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13 March, 18:27

A person carries a plank of wood 2 m long with one hand pushing down on it at one end with a force F1 and the other hand holding it up at 50 cm from the end of the plank with force F2. If the plank has a mass of 20 kg and its center of gravity is at the middle of the plank, what are the forces F1 and F2?

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  1. 13 March, 18:39
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    F1 = 196 N

    F2 = 392 N

    Explanation:

    Given:

    length of the plank = 2 m

    mass of the plank = 20 kg

    Weight of the plank = 20 x 9.8 = 196 N

    Torque due to the weight of the plank with respect to the pivoted end (i. e the end held by the hand) Counter clockwise torque = 196 x cog of wood

    = 196 x 1 = 196 Nm

    Clockwise torque = F2 x 0.5

    for the balanced case

    F2 x 0.5 = 196

    F2 = 196 / 0.5

    F2 = 392 N

    now,

    the net force

    Net downward force = Net upward force

    F1 + weight of plank = F2

    F1 + 196 = 392N

    F1 = 392 - 196

    F1 = 196 N
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