A uniform, 237-N rod that is 1.96 m long carries a 225-N weight at its right end

Question

A uniform, 237-N rod that is 1.96 m long carries a 225-N weight at its right end and an unknown weight W toward the left end (see the figure (Figure 1)). When W is placed 50.1 cm from the left end of the rod, the system just balances horizontally when the fulcrum is located 71.0 cm from the right end. Find W. If W is now moved 29.8 cm to the right, how far must the fulcrum be moved to restore balance? If W is now moved 29.8 cm to the right, in what direction must the fulcrum be moved to restore balance? to the left to the right

Explanation / Answer

The length of the beam = 196 cm

The fulcrum is located at 71 cm from right end

The moment of weight at right end about fulcrum = 225*71 N cm

The moment of weight toward left = W*(196-50.1-71) N cm

The moment of weight of balance = 237*(196/2-71) N cm

Since the beam is balanced, we have,

225*71 = W*(196-50.1-71) + 237*(196/2-71)

W*(196-50.1-71) = 225*71 - 237*(196/2-71) = 9576

W = 127.85 N

Part B:

127.85*(196-50.1-71-29.8) = 225*(71-x) - 237*(196/2-71+x)

5766.035 = 225*71- 237*(196/2-71) - (225*71+237)x

x = 0.237 cm

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