A horse pulls a boat along a canal by a rope at an angle of 60° to the bank. He produces a tension of 1500N in the string. The boat moves through a distance of 30m. Find the amount of work done by horse?
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To find the amount of work done by the horse, we need to use the formula:
Work = Force × Distance × cos(θ)
Where:
- Force is the tension in the rope, which is 1500N.
- Distance is the distance the boat moves, which is 30m.
- θ is the angle between the force and the direction of motion, which is 60°.
First, we need to calculate cos(θ). To do that, we use the formula:
cos(θ) = adjacent side / hypotenuse
Since the angle is 60° and the adjacent side is the force (1500N), we have:
cos(60°) = 1500N / hypotenuse
Rearranging the equation, we find:
hypotenuse = 1500N / cos(60°)
Next, let's calculate the hypotenuse:
hypotenuse = 1500N / cos(60°)
≈ 1500N / 0.5
= 3000N
Now we have the force and the distance, so we can find the work done:
Work = Force × Distance × cos(θ)
= 1500N × 30m × cos(60°)
= 1500N × 30m × 0.5
= 22500Nm
Therefore, the amount of work done by the horse is 22500Nm.