# Work

Key concepts regarding work

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## Work (introduction)

Work is defined as the use of a force to move an objiect an the amount of work done is the amount of energy transferred by a force acting through a distance (force must be acting throughout the distance)

S.I unit:Joule (not newton-metere same SI as energy)

Eqn: force (N) × distance moved by object in the direction of the force (m)

Amount of work done = Amount of energy expended

*If A pushed an object across a floor, it might continue to slide for a short distance after you stopped pushing. Your work would be measured only for the distance you pushed the object (when the force is app)

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## Examples when no work is done

Examples when no work is done

• Work is zero if applied force is zero (W=0 if F=0): If a block is moving on a smooth horizontal surface (frictionless), no work will be done. Note that the block may have large displacement but no work gets done.
• Work done is zero when displacement is zero. This happens when a man pushes a wall. There is no displacement of the wall. Thus, there is no work done
• A car is moving on a road, there will be a frictional force applied by the road on the car. There will be work done by the frictional force on the car. What is the work done on the road by the car? The force applied by the road on the car will be equal and opposite to the force applied by the car on the road. Since, there is no displacement of the road, there will be no work done on the road.
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## Work against gravity

### Work against gravity

When you lift a heavy object, you are doing work against the force of gravity. The force required to lift the object is its weight

F = mg

where

• F is the force required to lift the object and is its weight
• m is the mass of the object
• g is the acceleration due to the force of gravity (9.8 m/s² or 32 ft/s²)

The amount of work you must do is the weight of the object times the height you are lifting it. Thus W = mgh, where h is the height you are lifting it. The amount of work you do to lift an object of mass m to a height h is the same amount of work done by gravity if you drop the object from that height Hence, Gravity can do work against inertia.

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## Work against friction

### Work against friction

Friction is a force of resistance to anything that is moving or sliding along a surface or material. For example, if you push an object along the floor, the force of friction provides the resistance to the motion. If you slide the object a certain distance along the floor, the work done is

W = Frd

where:

• W is the work done
• Fr is the resistive force of friction
• d is the distance you slid the object (while applying force)
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## Work against inertia

Work against inertia

When you apply a force on a stationary but freely moving object, you are working against its inertia or tendency to remain stationary. This also applies to changing the velocity or direction of an object. The work done on a freely moving object only occurs over the distance while you are applying the force.

For example, if you throw a ball, the work done consists of the distance you accelerated the ball until you let it go. Once you have thrown the ball, it will continue at a constant velocity (minus the effect of air resistance) and no further work is done.

Another example of work against inertia is the work done by the force of gravity, when you drop an object from some height. Since the force of gravity is F = mg, where m is the mass of the object and g is the acceleration of gravity, the work done in dropping an object from a height h is W = Fd = mgh.

Note that the equation W = mgh is the same as for the potential energy of an object at some given height: PE = mgh.

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