Question

A little league player balances a bat 65.0 cm from one end. She then hangs her 0.540-kg batting helmet on that end of the bat and the balance point moves 24.5 cm toward the helmet. Determine the mass of the bat.

Answer 1

Take the bat's center of mass initially at xb = 0.650 m from the end. The helmet (mh = 0.540 kg) is hung at xh = 0.00 m, and the combined center moves to x = 0.650 - 0.245 = 0.405 m.

The combined center-of-mass condition:
x = (mb xb + mh xh)/(mb + mh) = mb·0.650/(mb + 0.540).

So
0.405(mb + 0.540) = 0.650 mb
=> (0.650 − 0.405) mb = 0.405·0.540
=> 0.245 mb = 0.2187
=> mb = 0.2187 / 0.245 ≈ 0.893 kg.

Mass of the bat ≈ 0.893 kg (3 significant figures).