Handle Scales Figured
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Figuring Physics: Broom Problem?
The broom balances at its center of gravity. If you saw the broom into two parts through the center of gravity you’ll have a “handle part” and a “broom part.” If you then weigh each part on a scale, you’ll find the part that weighs more will be the a) handle part b) broom part c) neither, for both will weigh the same
Unfortunately all the above answers are wrong, but it is a common mistake when dealing with center of gravity problems.
Obviously, the “handle part”, as you have called it, is longer than a “broom part”. The center of gravity of the handle part is in the middle of it, while the CG of the broom part is somewhere at the contact of the broom and the handle. The torques of both parts of the handles in a reference to the CG-axis of the whole broom are equal and opposite, otherwise this point wouldn’t make a CG. The moment of arm of the handle torque is longer because this part has got its CG placed more outside, if you compared it to the moment of arm of the broom part torque. Since the torques are equal, the weight force of the handle part must be lesser than the weight force of the broom part, therefore, the part that weighs more is the broom part (b).
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