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Relationship between Work and Mechanical Energy

by Ron Kurtus (revised 7 October 2013)

Work is the measurement of the force on an object that overcomes a resistive force times the distance the object is moved. In certain situations there is a relationship between that work and mechanical energy (as opposed to heat or radiant energy).

When you accelerate the object, you are doing work against inertia, such that the work equals the change in kinetic energy of the object.

When you are doing work against continuous resistive forces, such as gravity or spring tension, work done equals the change in potential energy of the object.

Questions you may have include:

This lesson will answer those questions. Useful tool: Units Conversion



Work is force times distance

The definition of work is that it equals a force against some resistance times the distance traveled while that force is being applied. The equation is:

W = Fd

where:

Thus, if you would apply a force of F = 3 newtons (3 N) to move an object a distance of d = 5 meters (5 m), the work done would be W = Fd = 15 joules (15 J).

Work as change in kinetic energy

When you accelerate an object, you are doing work against inertia plus any resistive forces such as gravity or friction over the distance that the object is accelerated. This means that the object's velocity—and thus its kinetic energy—changes over the distance moved.

The kinetic energy of an object is:

KE = mv2/2

where

The work done in changing the velocity against some resistance is then equal to the change in kinetic energy of the object:

ΔKE = mvf2/2 − mvi2/2

W = ΔKE

where

Thus, in certain situations, work is the change in kinetic energy.

(See Proof that Work Can be the Change in Kinetic Energy for more information.)

Work as the change on potential energy

Some resistive forces, such as gravity and spring tension, act continuously on an object, such that the object has a potential of moving from its present position. This is called its potential energy (PE).

Moving the object from one PE to a higher one requires work, which can be measured by the change in potential energy (ΔPE).

Example with gravity

For example, the PE of an object due to the force of gravity is:

PE = mghi

where

If you lifted the object to another height (hf), the new potential energy would be:

PE = mghf

The amount of work done would be

W = Fd

where

Thus:

W = mg(hf − hi)

W = mgf − mghi

W = PEf − PEi = ΔPE

W = ΔPE

Thus in certain situations, work is the change in potential energy.

Work as a combination of KE and PE

If you project an object upward, you are doing work both against gravity and inertia. In this situation, the total work done is:

W = ΔPE + ΔKE

Summary

When you apply enough force on an object to overcome a resistive force, such that you move that object, you are doing work on that object. There is a relationship between that work and mechanical energy.

When you accelerate the object, you are doing work against inertia, such that the work equals the change in kinetic energy of the object.

When you are doing work against continuous resistive forces, such as gravity or spring tension, you change the potential energy of the object.


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Top-rated books on Physics of Work


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Relationship between Work and Mechanical Energy



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