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Physics: Problems and Solutions

Gravity

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Gravity is one of the four fundamental forces. It is the weakest of the four forces, yet one of the most easily observed. It causes a mutual attraction between two bodies by virtue of their masses. Gravitational force is believed to be caused by the exchange of yet to be discovered particles called gravitons. On earth, the force of gravity on an object is equal to 9.8 N/kg; therefore, all falling objects accelerate at 9.8 m/s2. According to Newton's Law of gravitation: Given masses m1 and m2 at a distance of r, the force between them is equal to

F= \frac{G m_1 m_2}{r^2}

G is the gravitaional constant, equal to 6.673×10−11 N·(m/kg)2.

The same two masses will have a potential energy of

E_p = - \frac{G m_1 m_2}{r}

with respect to infinity; in other words, this is the amount of work required to push one of the objects infinitely far away from the other. This gives a formulation for escape velocity, or the velocity needed to escape an object's gravitational pull:

\frac{G M m}{r} = \frac{1}{2} m v^2
\frac{G M}{r} = \frac{1}{2} v^2
v_e = \sqrt{ 2 \frac{G M}{r} }

For earth, this equals approximately 11186.1 m / s.

Gravity is a central force i.e. it acts along the line joining the centres of the two bodies. It is a conservative force and thus the work done by the gravity on an object is path independent.

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