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

Answer:

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

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 $\dot s = 2.3\,\frac{m}{s}$, then the power supplied by the force is:

$\dot W = F\cdot \dot s$

$\dot W = (60\,N)\cdot \left(2.3\,\frac{m}{s} \right)$

$\dot W = 138\,W$

The power supplied by the force is 138 watts.