BALANCING FORCES AND LEVERS

The centre of gravity of a body is the point where its whole weight acts.

EXPERIMENT To find the centre of gravity of a piece of cardboard
Procedure
  • Set up the apparatus as in diagram.
  • Allow everything to come to rest.
  • Make some marks on the cardboard directly behind the plumbline.
  • Remove the cardboard and draw a straight line through the marks.
  • Hang the carboard from a different point and repeat the above steps.
  • The centre of gravity is the point where the two lines meet.

EQUILIBRIUM AND STABILITY

An object that stays in one place is said to be in equilibrium.

An object is stable if it returns to its original position after being tilted.

For greatest stability:
the centre of gravity should be as low as possible
and the base should be as wide as possible.
Race cars have wide wheels for extra stability. Surfers increase their stability by crouching. This lowers their centre of gravity.

An object is unstable if, when it is tilted slightly, it then falls over.

A rugby ball is unstable if placed on its end.

 
Objects with high centres of gravity and narrow bases are unstable.

 

LEVERS

A lever is a rigid body which can rotate about a fixed point called a fulcrum.

Examples of levers

The fulcrum is in the middle.

The load is in the middle.

The effort is in the middle.

 

Other examples of levers

Click here for a website on levers.

Moment of a force

The moment of a force is a measure of its turning effect.

To calculate the moment, M, of a force, F, multiply the force by its distance, d, from the fulcrum.

M = Fd

The law of the lever (principle of moments)
When a lever is balanced,
the total clockwise moment is equal to
the total anti-clockwise moment.

 

Example: Investigate whether the levers below are balanced or not.

Anti-clockwise Moment = Fd = 6x20 =120

Clockwise Moment = Fd = 3x40 = 120

The anti-clockwise moment is equal to the clockwise moment.

This lever is balanced.

Anti-clockwise Moment = Fd = 9x10 = 90

Clockwise Moment = Fd = 2x30 = 60

The anti-clockwise moment is not equal to the clockwise moment.

This lever is not balanced.

 

Example: The levers in the diagrams below are balanced. Find the value of x in each case.

Anti-clockwise Moment = Fd = 4x25 =100

Clockwise Moment = Fd = x x 20 = 20x

20x = 100 thus x = 100/20 = 5 N.

 

Anti-clockwise Moment = Fd = 8x

Clockwise Moment = Fd = 2x40 = 80

8x = 80 thus x = 80/8 = 10 cm.

Click here for more questions on the law of the lever.