# Work is a Result of Force

by Ron Kurtus

When you apply enough force on an object to *overcome some resistance*, such that you move that object, you are doing work on that object. In other words, work equals the applied force times the distance moved.

If you are moving an object that is initially stationary, you are accelerating the object, and the resistance to motion is the inertia of the object. Thus, you are doing work is against inertia. Since objects tend to continue moving after a force is applied, the distance is only measured while that force is being applied.

Typically, you consider doing work against a resistive force, such as friction or gravity. The force applied must be greater than the 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. Useful tool: Units Conversion

## Work is force times distance

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

W = Fd

where:

**W**is the work in joules (J or kg-m²/s²) or foot-pounds**F**is the force required to move the 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:Windicates work. SometimesWis also listed as weight. You should always make sure you read the definition below the equation to make sure you understand what the letters stand for.

### When resistance too great

If a force is applied on an object and there is no movement because the resistance is too great, 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.

Newton's first law of motion is often called the *Law of Inertia*. It states that:

Matter remains in its state of motion and direction unless acted upon by a force.(See

Motion and the Law of Inertiafor more information.)

### Force required

The force requierd to move an object against inertia is:

F = ma

where

**m**is the mass of the object**a**is the resulting acceleration

Thus, the work against inertia is:

F = mad(Don't get "mad" about this!)

The work done on a freely moving object only occurs over the distance* while you are applying the force*. Once you stop applying the force, the object moves freely and no more work is being done.

### Throwing a ball

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.

### 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.

Notethat some textbooks say that this isnotwork, 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 inertiaof the box, while lifting the box up iswork 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 also 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.

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**.

Notethat the equationW = mghis the same as for the potential energy of an object at some given height:PE = mgh. (See Potential Energy for more information.)

### 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_{r}d

where:

**W**is the work done**F**is the resistive force of friction_{r}**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.

Work hard to achieve your goals

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## Work is a Result of Force