A lawn roller is pushed across a lawn by a force of 125 N along the direction of the handle, which is 22.5° above the horizontal. If 63.5 W of power is developed for 90.0 s, what distance is the roller pushed?
152.4 m
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To find the distance the lawn roller is pushed, we can use the formula:
Work = Force * Distance
The work done can also be calculated using power and time:
Work = Power * Time
Since the power is given as 63.5 W and the time is given as 90.0 s, we can calculate the work done:
Work = 63.5 W * 90.0 s = 5715 J
Now, we can express the force applied along the handle in the horizontal and vertical directions:
Horizontal Force = Force * cos(angle)
Vertical Force = Force * sin(angle)
where the angle is 22.5°.
Given that the applied force is 125 N, we can calculate the horizontal and vertical components:
Horizontal Force = 125 N * cos(22.5°) ≈ 115.14 N
Vertical Force = 125 N * sin(22.5°) ≈ 52.82 N
Since the work done is equal to the force applied along the direction of motion multiplied by the distance:
Work = Horizontal Force * Distance
We can rearrange the formula to solve for the distance:
Distance = Work / Horizontal Force
Distance = 5715 J / 115.14 N ≈ 49.65 m
Therefore, the roller is pushed a distance of approximately 49.65 m.