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A 35-kg trunk is dragged 10 m up a ramp inclined at an angle of 12 degrees to the horizontal by a force of 90 N applied at an angle of 20 de
Question
A 35-kg trunk is dragged 10 m up a ramp inclined at an angle of 12 degrees to the horizontal by a force of 90 N applied at an angle of 20 degrees to the ramp. At the top of the ramp, the trunk is dragged horizontally another 15 m by the same force. Find the total work done.
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Mathematics
3 years
2021-08-23T16:00:04+00:00
2021-08-23T16:00:04+00:00 1 Answers
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Answer:
The total work done is approximately 2,114.308 J
Step-by-step explanation:
The mass of the trunk = 35 kg
The height to which the trunk is dragged, d₁ = 10 m
The inclination of the plane on which the trunk is dragged = 12°
The applied force F = 90 N
The angle of inclination of the force to the ramp = 20°
The distance the trunk is dragged horizontally at the top of the ramp, d₂ = 15 m
Work = Force × Distance
The work done along the inclined plane, W₁ = 90 N × cos(20°) × 10 m ≈ 845.723 J
The work done along the horizontal, W₂ = 90 N × cos(20°) × 15 m ≈ 1,268.585 J
The total work done, W = W₁ + W₂
∴ W = 845.723 J + 1,268.585 J = 2,114.308 J