Grade 12th passMechanics

Why does acceleration of a freely falling object not depends on weight of object?

Salman

10 Years agoGrade 12th pass

1 Answer

Amogh Gajare

10 Years ago

All objects fall at the same rate in vacuum – Gallileo

it is a fact that acceleration doesn’t depend on weight of object.If we try to prove this mathematically,

We know that,

Weight = mass * g........where g = 9.8 m/s

Also by Newton’s second law,

F = m*a therefore a = F/m.............1

As weight is a type of force (Important point)

a = W/m..............(From 1)

But W = m*g

Therefore, a = m*g / m

Therefore a = m*g / m

a = g

So in freely falling body case, acceleration doesnt depend on weight of object.

The acceleration of the object equals the gravitational acceleration. The mass, size, and shape of the object are not a factor in describing the motion of the object. So all objects, regardless of size or shape or weight, free fall with the same acceleration. On the figure, we show an orbiting Space Shuttle and a space walking astronaut. The astronaut and the Shuttle have very different weight, size and shape. But objects in orbit are in a free fall and the only force acting on the objects is the gravitational attraction of the Earth. So both the astronaut and the Shuttle are accelerated towards the Earth with the same acceleration. Because the objects orbit at some altitude above the Earth's surface, the acceleration is slightly less than the surface value. At a 200 mile orbit the acceleration is about 90% of the surface value. Since both Space Shuttle and astronaut are falling with the same acceleration, the astronaut appears to be "weightless" and "floats" relative to the Shuttle.