a plank of uniform construction 5m in length and of mass 25kg is balanced on a s

Question

a plank of uniform construction 5m in length and of mass 25kg is balanced on a sawhorse stand which acts as a fulcrum. A bag of sand having a mass of 20kg is suspended from one end of the plank. On the other end of the plank, a concrete block, of mass 15kg is hung at the end.

a) Where would you palce another bag of sand, of mass 10kg, to balance this plank?(reference the position from the fulcrum or else the ends of the plank, indicating also to the left or right)

b) When the plank is balanced, where is the center of gravity of the system located?

c) when the plank is balanced, what is the size of the upward force the sawhorse must exert?

d) When the plank is balanced, what is the sum of all the torques in the system?

need details, so please show all work

Explanation / Answer

Part A)

Balance the torques

(20)(2.5) = (15)(2.5) + 10x

x = 1.25 m from the fulcrum on the side of the 15 kg concrete block

Part B)

When the plank is balanced the center of gravity is at the fulcrum

Part C)

The force from the fulcrum is (15 + 10 + 20 + 25)(9.8)

F = 686 N

Part D)

When balanced, the sum of the torques is ZERO. Thats the whole point of balancing.

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