Gravitation

Asked by e-mora | 25th Mar, 2011, 04:29: PM

Expert Answer:

1. 

Consider a simple pendulum:

When the pendulum is given a small push, to start it swinging, the pendulum bob would continue to revolve continuously forever, in a vertical circle, (assuming the right sort of pivot), if it were not for the effects of gravity and friction. The restoring force, which makes the pendulum swing to and fro, is the force of gravity acting on the bob. When one calculates the formula for the periodic time of swing of the pendulum, one finds that the periodic time depends not only on the length of the pendulum and the acceleration due to gravity, but also on the ratio of thegravitational mass of the bob to its inertial mass. However, whatever material is chosen for the bob, this ratio is always found to be unity. Hence, experimentshows that the gravitational mass of any given body is equal to its inertial mass.

2.

f the energy of motion (kinetic energy) of a projectile just equals the pull of gravitational (potential) energy, the projectile can barely escape the Earth.

m  =  G M m
2 r
mv^2/2 = GMm/r
Where:   m = projectile mass (in kg)
   v = velocity (in km/s)
   r = radius of Earth (in km) = 6378 km
   M = Mass of Earth (in kg) = 5.96 X 1024 kg
 
G = Gravitational Constant = 6.67 × 10-11   m 3
kg sec2

Notice that the mass of the projectile can cancel on both sides of the equation. This is why the escape velocity is independent of the mass of the projectile.

vesc = sqrt(2GM/r)

Answered by  | 26th Mar, 2011, 02:19: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.