Solving Homework: Understanding Equations

[goonking]

Homework Statement

Homework Equations

The Attempt at a Solution

I chose the answer A, but it's not correct, can anyone explain why?

 

[robphy]

Is there a better answer?

 

[goonking]

Is there a better answer?

yes, B

but why?

If I hold a chain that's 4 meters long, from one end. I can say the center of mass of the chain is 2 meters below my hand.

I shouldn't say the center of mass of the chain is right below my hand, can I?

 

[robphy]

This object is subject to two forces...
gravitation (which can thought of as applied all at the center of mass) and
the normal force applied by the fulcrum (applied at the point of contact).
When balanced, the sum of the forces on the object is zero and the sum of the torques* on the object is zero [*torques taken about any point].
When balanced, where must the center of mass be in relation to the point of contact?

Among the choices in the posed question, the "end" in A could refer to the extreme position of the bat.

 

[jbriggs444]

I shouldn't say the center of mass of the chain is right below my hand, can I?

"directly above" in this problem is intended to mean "straight above" i.e. above and not offset a little to one side or the other.

 

[goonking]

so it wouldn't count if I held the bat? It has to be ONLY balanced?

 

[robphy]

The question says "balance[d]... on top of your finger" (implying a single point of contact).

 

[goonking]

The question says "balance[d]... on top of your finger" (implying a single point of contact).

ok, just making sure. makes sense since you can't hold up a chain with using just 1 point of contact.

 

[jbriggs444]

ok, just making sure. makes sense since you can't hold up a chain with using just 1 point of contact.

Sure you can. But how is that relevant?

 

[goonking]

Sure you can. But how is that relevant?

yes, actually you can, if you put your finger under one of the 'holes' , then would I say the center of mass is still directly above my finger?

 

[goonking]

lets say I balanced a ice cream cone on the floor:

would the center of mass still be at the point where the floor and cone contact?

 

[jbriggs444]

The center of mass of a chain hanging at rest below your finger is directly below your finger.

 

[jbriggs444]

lets say I balanced a ice cream cone on the floor:
would the center of mass still be at the point where the floor and cone contact?

The center of mass would be directly above the point at which the floor and cone contact. Refer to post #5 for a definition of "directly above".

 

[goonking]

The center of mass would be directly above the point at which the floor and cone contact. Refer to post #5 for a definition of "directly above".

i understand now, ty

 

[robphy]

Just to be clear... (because I don't think that this point was explicitly made)...
The center of mass of an object is determined by the positions and masses of the all of the bits that compose the object.
If the object is rigid, that location with respect to the object doesn't change... no matter where you place the object, how you orient the object, or apply forces to the object.

When an object is balanced against gravity by a single contact force,
the point of contact and the center of mass must be on the same vertical line.
(In your balanced cone example, the center of mass is located near the middle of the cone-and-ice-cream... [vertically] above the point of contact on the floor
... but not at the point of contact on the floor. Similarly, for the solid bat.)

 

[goonking]

so there can be an even better answer : the center of mass of the bat is directly above my finger, and at the heavier, thicker end of the bat, correct?

 

[jbriggs444]

so there can be an even better answer : the center of mass of the bat is directly above my finger, and at the heavier, thicker end of the bat, correct?

No.

The center of mass will not neccessarily be at the heavier, thicker end of the bat. But it will not be at the midpoint of the bat either. It will be closer to the heavy end than to the light end. Its position is (in a particular sense), the "average" position of the mass in the bat.

 

[robphy]

Model the bat as two objects with unequal masses:
http://astro.unl.edu/classaction/animations/binaryvariablestars/centerofmass.html