Equilibrium (CIE IGCSE Physics)

• In physics, the term equilibrium means:

A state of balance or stability

• In other words, a system in equilibrium keeps doing what it’s doing without any change

Conditions for equilibrium

• For objects in equilibrium:
  • The forces on the object must be balanced
    • There must be no resultant force
  • The sum of clockwise moments on the object must equal the sum of anticlockwise moments
    • There must be no resultant moment

 

Examples of systems in equilibrium

When the forces and moments on an object are balanced, the object will remain in equilibrium

 

Extended tier only

Aim of the experiment

• This experiment aims to demonstrate that there is no resultant moment for an object in equilibrium 

Variables

• Independent variable = force, ,  and distance, 
• Dependent variable = moment,  
• Control variables:
  • The length of the cotton loops should be equal on each side of the beam

Equipment

Equipment list

Equipment	Purpose
Metre ruler with a small hole at the centre	To provide the beam on which to add masses
2 × 100 g mass hangers	To attach the masses to the ruler
8 × 100 g masses	To add the mass at different points along the ruler
Clamp stand, boss & clamp	To secure the pivot in place
Optical pin and cork	To act as the pivot
Small piece of plasticine	To ensure the ruler is balanced at the start
2 loops of cotton	To attach the mass hangers to the metre ruler

Example set up of equipment to demonstrate equilibrium

The ruler acts as the beam with the pin as the pivot. Unequal masses are added at different distances until the beam is balanced and equilibrium is reached

Method

1. Hang unequal loads on either side of the pivot; one person holds the beam while the other person hangs the loads
2. Adjust the distances of mass 1, , and mass 2, , until the beam is balanced 
3. Adjust further to ensure the beam is perfectly horizontal with no resultant moment
4. Record the distance from the pivot of masses  and 
5. Repeat the process for different sized loads

Example results table

A results table should contain spaces for all the measurements taken and any calculations required

Analysis of results

• Force 1, , is providing the anticlockwise moment, 
  • Where:
    • 
    • 
• Force 2, , is providing the clockwise moment, 
  • Where:
    • 
    • 
• Remember to convert g to kg and cm to m for the calculations to give units of Nm for the moments
• The results should show that for all the systems tested, the anticlockwise moment is equal to the clockwise moment
  • Therefore, there is no resultant moment when the system is in equilibrium

Evaluating the experiment

Systematic errors

• The cotton loops should be added to the ruler when viewed straight on to avoid a parallax error
• The cotton loops should be measured to ensure they are equal in length
• The experiment should be checked to ensure there is no friction between the metre ruler and the optical pin pivot so the ruler is balanced, only because of the added masses

Random errors

• The precision of the experiment is improved by:
  
  • ensuring the experiment is done in a space with no draft or breeze, as this could affect the motion or position of the hanging masses
  • using an electronic system or a spirit level that identifies the angle of the beam would improve the experiment, or using a flat rod with masses placed on top
• The accuracy of the experiment is improved by:
  • taking more than five readings for each mass and position and then calculating the mean

• It is assumed that the mass of the cotton loops is negligible (zero)
• It is assumed that the mass of each mass and hangar is 100 g, this should be verified in advance using an electronic balance

Safety considerations

• Safety goggles should be worn because the cotton loops could snap and hit someone in the eye
• Use a G clamp to secure the clamp stand to the bench so it does not topple over and cause injury
• Stand up to carry out this experiment so you do not fall over when looking level with the metre ruler
• Place a mat or a soft material below the metre ruler to cushion any masses that may fall to the ground and to keep the area clear of feet and hands