Question

State and prove work energy theorem​

Answer 1

Answer:

The principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle. ... Kinetic Energy: A force does work on the block.

Answer 2

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ㅤㅤㅤㅤㅤㅤWork-Energy Theorem

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The term “work” is used in everyday life quite frequently and we understand that it’s an act of doing something. For example, you are working right now on your grasp of Physics by reading this article! But, Physics itself might not agree on this. The Work-energy theorem explains the reasons behind this Physics of no work!

Work is said to be done when an acting force displaces a particle. If there is no displacement, there is no work done. You might get tired if you keep standing for a long time, but according to Physics, you have done zero work.

Thus, work is a result of force and the resulting displacement. Now, we already know that all moving objects have kinetic energy. So, there must be a relation between Work and kinetic energy. This relation between the kinetic energy of an object and workdone is called “Work-Energy Theorem”. It is expressed as:

Work - Energy Theorem

Here, W is the work done in joules (J) and ΔK is the change in kinetic energy of the object. To learn how the Work-Energy Theorem is derived, we must first learn the nature of work as a scalar quantity and how two or more vector quantities are multiplied.Proof of Work-Energy Theorem

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,

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,

Work - Energy Theorem

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

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

Work - Energy Theorem

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

Work - Energy Theorem

Now, we already know that W= F.d and, K.E. = (mv²)/2,

So, the above equation may be rewritten as:

Work - Energy Theorem

Hence, we have:

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.

hope it helps you dear ❣️ ㅤㅤㅤㅤ▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃ㅤㅤㅤ