Parallel Forces

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

Statics refers to the bodies in equilibrium.

Equilibrium deals with the absence of a net force.

When the net equals zero, the forces are in equilibrium provided they are concurrent (they intersect). If they are non-concurrent, the body may rotate even if the vector sum of the forces equals zero. Hence, there must be another condition to set forces in equilibrium – that under the influence of forces, the body must have no tendency toward translational or rotary motion.

Statics refers to the bodies in equilibrium. Equilibrium deals with the absence of a net force.

When the net equals zero, the forces are in equilibrium provided they are concurrent (they intersect). If they are non-concurrent, the body may rotate even if the vector sum of the forces equals zero. Hence, there must be another condition to set forces in equilibrium – that under the influence of forces, the body must have no tendency toward translational or rotary motion.

An example of non-concurrent forces where the vector sum may be equal to zero but it still causes the body to move is parallel forces. They act in the same or opposite directions. Their lines of action are parallel.

Forces acting in the same or opposite directions are parallel.

translational or rotary motion.

An example of non-concurrent forces where the vector sum may be equal to zero but it still causes the body to move is parallel forces. They act in the same or opposite directions. Their lines of action are parallel.

Forces acting in the same or opposite directions are parallel.

TORQUE (MOMENT OF FORCE)

Torque or moment of force refers to the turning effect of the force upon a body about a point (fulcrum). It is the product of the magnitude of the force and perpendicular distance from the line of action of the force to the

Center of Gravity 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   Inside an object that is not at the geometric center   Outside the object

  If an object is irregularly shaped, the center of gravity can be found by spinning the object and finding the intersection of the three spin axes (x-y-z).

  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

The center of gravity is not the point that equally divides the weight on either side of a body or object

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

C of G

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.

Baseball Bat

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

cg

1

cg

3

cg

2 Center of gravity moves in the direction the arm moved; up and to the left.

Center of gravity moves in the opposite direction of the removed leg; up and to the man’s 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

  Linked to Principle of Moments

  When the object is suspended from a point it will come to rest when the clockwise moment is equal to the counter-clockwise moment.

Counter-Clockwise Moment = Clockwise 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

  The C of G is at lowest possible position.   The C of G needs to be raised in order to topple the object.   They are difficult to topple over.

Stable objects:

  the C.G. is at the highest possible position.   the C.G. is lowered in order to topple the object.   They are easy to topple down.

Unstable objects:

  the C of G is neither lowered nor raised when the object is toppled.

  they roll from one side to another.

Objects with neutral equilibrium:

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

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

  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