Question

proof of work energy theroem​

Answer 1

Answer:

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Explanation:

Proof of Work-Energy Theorem

The Work done on an object is equal to the change in its kinetic energy.

Answer 2

Explanation:

We will look at the Work-Energy Theorem in two scenarios:

Workdone Under a Constant Force

We have already learnt about the equations of motion earlier and know that,

v ^2 = u ^2 + 2as

Work - Energy TheoremHere, v is the final velocity of the object; u is the initial velocity of the object; a is the constant acceleration and s is the distance traversed by the object. We can also write this equation as,

v ^2 - u ^2 = 2as

Work - Energy Theorem

We can substitute the values in the equation with the vector quantities, therefore:Work - Energy Theore

v ^2 - u ^2 = 2a .d

If we multiply both sides with m/2, we get;

1 /2 mv ^2 - 1 /2 mu ^2 = ma.d

Work - Energy Theorem

From Newton’s second law, we know that F=ma, hence:

1 /2 mv ^2 - 1 /2 mu ^2 = F .d

Work - Energy Theorem

Now, we already know that W= F.d and,

K.E. = (mv²)/2,

So, the above equation may be rewritten as:

K f - Ki = W

Work - Energy Theorem

Hence, we have

delta K = W

Work - Energy Theorem

Therefore, we have proved the Work-Energy Theorem. The Work done on an object is equal to the change in its kinetic energy.

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