# Work

Work, Energy and Power is the last section of second chapter of SPM form 4 physics. In this section, we are going to discuss work, including what is meant by work done and the unit of work done. We will also discuss the equation of work done, when the direction of force is NOT the same as the direction of motion and the also equation when the direction of the force is the same as the direction of motion. It is also important for us know how to find work done from the Force-Displacement graph. So, this is what are we going to discuss in this lesson.

In next lesson, we will discuss work done by gravity and work done against gravity. Both of them can be calculated by using the equation W = mgh.

Work done by a constant force is given by the product of the force and the distance moved in the direction of the force. In equation, we write this as W = Fscosθ, where W is work done, F is the force, s is displacement and θ is the angle between the direction of the force and the direction of motion.

For example, if a 20N force acts on a box and make the box move 10m. Let’s say the force is 60o from the direction of motion. The work done by the force is W = Fscosθ. F is 20N, displacement is 10m, θ is 60o. Therefore the work done is 100 Nm, or 100J. Nm or Joule is the unit of work. 1 Nm is equal to 1 J.

If the direction of the force is same as the direction of the motion, the angle θ become 0. cos 0o = 1. Therefore, the equation become W = Fs. In SPM, most of the cases that we discuss are cases where force and motion are in the same direction. Therefore, this is the equation that we are going to use most.

Sometime, you are asked to find work done from a Force-Distance graph. In Force-Distance graph, work done is equal to the area between the graph and the x-axis.

For example, the graph above shows a consistent force of 20N acts on an object and moves the object for 10m. So, what is the work done to move the object for 10m? Work done to move the object is equal to the area between the graph and the x-axis, which is 20 x 10 = 200J.

Let’s see another example. In this case, an increasing force is acting on an object to move the object for 10m. What is the work done that moves the object for 10m? Well, work done is equal to the area between the graph and the x-axis. The area is equal to ½ x 20 x 10, which is equal to 100J.

So, remember, in a Force-Distance graph, work done is equal to the area between the graph and the x-axis.