Worked examples on work
Three problems, and the third is the one worth studying: when a mass is given rather than a weight, there is a step to do before the formula can be used at all.
Example 1 — a force along a surface
The problem
A force of 7.5 N moves an object 8 m in the direction of that force. How much work is done?
work done = force × displacement in the direction of the force
= 7.5 N × 8 m
= 60 J
Example 2 — lifting a known weight
The problem
An object weighs 40 N. How much work is done in raising it through a vertical height of 2 m?
To lift the object, the upward force applied must equal its weight, so the force = 40 N
displacement in the direction of the force = 2 m
work done = force × displacement
= 40 N × 2 m
= 80 J
Example 3 — lifting a known mass
The problem
An object has a mass of 5 kg. Find the work done in raising it 3 m.
mass of the object = 5 kg
weight of the object = m g
= 5 kg × 10 m s-2
= 50 N
work done = force × displacement
= 50 N × 3 m
= 150 J
A mass in kilograms is not a force
You cannot put 5 kg into the work formula. Multiply the mass by g = 10 m s-2 first to get the weight in newtons, and use that. Missing this step is the single most common mistake in the whole chapter.