4.37: Calculating Work
Clarissa is cutting the grass in her grandmother’s yard using an old-fashioned push mower. The mower has no motor, so Clarissa is doing all the work. How much work does Clarissa do pushing the mower around the yard? The amount of work depends on how much force she uses and how far she pushes the mower.
Work, Force, and Distance
Work is the use of force to move an object. It is directly related to both the force applied to the object and the distance the object moves. Work can be calculated with this equation:
Work = Force x Distance.
How Much Work?
The equation for work can be used to calculate work if force and distance are known. To use the equation, force is expressed in Newtons (N), and distance is expressed in meters (m). For example, assume that Clarissa uses 100 Newtons of force to push the mower and that she pushes it for a total of 200 meters as she cuts the grass in her grandmother’s yard. Then, the amount of work Clarissa does is:
Work = 100 N x 200 m = 20,000 N ∙ m
Notice that the unit for work in the answer is the Newton ∙ meter (N ∙ m). This is the SI unit for work, also called the joule (J). One joule equals the amount of work that is done when 1 N of force moves an object over a distance of 1 m.
Q: After Clarissa mows her grandmother’s lawn, she volunteers to mow a neighbor’s lawn as well. If she pushes the mower with the same force as before and moves it over a total of 234 meters, how much work does she do mowing the neighbor’s lawn?
A: The work Clarissa does can be calculated as:
Work = 100 N x 234 m = 23,400 N ∙ m, or 23,400 J
Calculating Force or Distance When Work Is Known
The work equation given above can be rearranged to find force or distance if the other variables are known:
\begin{align*}\mathrm{Force=\frac{Work}{Distance}}\end{align*}
\begin{align*}\mathrm{Distance=\frac{Work}{Force}}\end{align*}
After Clarissa finishes mowing both lawns, she pushes the lawn mower down the sidewalk to her own house. If she pushes the mower over a distance of 30 meters and does 2700 joules of work, how much force does she use? Substitute the known values into the equation for force:
\begin{align*}\mathrm{Force=\frac{2700J}{30m}=90N}\end{align*}
Q: When Clarissa gets back to her house, she hangs the 200-Newton lawn mower on some hooks in the garage (See the Figure below. To lift the mower, she does 400 joules of work. How far does she lift the mower to hang it?
A: Substitute the known values into the equation for distance:
Summary
- Work can be calculated with the equation: Work = Force x Distance.
- The SI unit for work is the joule (J), or Newton ∙ meter (N ∙ m). One joule equals the amount of work that is done when 1 N of force moves an object over a distance of 1 m.
- The equation for work can be rearranged to find force or distance if the other variables are known.
Vocabulary
- joule (J): SI unit for work, equal to the amount of work that is done when 1 Newton of force moves an object over a distance of 1 meter.
- work: Use of force to move an object; calculated as force multiplied by distance.
Practice
At the following URL, review how to calculate work from force and distance. Then solve the practice problems (except for problem 8) at the bottom of the Web page.
http://www2.franciscan.edu/academic/mathsci/mathscienceintegation/MathScienceIntegation-1011.htm
Review
- Write the equation for calculating work when force and distance are known.
- What is the SI unit for work? What does it represent?
- Clarissa helps her mom put the 200-Newton lawn mower in the back of her mom’s truck. They lift the mower up from the ground to the truck bed, which is 1.1 meters above the ground. How much work do Clarissa and her mom do?
- Clarissa climbs into the back of the truck to tie the lawn mower in place. If she does 528 joules of work raising herself to the truck bed, how much does she weigh?