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Explanation of how Work is a Result of Force - Succeed in Physical Science. Also refer to physics, force, distance, inertia, resistive force, friction, gravity, acceleration, lifting weight, throwing ball, Ron Kurtus, School for Champions. Copyright © Restrictions

Work is a Result of Force

by Ron Kurtus (revised 7 December 2007)

Work is defined in as the result of applying a force to an object to move it a certain distance. Since objects tend to continue moving after a force is applied, the distance is only measured while that force is being applied. When the force is used to change the velocity of the object, the work is against inertia. the work can also be done against a resistive force.

Questions you may have include:

• What is the relationship of work to force?
• What is work against inertia?
• What is work against a resistive force?

This lesson will answer those questions. There is a mini-quiz near the end of the lesson.

Useful tools: Metric-English Conversion | Scientific Calculator.

Work is force times distance

The definition of work is that it equals force times the distance traveled while that force is being applied or

W = Fd

where:

• W is the work in joules (J or kg-m²/s²) or foot-pounds
• F is the force applied to an object in newtons (N or kg-m/s²) or pounds (lbs)
• d is the distance the object moves in meters (m) or feet (ft)
• Fd is F times d

Note: W indicates work. Sometimes W is also listed as weight. We will use the small w for weight, but still, you should always make sure you read the definition below the equation to make sure you understand what the letters stand for.

If you would apply a force of 2 newtons to move an object 3 meters, the work done would be 6 joules.

If a force is applied on an object and there is no movement, then there is no work. If you push on a heavy object but are unable to move it, you are making an effort but you are not doing any work, according to the scientific definition of work.

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.

Examples

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. (See Potential Energy for more information.)

Carrying a heavy box

If you are holding a heavy box and carry it across the room, the work you are doing against inertia is the force you apply to move the box (F = ma) times the distance you carry it.

Note that many textbooks say that this is not work, because the force of gravity is perpendicular to your motion. Unfortunately, they are unclear about the type of work they are talking about. Moving the box across the room is work against the inertia of the box, while lifting the box up is work against the resistive force of gravity.

Work against a resistive force

A resistive force is a force that causes a moving object to slow down or tends to prevent a stationary object to move. The resistive force acts in a direction opposite to the one that you want to move the object. Just as going against inertia, the distance is only measured while the force is applied, since it is possible for an object to continue moving a short distance after the force is released, even though it is moving against a resistive force.

Work against gravity

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

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 = F_rd

where:

• W is the work done
• F_r is the resistive force of friction
• d is the distance you slid the object

(See Resistive Force of Friction for more information.)

If you pushed an object across a slippery 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.

Summary

Work is the result of a force moving an object a distance, measured while that force is being applied. The equation for work is W = Fd. Work can be to overcome inertia, as well as to work against a resistive force. Gravity can do work against inertia and you may do work against the force of gravity.

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Mini-quiz to check your understanding

1. If you do 10 joules of work to move an object 20 meters, what force do you apply?

2. What distance is measured to determine the work when throwing a ball?

3. How much work is done when a 2-pound brick is lifted 6 feet?

If you got all three correct, you are on your way to becoming a Champion in Physical Science. If you had problems, you had better look over the material again.

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Work is a Result of Force