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A person of mass 70 kg stands 0.5 m from one end of a 2 m long uniform plank (of negligible mass) that is being held in equilibrium by two vertical ropes attached to the ends of the plank. What is the
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25 votes
A person of mass 70 kg stands 0.5 m from one end of a 2 m long uniform plank (of negligible mass) that is

being held in equilibrium by two vertical ropes attached to the ends of the plank. What is the tension in the
rope closer to the person?
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User Matisetorm
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3.2k points

1 Answer

11 votes
11 votes

Hi there!

We can begin by using a summation of torques, with the fulcrum being at the rope farthest from the person (the other end).

Thus:

F1 = weight of person

R1 = distance of person to fulcrum (farther end)

F2 = Tension of rope closest to person

R2 = distance of rope to fulcrum

∑τ = 0 = R2F2 - R1F1

R2F2 = R1F1

Plug in values:

2F2 = 1.5(700N)

2F2 = 1050 N

F2 = 525 N = Tension of closest rope

User Mirkokiefer
by
3.2k points
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