Force times distance
Work done by a constant force.
Wheat bags on a shelf
A shopkeeper lifts a bag of wheat from the floor to a low shelf. Then she lifts the same bag to a higher shelf.
How do you think the work for the higher shelf compares with the work for the low shelf?
What this lesson covers
The idea
Work done on an object by a constant force = force × displacement in the direction of the force, W = F × s; the force doing the work and the object it acts on must be specified.
Wheat bags on a shelf
A shopkeeper lifts a bag of wheat from the floor to a low shelf. Then she lifts the same bag to a higher shelf.
How do you think the work for the higher shelf compares with the work for the low shelf?
- It is more
- It is the same
- It is less
Push the crate
Change the force and the displacement, and watch the work.
Both matter
When the force doubled, the work doubled. When the distance doubled, the work doubled too. So work depends on the force and on the displacement, and we get it by multiplying them. The book also says to name who or what applies the force and which object it acts on.
The work done on an object by a constant force is force × displacement in the direction of the force: W = F × s. We must specify the force (or agency) doing the work and the object on which the work is done.
Notes
Work by a constant force = force × displacement in the direction of the force: W = F × s. Name the force and the object.
Check yourself
A constant force of 5 N moves a box 3 m in the direction of the force. What is the work done, in N m?
Answer: 15 N m
W = F × s = 5 N × 3 m = 15 N m.
You lift one bag of wheat 1 m. Then you lift three such bags together through 1 m. Compared with one bag, the work for three bags is…
A constant force F moves an object through a displacement s in the direction of the force. The work done is…
When we describe the work done, what must we specify?
- the same, since the distance is the same. Three bags together need a force 3 times larger, so over the same distance the work is 3 times as much.
- 3 times as much — correct. Yes!
- one third as much. A larger force over the same distance means more work, not less.
- F + s. Adding a force to a distance makes no sense; work is the product of the force and the displacement.
- F ÷ s. Work is found by multiplying the force by the displacement, not by dividing.
- F × s — correct. Yes!
- The force (or agency) doing the work and the object on which it acts — correct. Yes!
- The time taken to do the work. Time is needed for power, later in this chapter, but not to say which force does the work on which object.
- The colour of the object. The colour of an object has no part in the definition of work. The force and the object matter.