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Wayne exerts a force of 98.5 N to pull a 421 N sled along a snowy path using a rope that makes a 30° angle with the ground. The sled moves 37.9 m in 2.1 s. What is Wayne's power?

Answer :

Final answer:

To find Wayne's power, multiply the force he applies by the distance the sled moves and the cosine of the angle of the rope with the horizontal, and then divide by the time taken.

Explanation:

To calculate Wayne's power when pulling the sled, we can use the formula:

Power = Work / Time

First, we need to determine the work done by Wayne pulling the sled. Work is defined as the force exerted in the direction of motion times the distance moved, which can be expressed as:

Work = Force × Distance × cos(θ)

Where θ is the angle between the force and the direction of motion. Since Wayne is pulling the sled at a 30° angle, we use the cosine of 30°:

Work = 98.5 N × 37.9 m × cos(30°)

To find power, we then divide this work by the time it took to do the work:

Power = (98.5 N × 37.9 m × cos(30°)) / 2.1 s

After performing these calculations, we will get Wayne's power output in watts, which is the SI unit for power. Remember, resolving the vertical component of the force is necessary as only the horizontal component does work in moving the sled forward.

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