Question

A lawn mower is pushed a distance of 100 ft along a horizontal path by a constant force of 60 lbs. The handle of the lawn mower is held at a downward angle of 45° toward the horizontal. Explain what each value listed in this situation represents in relation to the formula W = F x line segment PQ = ||F|| || line segment PQ|| cos theta. Then find the work done pushing the lawn mower.

Answer 1

[AI-generated answer — Bot GPT 3.5]

In the formula W = F x line segment PQ = ||F|| || line segment PQ|| cos theta, the values represent the following:

- W represents the work done, which is the amount of energy transferred to the lawn mower by the force applied.
- F represents the force applied to push the lawn mower, which is 60 lbs in this case.
- line segment PQ represents the displacement of the mower, which is the distance pushed along the horizontal path, 100 ft.
- ||F|| represents the magnitude of the force, which is 60 lbs.
- || line segment PQ|| represents the magnitude of the displacement, which is 100 ft.
- cos theta represents the angle between the force applied and the direction of the displacement which is cos(45°) = sqrt(2)/2.

Now, substitute the values into the formula and calculate the work done:

W = 60 lbs x 100 ft x sqrt(2)/2
W = 3000 lbs*ft*sqrt(2)/2
W ≈ 2121.32 ft*lbs

Therefore, the work done pushing the lawn mower is approximately 2121.32 ft*lbs.