A lawn roller is pushed across a lawn by a force of 128 N along the direction of the handle, which is 22.5° above the horizontal. If you develop 63.2 W of power for 90.0 s, what distance is the roller pushed?
Question
A lawn roller is pushed across a lawn by a force of 128 N along the direction of the handle, which is 22.5° above the horizontal. If you develop 63.2 W of power for 90.0 s, what distance is the roller pushed?
Solution
To solve this problem, we need to use the formula for power, which is work done per unit time.
Step 1: Convert the power to Joules Power (P) = Work done (W) / Time (t) We know the power (P) is 63.2 W and the time (t) is 90.0 s. We can rearrange the formula to solve for Work done (W): W = P * t W = 63.2 W * 90.0 s = 5688 Joules
Step 2: Calculate the work done Work done is also equal to the force (F) times the distance (d) times the cosine of the angle (θ) between the force and the direction of motion. W = F * d * cos(θ) We know the force (F) is 128 N and the angle (θ) is 22.5°. We can rearrange the formula to solve for distance (d): d = W / (F * cos(θ)) d = 5688 Joules / (128 N * cos(22.5°))
Step 3: Calculate the distance Plug in the values and calculate the distance. Make sure your calculator is set to degrees before calculating the cosine of 22.5°. The final answer will be in meters.
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