Chap 10 Notes Center of Gravity
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Topic: Chap 10
Conceptual Physics Chapter 10 Center of Gravity
10.1 Center of Gravity
The Center of Gravity of an object is the point located at the object’s average position of weight.
See fig 10.2
When thrown, an object’s center of gravity will follow a parabolic path even though the object itself may rotate wildly:
See fig 10.1
See fig 10.4
Even the internal forces during an explosion do not alter the parabolic path of the center of gravity of the fragments:
See fig 10.5
10.2 Center of Mass Center of mass and center of gravity may be used interchangeably for our purposes.
The sun and all the planets actually rotate around the center of mass of the solar system:
See fig 10.6
10.3 Locating the Center of Gravity
CG = Center of Gravity
For a meter stick: CG = the balance point, usually at the 50 cm mark
See fig 10.7
For an irregularly shaped object, If you suspend a pendulum
- from one point on the object, the CG is directly below that point
- from several points. Where the lines intersect, is the CG.
See fig 10.8
The CG of an object may be located where no actual material exists:
See fig 10.9
Questions: - Where is the CG of a donut?
- Can an object have more than one CG?
10.4 Toppling
An object will topple when its CG no longer lies over its base:
See fig 10.10, 10.11 and 10.12
The leaning tower of Pisa does not topple because its CG lies above its base.
Try This: (See p 141) - Stand exactly two footlengths away from a wall.
- Place a chair between yourself and the wall
- Bend over with a straight back
- Let your head lean against the wall like this:
- Lift the chair off of the floor while your head is still leaning against the wall.
- Straighten up.
(Generally, females can do this while males cannot—why?)
Questions:
- When you carry a heavy load (like a pail of water) with one arm, why do you tend to hold your free arm out horizontally?
- To resist being topped, why does a wrestler stand with
- Feet wide apart
- Knees bent?
- How will the support base of the chair in Fig 10.13 change if one of the front legs is removed
- Will the chair topple?
See fig 10.13
10.5 Stability
Unstable Equilibrium: when the CG is lowered with displacement
Stable Equilibrium: when work must be done to raise the CG
Neutral: displacement neither raises nor lowers CG
See fig 10.14
Objects are most stable when CG is lowest!
See fig 10.16
Lower the CG of the book and it is more stable.
See fig 10.17
The pencil by itself is not in stable equilibrium. Add the potatoes and the CG is lowered and the pencil is more stable.
The CG of the following toy is below the point of support. It is very stable.
Explain why this toy cannot remain on its side:
See fig 10.3
10.6 Center of Gravity of People
Location of center of gravity: roughly at the navel
Men: slightly lower
Women: slightly higher because of larger pelvis
Children: slightly higher because of larger head and shorter legs
Change your CG: raise your arms, crouch, bend over
Sometimes CG is outside your body:
See fig 10.23
Stability:
See fig 10.22 and 10.24
Posted by physicscp
at 9:03 AM EST
Updated: Thursday, 21 December 2006 9:06 AM EST
