General Question

Jasonbucy's avatar

A broom balances at it's center of gravity. If you cut the broom in half at the center of gravity and weigh each part of the broom, which end would weigh more.

Asked by Jasonbucy (12points) May 21st, 2009 from iPhone

Think about it… Im not sure if it’s the obvious choice..

Observing members: 0 Composing members: 0

20 Answers

PapaLeo's avatar

Is this a trick question?

Reminds me of “What weighs more, a pound of feathers or a pound of bricks?”

SeventhSense's avatar

No broom can exist in a vacuum.

critter1982's avatar

neither would weigh more.

cwilbur's avatar

The center of gravity is a point, and the cut needs to be a plane. There’s insufficient information in the question to answer it meaningfully.

PapaLeo's avatar

“Center of gravity” . . . “center of gravity” . . . I’m having difficulty with that term. Shouldn’t it be “center of balance”?

ben's avatar

The shorter half. (Torque would amplify the weight of the longer, lighter side).

PapaLeo's avatar

@ben Torque? Ah, he didn’t say it was a MOTORIZED broom!!!

Simone_De_Beauvoir's avatar

@ben yeah, I was like is it spinning?

jonketo's avatar

I cut my broom in half and now I can’t sweep my floors. My 8 year old son now sweepsthe floot with a short broom.

ragingloli's avatar

i’d say the shorter half.

noelasun's avatar

well, center of gravity has nothing to do with the mass. As such, I’d say after you cut it in half, whichever side felt heavier in your hand… That’d be my guess.

critter1982's avatar

ah, Ben is right. Long moments can significantly shift the COG. The shorter side will weigh less.

FireMadeFlesh's avatar

This question cannot be answered adequately from the information given. The centre of gravity will be closer to the head end than the ‘end’ end. Since the centre of gravity is not in the spatial centre, one end will have a greater leverage with its mass than the other, and therefore exert a greater force from the same unit mass.

What you will find though, is that the shorter end is heavier, as it requires a greater mass to exert the same force as the other end, since it lacks the advantage of leverage.

Apologies @ben, I just saw you said it first…...

eupatorium's avatar

I think they’d weigh the same. The fact that you cut it where it balances means that the sides exert equal force. I’m no engineer, but I feel like the issue of torque as mentioned by @ben and @FireMadeFlesh would apply if the objects in question were weights, attached to the end, and not the actual stick. Of course, I could be wrong.

Also, answering this question would be largely dependent on how you went about weighing the individual pieces, no? Because depending on what sort of scale you used, or how the longer piece was positioned, this would distort the force of weight. Wow. I sort of contradicted myself.
Good question. I’m confused.

astrocom's avatar

This is something that requires me to do conscious evaluation of my subconscious understanding of physics (Here comes the calculus). I’ll check back in a few days after confirming it for myself and possibly checking with a mechanics professor. (Mechanics as in the field within physics).

Shuttle128's avatar

Yay for physics brain teasers!

It’d be the end that weighs the most! Really it can’t be determined from the information given. You might assume that the longer end would weigh less since the moment created by a long handle would have to equal the moment of the shorter brush end, but it’s not necessarily less weight. It is entirely possible that the center of gravity is at the center of mass.

astrocom's avatar

Alright, It depends on various things, most of which you haven’t told us, several of which you probably don’t know. In all likelihood, the shorter end will be more massive, because distribution of mass around an object’s center of mass is weighted by distance from the center of mass (less mass counts for more, the farther out you get). Again, in general, if an object stretches out further in any one direction from it’s center of mass, or has more volume in one direction from it’s center of mass, the opposite direction will have more mass closer, or in less volume, to compensate (in order to keep the center of mass where it is). In an object of constant density, the center of mass will be the same as the geometric center, but only if the object is split in half along a plane of symmetry will both halves have the same mass. On top of that, if an object varies in density, there’s no guarantee that even that will be the case. If your broom had a lead weight in the stick, placed in the right location, and was then cut in two, through it’s center of mass in the way we’ll assume is obvious, both sides could have the same mass. For a short, simple answer that’ll do in most cases: see ben.
It should be noted that when considering things in physics, short, simple answers that’ll do most of the time, but we know don’t work all the time aren’t good enough answers.

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