Question

Using a horizontal force of 60 N, a wagon is pushed horizontally across the floor a distance of 12 meters at a constant speed of 2.3 m/s

a) What is the work done by the force?
b) What is the power supplied by the force?

Answer 1

a) The work done by the force is 720 joules, b) The power supplied by the force is 138 watts.

Step-by-step explanation:

a) Since force is uniform and parallel to the direction of motion, the work (
`W`), in joules, done by the force (
`F`), in newtons, is defined by this formula:

`W = F\cdot s` (1)

Where
`s` is the travelled distance, in meters.

If we know that
`F = 60\,N` and
`s = 12\,m`, then the work done by the force is:

`W = F\cdot s`

`W = (60\,N)\cdot (12\,m)`

`W = 720\,J`

The work done by the force is 720 joules.

b) And an expression for the power supplied by the force (
`\dot W`), in watts, is concieved by differentiating (1) in time:

`\dot W = F\cdot \dot s`

Where
`\dot s` is the speed of the wagon, in meters per second.

If we know that
`F = 60\,N` and
`\dot s = 2.3\,(m)/(s)`, then the power supplied by the force is:

`\dot W = F\cdot \dot s`

`\dot W = (60\,N)\cdot \left(2.3\,(m)/(s) \right)`

`\dot W = 138\,W`

The power supplied by the force is 138 watts.