the work done by the force of gravity in the following cases?
(a) Satellite moving around the earth in a circular orbit of radius 35000 km.
b) A stone of mass 250 g is thrown up through a height of 2.5 m.
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Answer 1

Answer:

It is thrown up to a height of 2.5 meters. So, the work done by the force of gravity is 6.12 Joules. Hence, this is the required solution.

1 Gravity acts towards the center of the earth. So if the satellite moves in a circular orbit with center of earth as the orbit center the work done at any point is zero, since the force and the displacement are perpendicular.

2 The total work done to throw a stone upward and raise to it a height of 2.5 m is done against the gravitational force. Thus, it is equal to the potential energy of the body at that height. Thus, total work done will be 6.25 J.

Answer 2

Answer:

The work done in the case of the satellite will be zero and in the case of mass 250 g will be 6.25J.

Explanation:

The work done is given as,

$Work=F.r=Frcos\theta$     (1)

F=force

r=displacement of the body

(a) The satellite moves in a circular orbit with the center of the earth as the orbit center and the work done at any point is zero since the force and displacement are perpendicular to each other.

$cos 90\textdegree=0$

So, from equation (1) work done is zero.

(b)

Values given in the question are,

m=250g=0.25kg

r=2.5m

$F=mg=0.25\times 10=2.5$     (2)

Here in this case θ will be 0°

by putting (2) , cos0°=1and r in equation (1) we get;

$W=2.5\times 2.5\times cos0\textdegree$

$W=6.25J$

Hence, the work done in the case of the satellite will be zero and in the case of mass 250 g will be 6.25J.