Work – the product of force and the distance moved in the direction of the force.
We can define work (W) with the following equation:
Where F is the Force and d is the distance moved in the direction of the force.
The distance in the direction of the force could also be called the displacement (a vector quantity). As work is the product of two vector quantities (forces are also vector quantities) work is a scalar quantity (it only has magnitude, not direction).
Let’s look at an example:
If the box above is pulled 10m in the direction of the force, we can calculate the work done as follows:
Work done is a measure of energy transfer. If there is a force in the direction opposite to the direction of movement, such as friction, negative work is done. Negative work on an object means that the object is losing energy. Whereas positive work means the object is gaining energy.
From this we know that if an object is moving at constant velocity, against resistive forces, it must be gaining energy at the same rate as it is losing it. Otherwise the object would be speeding up or slowing down.
The Joule
The SI unit of work is the Joule as energy is required to do work. The Joule can be defined as:
Joule – the work done by a force of one Newton on an object to move it through a distance of one metre.
Therefore, the work done in the example above can be given as W = 75J
Forces at an Angle
Quite often the force acting on an object isn’t parallel to the direction of movement; it can be at an angle like the object below.
The box is being dragged along the floor, however, the force doing this is at an angle to its direction of movement.
Therefore, to calculate the work done on the box we need to amend the previous equation:
Where theta is the angle between the force and the direction of travel.
Therefore, if we know that the box above is moved 12m and the force is 15N at 25 degrees to the horizontal we can calculate the work done as follows:
IMPORTANT NOTE – If the force and direction of movement are perpendicular (at right angles) to each other NO work will be done.
Worked Examples
Example 1
An object attached to a string is pulled along 15.7m with the string at 17° to the horizontal. If the tension in the string is 9N calculate the work done.
Example 2
A 6kg ball is pushed up a ramp that is at 16° to the horizontal. Calculate the work done in pushing the ball 5m up the ramp and calculate the force required to push the ball. Assume that g = 9.81ms-2.
Example 3
Calculate the work done by both forces on the object below if it is moved 50m and describe the motion of the object. Assume that right is the positive direction.
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