Hammer Ruler Balance

tanyh123

http://resources.scienceworld.ca/pdf...nce_Hammer.jpg

How do I explain this in terms of centre of mass?

And what's the definition of centre of mass in this context?

Doc Al

Where's the center of mass of the hammer?

The same as it is in any context. Think of it as the (weighted) average location of the mass.

tanyh123

The centre of mass of the hammer is near the hammer head, so the centre of mass of the whole mobile should be found there as well?

Does the centre of mass of the mobile have to be vertically aligned with the table and a part of the ruler which is resting on the table or does it have to be under the table only?


But the centre of gravity of a donut is found around the centre of the donut, which is actually empty space. How do I explain that then?

CWatters

The center of mass is below the pivot point therefore the system is inherently stable.

tanyh123

Can you explain to me why does positioning the centre of mass of the mobile below the pivot point, which I'm assuming is the edge of the table, makes the mobile stable and balanced?

Doc Al

Right.

The center of mass must be under the part of the ruler resting on the table.

Explain what? The center of mass does not have to be located where there is any mass. Think of it as a mathematical point that is useful for describing the behavior of a system, not as a part of a body.

tanyh123

Which is the pivot point, the part of the ruler resting on the table of the table itself?

CWatters

The center of mass is EXACTLY below the pivot point (eg like a stationary pendulum).

The question is where is the pivot point? In the example photo it can move. It can be anywhere between the edge of the table or the right hand end of the ruler. This actually helps increase stability....

If the hammer is disturbed by pushing/swinging it slightly to the left the pivot point will probably move to the right hand end of the ruler. This increases the restoring force on the hammer.

If the hammer is disturbed by pushing it slightly to the right the pivot point will probably move to the left eg the edge of the table. This also increases the restoring force on the hammer.

tanyh123

What do you mean by restoring force? And if the hammer is disturbed to an extent where the centre of mass is no longer under the pivot point, the mobile will collapse, won't it?

Doc Al

If you displace the hammer from its equilibrium position, its weight will create a torque that tends to bring it back to equilibrium. Imagine you had a ball on the end of a string, hanging down from your hand. If you move the ball aside, it will naturally tend to swing back. Same idea.
No. When released from that point, it will tend to return to its equilibrium position.

tanyh123

What is required for it to fall?

CWatters

If you add weight to the left hand side of the rule the center of mass will move to the left. Keep adding weight and the rule will take up an angle to the horizontal (down on the left). The pivot point will move to the edge of the table and eventually the rule might reach an angle steep enough for the rule to slip off the edge of the table. That's if the head of the hammer doesn't hit the underside of the table first.