§  Pick-Up Section #8 Packet

§  Pick-Up Section #8 Worksheet

So far in our study of forces, we have treated all the forces acting on an object as if they were acting on a single point. However, there can be many forces, each acting at a different point on an object.

Parallel Forces Forces acting in the same or in opposite directions at different points on an object.

Center of Gravity (Mass) The point at which all of an objects weight can be considered to be concentrated OR the point from which the object will balance. Center of Gravity may be: §  At the geometric center (Uniform) §  Inside an object that is not at the geometric center §  Outside the object

¡  If an object is irregularly shaped, spinning the object and finding the intersection where axes meet can find the center of gravity.

¡  There is not always material at an object’s center of mass.

Example #1: Center of Gravity at the Geometric Center

Center of gravity

There are numerous particles in the bar or stick that each have a mass. Gravity acts on all of these masses producing forces which act at a distance from the center of gravity

A uniform bar or stick

Example #2: Center of Gravity inside an object that is not at the geometric center

C of G

The center of gravity is not the point that equally divides the weight on either side of a body or object . There is much more weight to the right, but the length or distance of the arm is also much smaller on the right, therefore the torques will balance out.

Example #3: Center of Gravity inside an object that is not at the geometric center

When we throw a baseball, we expect it to follow a smooth, parabolic trajectory as we have discussed with projectile motion.

When we throw a baseball bat, however, its path or trajectory does not seem smooth at all. While the bat rotates around the center of mass, the center of mass itself is following the same smooth, parabolic path that we expect for a smaller, simpler object, like a baseball.

The center of mass itself follows the same smooth path that we expect for a smaller, simpler object, like a "point particle".

•  How can we locate the Center of Mass in an extended object? •  We can suspend it. •  The Center of Mass will always be directly under the point of support. •  Then we can suspend it from some other point and know that the

Center of Mass will always be directly under this point of support as well.

cog

1

cog

3

cog

2 CoG moves in the direction the arm moved; up and to the left.

CoG moves in the opposite direction of the removed leg; up and to the left.

Example #4: Center of Gravity inside an object that is not at the geometric center

Example #5: For some objects the Center of Gravity is located outside the actual object.

Ring Stool

2 uniform perpendicular planks

FW FW FW

¡  When the object is suspended, it will come to rest when the CW moment is equal to the CCW moment.

Counter-Clockwise (CCW) Moment Clockwise (CW) Moment

Moment is the tendency of a force to twist or rotate an object

When an object is suspended, so that it can swing freely, it will come to rest with its Center of Gravity vertically below the point of suspension.

States of Equilibrium

Any object at rest may be in one of three states of equilibrium: Stable: The condition of an object to return it is original position when slightly disturbed. Unstable: When disturbed slightly, it will fall over. Neutral: The condition where an object is lying on its side and displace but manages to remains its equilibrium about its new position

¡  COG is at lowest possible position ¡  COG needs to be raised in order to topple the object ¡  Difficult to topple over

Stable Objects

¡  COG is at the highest possible position ¡  COG is lowered in order to topple the object ¡  Easy to topple down

Unstable Objects

¡  COG is neither lowered nor raised when the object is toppled ¡  Roll from one side to another

Objects with neutral equilibrium:

An object becomes unstable when its Center of Gravity falls outside of the object’s base

Why?

All of the object’s weight can be considered as acting through the COG. If this acts outside the base then it will cause a moment or a turning effect

For an object to start rotating it needs to have an unbalanced moment acting on it

FW FW FW

Stable

Pivot Pivot

Stable Unstable

Moment is the tendency of a force to twist or rotate an object

A great example of a VERY stable object.

What features of the cone make it so stable?

§  Low Center of Gravity §  Wide base

Animals such as chickens have easier systems to control. The diagram shows that the cog of a chicken lies below its hip joints and between its widely separated and broad feet.

Position of Center of Gravity

Each of the diagrams on the right represent a Double Decker bus with passengers inside. Which one of these drawings shows all passengers on: The lower level The upper level Both levels

1

2

3

¡  If more people sit upstairs on the bus the COG will rise/fall. This will make the bus more stable/unstable and it can be tilted by a greater/lesser angle

¡  The bus will fall over when the COG acts inside/outside of

the bus’ base

¡  A stable object has a low/high COG and a narrow/wide base