You pick up a board of length 3.40 m and mass 17.00 kg. To do this, you exert a

Question

You pick up a board of length 3.40 m and mass 17.00 kg. To do this, you exert a force upward with your left hand a distance LL=0.986 m from the left end of the board and you need to exert a force with your right hand a distance LR=0.414 m from the left end of the board. Assume the board to be in static equilibrium and that the board is symmetrical with the mass evenly distributed.
What force does the right hand need to exert to keep the board in static equilibrium? (you need to get both the magnitude and the direction)

Explanation / Answer

Fl be the force exerted by the left hand and Fr be the force exerted by the right hand

Fl , weight are in vertical direction and there is no horizontal force hence, Fr must also be in vertical plane or along y axis.

Assume Fl and Fr are upwards

=> Fl+Fr = mg = 17*9.81 = 166.77 =. Fl+Fr = 166.77-------------(1)

The plate is in statical equilibrium => Net moment is 0

Writing moment equation about the center of mass and moment along clockwise direction is taken positive

=> Fl*(1.6-0.986)+Fr(1.6-0.414) = 0

=>0.614Fl+1.186Fr = 0-------------(2)

Sloving Solving (1) and (2) , we get

Fl = 345.78N and Fr = -179.01N

=>Force exerted by right hand is 179.01N and is downward

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