If you balance a broom horizontally on one finger, the center of gravity will be above your finger?

Question

which is closer to the bristles end than the handle end. If you saw the broom in 2 pieces at that point & weigh the 2 parts on the scale, you'll find that the heavier part is the:
a) both are the same
b) handle part
c) bristles part

I think the answer is C) the bristles part. Am I right?

Answer 1

Yes, you are right. Think see-saws and kids of different weights.

Consider a stick which weighs nothing, but has a weight W at each end. It balances half way between the ends. If you cut at the balance point, each piece will have weight W.

Now suppose one end has weight W but the other has twice that or 2W. Now the balance point is closer to the heavier end. (1/3 of the length from the heavier end, 2/3 from the lighter end). Cut the stick at that point and one piece will weigh W while the other will weigh 2W.

In the case of the broom, you say the balance point is closer to the bristle end. That means the bristle end is heavier

Answer 2

Consider that in the balance enters the force momentum (the product between distance and force). So you just have to see which part is shorter: that part will be heavier (the momenta must be equal, so if the distance is bigger then the weight is shorter). i suppose that the heavier part is that one made by only handle. So i'd say b) naswer.

Answer 3

You will find they are the same weight.

What was that phrase... taking moments about the pivot point... was it?

You measure the distance from the pivot to one end and weigh it and the pivot to the other end and weigh it.

Since they balance, the moments (and the weights) must be the same.

Answer 4

If it balances, then both sides weigh the same! If one side weighed more it would have tipped that way!

Answer 5

Both are the same, or it wouldn't have balanced.