Work is done when a force is applied over a distance
W = Fd
Where:
W = work (Joules)
F = force (Newtons)
d = distance (meters)
The units of work (Joules) are the same as the metric units for energy. Recall that Joules (J) are the same as Newton Meters (Nm). In the case of work, we are multiplying Newtons by meters to get Newton meters.
If a force is applied to an object, but the object doesn’t move, no work is done.
Similarly, if an object is moving and no force is applied to it, no work is being done. This can happen if an object in motion is staying in motion at a constant velocity.
Example 1:
A person pulls a box across a floor against a friction force of 40 Newtons, and the box moves 2.0 meters.
W = Fd = (40 N)(2.0 m) = 80 J
The person has done 80 Joules of work.
Example 2:
A person lifts a 6.0 kg weight from the floor up to a shelf that is 1.5 m above the floor.
In this case, the force is the gravitational force of the 6.0 kg object.
Fg = mg = (6.0 kg)(10 N/kg) = 60 N
W = Fd = (60 N)(1.5 m) = 90 J
Power
Power is the rate at which work is done. In other words, power is how fast work is being done.
Where:
P = power (Watts, W)
W = work (Newtons, N)
Δt = time (seconds, s)
The metric unit for power is the Watt (W).
If the person from above lifted the 6.0 kg weight to the 1.5 m shelf in 0.5 seconds, they would be doing 90 J of work in 0.5 seconds.
P = (90 J) / (0.5 s) = 180 Watts
If instead it took 3.0 seconds to lift the weight onto the shelf:
P = (90 J) / (3.0 s) = 30 Watts
Less power is required to do that task in a longer amount of time, even though the amount of work done is the same in each case.
Tip:
Avoid getting mixed up between work (W) and Watts (W).