A person carries a plank of wood 2.00 m long with one hand pushing down on it at one end with a force f1 and the other hand holding it up at. 500 m from the end of the plank with force f2. if the plank has a mass of 20.0 kg and its center of gravity is at the middle of the plank, what are the magnitudes of the forces f1 and f2?

Question

Physics

Marcel

16 May, 15:22

A person carries a plank of wood 2.00 m long with one hand pushing down on it at one end with a force f1 and the other hand holding it up at. 500 m from the end of the plank with force f2. if the plank has a mass of 20.0 kg and its center of gravity is at the middle of the plank, what are the magnitudes of the forces f1 and f2?

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Answers (1)

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Case Whitney · Answer 1

F₁ = 4,120.2 N

F₂ = 3,924N

Explanation:

1) Balance of angular momentum around the end where F₁ is applied.

F₂ * 0.5m - F₁ * 0 = mass * g * 1m

⇒ F2 * 0.5 m = 20 kg * 9.81 m/s² * 1 m = 1,962 N*m

F₂ = 196.2 Nm / 0.5m = 3,924 N

2) Balance of forces

F₁ - F₂ = mg

F₁ = F₂ + mg = 3,924N + 20kg (9.81 m/s²) = 4,120.2 N