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## Class 11 Physics (India)

### Unit 10: Lesson 3

Work-energy theorem

# Work-energy theorem review

Review the key concepts, equations, and skills for the work-energy theorem.  Understand how the work-energy theorem only applies to the net work, not the work done by a single source.

## Key terms

Term (symbol)Meaning
Net work (W, start subscript, start text, n, e, t, end text, end subscript)Work done by the net force on an object. SI units of start text, J, o, u, l, e, s, space, left parenthesis, J, right parenthesis, end text or start text, N, end text, dot, start text, m, end text
Work-energy theoremNet work done on an object equals the object’s change in kinetic energy. Also called the work-energy principle.

## Equations

EquationSymbolsMeaning in words
\begin{aligned}W_{\text {net}} &= K - K_0 \\&= \Delta K\end{aligned}W, start subscript, start text, n, e, t, end text, end subscript is net work, K is final kinetic energy, K, start subscript, 0, end subscript is initial kinetic energy, and delta, K is change in kinetic energyThe net work on an object is equal to the object’s final kinetic energy minus the initial kinetic energy.

## Common mistakes and misconceptions

Sometimes people forget that the work-energy theorem only applies to the net work, not the work done by a single force. The work-energy theorem states that the net work done by the forces on an object equals the change in its kinetic energy.

For deeper explanations of the work-energy theorem, see our video work and the work-energy principle.
To check your understanding and work toward mastering these concepts, check out calculating change in kinetic energy from a force and velocity and mass from force vs. position graphs.

## Want to join the conversation?

• If we're lifting an object up, wouldn't the net work be equal to the change in kinetic energy PLUS the change in potential energy? (total change in mechanical energy?)
• The work done by your force would be positive, and the total work done would be mgh, assuming the change in height to be h meters. So, according to the work-energy theorem, the final kinetic energy is mgh. Therefore, the square of final velocity should be 2gh. So, use the equations of motion to find out the final velocity. There is no need to find the initial velocity, assuming it started from rest.

From the 3rd equation of motion, v^2 - u^2 = 2as, we find that v^2 = 2gh.

Hence proved.
Cheers!
• how to find of an objects mass from force vs position graph?
• First we need to find out the area under the force vs position graph which will give us the net work done and then we will set the
net work = change in kinetic energy
(Work-energy theorm)
then we will be able to find the objects mass using the given data.
• How do you find the initial kinetic energy?
• initial kinetic energy is equal to 1/2*(mass of body)*(initial velocity of body)^2
• This comment will now be lost to time...
• since work is a vector, do we have work both on the y-axis and x-axis? for instance, if the force is made to a degree from the horizontal axis?
(1 vote)
• Work is not a vector. It is simply a quantity. If work is positive that means work is being done ON a system and if work is negative then that means that work is being done against the system. Hope this helps!
• So the net force is all the work done on an object at the same instant?
(1 vote)
• the net force is different from the work done. first, they are different units. the net force is the vector sum of all the forces acting on an object while the total work is done is the sum of all the work done on the object. keep this in mind and don't confuse. Also, this may refer to the same instant or a period of time.
(1 vote)
• Is it for external forces or internal forces also be counted?
(1 vote)
• if you are dealing with work energy theorem then internal energy may not be counted in some case.....[like if the internal energy doesnot do any work]
(1 vote)
• very perfect explaination
(1 vote)
• How Can We Use the Work-Energy Theorem to Explain and Predict Behavior of a System That Consists of a Ball, a Ramp, and a Cup?
(1 vote)
• Why work equals change in kinetic energy though? Wouldn't it be right to say the change in energy since kinetic is equal to potential??
(1 vote)