You are on a pirate ship and being forced to walk the plank. You are standing at

Question

You are on a pirate ship and being forced to walk the plank. You are standing at the point marked C. The plank is nailed onto the deck at point A, and rests on the support 0.75 maway from A. The center of mass of the uniform plank is located at point B. Your mass is 68kgand the mass of the plank is 45 kg.

What is the minimum downward force the nails must exert on the plank to hold it in place?

Express your answer to two significant figures and include the appropriate units.

If you could show the formulas, and how you did it that would be helpful - thank you!

You are on a pirate ship and being forced to walk the plank. You are standing at the point marked C. The plank is nailed onto the deck at point A, and rests on the support 0.75 m away from A. The center of mass of the uniform plank is located at point B. Your mass is 68kg and the mass of the plank is 45 k

Explanation / Answer

Let the force through nails be F and force through pivot be F2 ..
so for equillibrium of all the forces along vertical direction

F + F2 = ( 68 + 45 ) * 9.8 = 1107.4 N

taking moment of all the forces about A ..

0.75 * F2 = (1.5*45*9.8) + ( 3 * 68*9.8)

so.. F2 = 3547.6 N


so force through nails = 1107.4 - 3547.6= -2440.2 N

so the nails must apply 2440.2 N in downward direction on plank

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