Principle moments

When a see saw is balanced and is not moving it is in equilibrium.  

This is called the principle of moments.  

In equilibrium the total anticlockwise movement = total clockwise moment

Will this seesaw be in equilibrium?

In short no!  The elephant is much heavier than the child. 

For the seesaw to be in equilibrium, the elephant will need to be closer to the pivot. 

Activity:

1. Click on the link below:

Example:

A seesaw needs to balance. One side, 3 m from the pivot, is a box which has a weight of 5 N, and on the other is a box which has a weight of 3 N. Calculate the distance needed between the mass which has a weight of 3 N box and the pivot.

Remember: anti-clockwise moment = clockwise moment

1. Calculate the clockwise moment using the following equation:

M = F x d

M =?

F = 5 N

d = 3 m

Substitute in the values you know:

M = 5 x 3

M = 15 Nm.  The clockwise moment is 15 Nm

2. The seesaw needs to be balanced:

Remember - total anti-clockwise moment = total clockwise moment.

We have already calculated that the clockwise moment is 15 Nm.

Use the equation:

M = F x d

Substitute in the values you already know:

M = 15 Nm

F = 3 N

d =?

$15=3\times d$

Now divide both sides by 3:

This cancels to give 5 = d

So, the distance between the box weighing 3 N and the pivot is 5 m. 

Example

If the ruler in the diagram below is balanced, what is the weight W?

Investigation: Principle moments

Purpose: To plan and carry out experiments to verify the Principle of Moments using a suspended metre rule and attached weights.

The Principle of Moments states that when a body is balanced, the total clockwise moment about a point equals the total anticlockwise moment about the same point.

Remember: Moment =force F x perpendicular distance from the pivot d.

Moment = Fd

What you will need:

uniform metre rule

retort stand

boss and clamp

two 100 g mass hangers

100g slotted masses, 

a g-clamp, 

three lengths of string.

What you will do:

1. Set up the retort stand and clamp it to your desk. Suspend the metre rule at the 50 cm mark so that it is balanced horizontally. The ruler is said to be in equilibrium. The 50 cm mark is the pivot.

Remember that 1 newton = 100 g

2. Suspend a 100g mass, m₁, from one side of the ruler a distance 40 cm, d₁, from the pivot. Read the distance d₁ in cm, from m₁ to the pivot. Create a table like the one below and record this distance in the table. Record the value of mass m₁ in kg.

Anticlockwise

Clockwise

3. Suspend a 200g mass, m₂, from the other side of the pivot. Carefully move this mass backwards and forwards until the ruler is once more balanced horizontally. Read the distance d₂ in cm from the mass m₂ to the pivot. Record d₂ in cm, in your table, along with the mass m₂ in kg.

4.  Repeat with other weights at different distances and record the weight and distances in your tables.  

Conclusion:

Each time the ruler balances horizontally we can see from our results that, the anticlockwise moment about the pivot = the clockwise moment about the pivot.

This verifies the Principle of Moments.