Center of gravity

Center of Gravity

The WHY’s about Center of Gravity

• Why doesn’t the leaning tower of Pisa topple over?

• How far can it lean before it does topple over?• Why is it impossible for us to stand with our

back and our heels against a wall and bend over and touch or toes without toppling forward?

What is center of gravity (CG)?

• Center of Mass – is the point where a body can be balanced in a uniform gravitational field. Point where most of the mass is concentrated.

• The Center of Gravity is the single point on an object where all of its weight is assumed to be located.

Examples of center of mass/center of gravity

Locating the Center of Gravity

• The center of gravity of a uniform object is at the midpoint, its geometric center. Supporting that single point supports the whole object.

Locating the Center of Gravity

• When the distribution of mass of the object is not constant or the object is not uniform the center of gravity shifts to the direction of greater mass.

Locating the Center of Gravity

• The CG of an object may be located where no actual material exists.

Try this!

• Rest a meter stick on two extended forefingers. Slowly bring your fingers together. Note what occurs as your fingers meet at the CG. When one finger gets ahead of the other, weight on it increases, enough to keep it from moving, while the other finger, with less friction, slides and catches up. You end up at 50 cm mark because the fingers always meet at CG!

Locating the Center of Gravity

• Center of gravity of people.– When you stand erect with your arms hanging at

your sides, your CG is within your body. It is typically 2 to 3 cm below your navel and midway between your from and back.

– The CG is slightly lower in women than in men because women tend to be proportionally larger in the pelvis and smaller in the shoulders.

– In children, the CG is slightly 5% higher because of their proportionally larger heads and short legs.

• Can an object have more than one CG• Where is the center of gravity of a donut?

• In the center of the hole!• A rigid object has one CG. If it is non-rigid, such

as a piece of clay or putty, and is distorted into different shapes, then its CG may change as its shape does. Even then, it has one CG for any give n shape.

Toppling

• If the CG of an object is above the area of support, the object will remain upright. If the CG extends outside the area of support, the object will topple over.

• The Leaning Tower of Pisa does not topple over because its CG does not extend beyond its base! And so the tower has stood for centuries.

Just a thought.......

• When you carry a heavy load –such as a pail o water-with one arm, why do you tend to hold your free arm out horizontally?

• You tend to hold your free arm outstretched to shift the CG of your body away from the load so your combined CG will more easily be above the base of support.

Just a thought.......

• To resist being toppled, why does a wrestler stand with feet wide apart and bent knees?

• A wide apart feet increase the support base. Bent knees lower the CG.

Just a thought.......

• What is the importance of tails of an animal in terms of toppling?

• Tail gives an animal the ability to shift its CG and increase stability

Stability

measure of maintaining equilibrium: a measure of the difficulty of displacing an object or system from equilibrium.

Equilibrium is UNSTABLE when the CG is lowered with displacement, STABLE when work must be done to raise the CG and NEUTRAL when displacement neither raises nor lowers the CG.

Stability

• A cone balances easily on its base. To make it topple, its CG must be raised. This means the cone’s potential energy must be increased, which requires work. We say an object that is balanced so that any displacement raises its CG is in STABLE EQUILIBRIUM.

Stability

• If you position the cone so that its CG is exactly above its tip, the slightest vibration or air current will cause the cone to topple. The CG is lowered by any movement. We say that an object balanced so that any displacement lowers its CG is in UNSTABLE EQUILIBRIUM.

Stability

• When the cone is placed on its side its CG is neither raised nor lowered with displacement. An object in this configuration is in NEUTRAL EQUILIBRIUM.

On Sky Scrappers

• The CG o a building is lowered if much of the structure is below ground level. This is important for tall, narrow structures. The CG is deeply rooted that its CG is actually below ground level. It can not fall over intact because falling would not lower its CG at all.

The CG of the three trucks parked on a hill are shown by the X’s. Which truck/s will topple

over?

Answer the following:

1. Why is the CG of a baseball bat not at its midpoint?

2. When are the CG and CM of an object the same?

3. Cite an example of an object that has CG where no physical material exists.

4. Why does the Leaning topple of Pisa not topple?

Answer the following:5. How far can an object be tipped before it

topples over?6. Is the potential energy MORE, LESS, or

UNCHANGED when the CG of an object is raised?

7. What accounts for the stability of the tall narrow buildings?

8. What happens to the CG of a glass of water when filled with ice? Rises, lowers, unchaged.

Answer the following:

9. Why do you spread your feet farther apart when standing in a bumpy-riding vehicle?

10. Why can you not successfully bend over and touch your toes when you stand with your feet back and heels against a wall?

11. Differentiate the three kinds of equilibrium according to stability.

ANSWERS

1. The bat has more mass at one end.2. When the gravity does not change over

object.3. Donut, boomerang, hollow ball, etc.4. The CG is above the area of support.5. Until the CG extends beyond area of support.6. More7. CG is below ground level.

ANSWERS

8. Rises9. To increase the support base/ area of support

for stability.10. CG will extend beyond support base/area of

support.11.When object is displaced, CG lowers

(UNSTABLE), CG rises (STABLE), neither rises nor lowers (NEUTRAL)

Stability and Balance

Stability: resistance to disruption of equilibrium• Factors that affect stability:– Mass, friction, horizontal position and height of

center of gravity with respect to the base of support

Balance: ability to control equilibrium• Foot position affects standing balance

13-22

Summary• A muscle develops tension and produces torque at the

joint that it crosses.• Muscle and bones function as levers.• The angle of muscle pull on a bone produces rotary and

parallel components of force• When a body is motionless, it is in static equilibrium.• The behavior of a body is greatly influenced by the

location of the center of gravity.• Stability is the resistance to disruption of equilibrium