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×PQ−→−=||F||||PQ−→−||cosθ
. Then find the work done pushing the lawn mower.
In the formula W = F * PQ→ = ||F|| * ||PQ→|| * cosθ:
- W represents the work done, which is the energy transferred to the object in order to push it a certain distance.
- F represents the force applied to the object, in this case 60 lbs.
- PQ→ represents the displacement vector, which is the distance the object is pushed in a particular direction.
- ||F|| represents the magnitude of the force, which is 60 lbs.
- ||PQ→|| represents the magnitude of the displacement vector, which is 100 ft.
- cosθ represents the angle between the force and the displacement vector, in this case 45°.
Now we can find the work done pushing the lawn mower:
W = ||F|| * ||PQ→|| * cosθ
W = 60 lbs * 100 ft * cos(45°)
W = 60 lbs * 100 ft * 0.7071
W = 4242.6 ft-lbs
Therefore, the work done pushing the lawn mower is 4242.6 ft-lbs.