A neighbor pushes a lawn mower on a lawn that is level with a force of 230 Newtons. If 45% of this force is directed downward, how much work is done by the neighbor in pushing the mower 8 meters?
The force directed horizontally is not the remaining 55%, it is
sqrt[1 - (0.45)^2] = 89.3%,
which amounts to 205.4 Newtons.
Multiply that by 8 meters for the work done.
Note that Fx^2 + Fy^2 = Ftotal^2
To find the work done by the neighbor, we can use the formula:
Work = Force × Distance × Cosine(θ)
In this case, the force applied by the neighbor is 230 Newtons and the distance is 8 meters. However, we need to find the component of the force directed downward, so we need to calculate that first.
Given that 45% of the force is directed downward, we can find the downward force component as follows:
Downward force = 45% × Force
Downward force = 0.45 × 230 Newtons
Downward force = 103.5 Newtons
Now, we can calculate the work done:
Work = Downward force × Distance × Cosine(θ)
Since the lawn is level, the angle θ between the force and displacement is 0 degrees (or 180 degrees). The cosine of 0 degrees is 1.
Work = 103.5 Newtons × 8 meters × 1
Work = 828 Newton-meters
Therefore, the neighbor does 828 Newton-meters of work in pushing the mower 8 meters.