Question

A meter stick has a mass of 0.18 kg and balances at its center. When a small chain is suspended from one end, the balance point moves 32.0 cm toward the end with the chain. Determine the mass of the chain.

Answer 1

Take the left end as x = 0. The stick’s center is at x = 0.50 m. With the chain at the right end (x = 1.00 m) the new center is at x = 0.50 + 0.32 = 0.82 m.

Use the center-of-mass formula:
x_cm = (M_stick x_stick + m_chain x_chain)/(M_stick + m_chain).

So (0.09 + m)/(0.18 + m) = 0.82 (since 0.18·0.50 = 0.09).

Solve: 0.09 + m = 0.82(0.18 + m) = 0.1476 + 0.82m
=> 0.18m = 0.0576 => m = 0.0576/0.18 = 0.320 kg.

Mass of the chain = 0.320 kg.