Work Done Against a Particular Force

In some circumstances we are more concerned about the work that is needed to overcome an opposing force. Consider, for example, an object that is pulled at constant speed from A to B, a distance s along a rough surface.

 

 

 

 

 

 

 

 

 

 

 

 

A frictional force of magnitude F acts on the object, opposing the motion.

Because there is no acceleration, the force causing the displacement is equal and opposite to the frictional force, i.e. it is of magnitude F and therefore the amount of work it does is given by Fs.

This work is done to overcome friction and is called the work done against friction. So we see that

the work done against a force is given by

the magnitude of that force x the distance moved in the opposite direction.

Now consider a body of mass m, raised vertically through a height h. The weight, mg, acts vertically downward and has to be overcome by an upward force in order to raise the body.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The force needed to raise the body vertically at constant speed is mg upwards. The work done by this force is mg x h. The amount of work is needed to overcome the opposing force of gravity, i.e. the work done against is mgh.

Again we see that the work done against gravity is given by

            The magnitude of the gravitational force (mg downwards)

                        x the distance moved in that opposite direction (h upwards)

It is sometimes convenient to regard work done against a force as being negative work done by that force. In the situation above, for example, the work done by gravity is –mgh.

 

Work Done by a Moving Vehicle

A variety of forces can act on a moving vehicle, including friction, air resistance, the weight of the vehicle, reaction with the ground etc., but most important is the driving force.

 

Examples 7a

Whenever a force is represented on a diagram by a letter, e.g. P, it is understood that the force is P newtons.

 

A body resting in smooth contact with a horizontal plane, moves 2.6 m along the plane under the action of a force of 29 N. Find the work done by the force if it is applied

(a)   horizontally

(b)  at 60^o to the plane