Answered

Anne releases a stone from a height of 2 meters. She measures the kinetic energy of the stone at 9.8 joules at the exact point it hits the ground. What is the mass of the stone?

A0.5 kilograms

B0.6 kilograms

C0.4 kilograms

D0.9 kilograms

Verified Answer :

DuxGinger

A. 0.5kg

To get this answer you need to follow the equation of KE=0.5*mv^2 
But we don't have the m part in the equation. So just plug in the numbers to see which works best, though I can tell you before we do that the answer would be a. 

As you may know, gravity, is a force of 9.8 m/s. And we want to get 9.8 Joules. So if we take a half a kg stone, release it at one meter, we get half of the normal gravity pull, 4.90 Joules. That means if we take half a kg stone and drop it at a doubled height, we get 9.8 Joules.

That is also to say that if we have a 1kg stone and drop it at one meter you will get the normal pull of gravity in Joules, 9.8J. 

Be careful though, this does not mean if you drop a 1kg stone and a .5 kg stone the 1kg will hit first. This simply means that the 1kg stone will have twice the Joules that the .5kg stone has.

The correct answer to the question is A) 0.5 Kg.

CALCULATION:

Before going to answer this question, first we have to understand the law of conservation of energy.

As per law of conservation of energy, the energy can neither be created nor be destroyed. It can only change from one form to another form and the total energy of universe is always constant.

As per the question, the stone was initially at a height of 2m from the ground.The energy possessed by the stone at this height is gravitational potential energy.

When the stone is released, the stone moves downward under gravity. It gains kinetic energy. When it just hits the ground, whole of its potential energy must have been converted into kinetic energy.

Hence, P.E  at height 2m = K.E of the stone just before hitting the ground.

The potential energy of a body at a height h from the surface of earth is calculated as-

                     Potential energy P.E = mgh

 Here, g is known as the acceleration due to gravity and its value is \(9.8\ m/s^2\).

It is given that the height of the stone h = 2m.

The kinetic energy of the stone just before reaching ground K.E = 9.8 J.

We know-  P.E of stone at height 2m =  K.E of stone when it hits the ground.

                             ⇒ mgh = 9.8 Joules

                              ⇒ m = \(\frac{9.8}{gh}\ Kg\)

                                       = \(\frac{9.8}{2\times 9.8}\ Kg\)

                                       = \(0.5\ Kg\)                   [ans]