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.
In this situation, the values represent the following:
- W represents the work done in pushing the lawn mower.
- F represents the constant force of 60 lbs.
- line segment PQ represents the distance the lawn mower is pushed, which is 100 ft.
- cos theta represents the cosine of the angle between the force vector and the direction of movement, which in this case is 45 degrees.
To find the work done pushing the lawn mower, we can use the formula W = F x line segment PQ x cos theta:
W = 60 lbs x 100 ft x cos(45°)
W = 60 lbs x 100 ft x 0.707
W = 4242 lb-ft
Therefore, the work done pushing the lawn mower is 4242 lb-ft.