Investigating the Principle of Moments (WJEC GCSE Physics)

Aim of the Experiment

• This experiment aims to determine whether the principle moments apply to adding different masses at different distances on a beam from a pivot

Variables:

• Independent variable = force, F,  and distance, d
• Dependent variable = moment, M 
• Control variables:
  • Use of the same equipment and set-up for each investigation

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

Diagram of Equipment Used in Principle of Moments Investigation

Set up the ruler on its pivot on the clamp stand and add the masses and different distances d₁ and d₂ as per the experiment

Method

• Set up the clamp stand, optical pin and metre ruler. Ensure the ruler is balanced by placing plasticine on one end

Investigation 1:

1. Use a cotton loop to hang a 200 g mass at the 10 cm (d₁  = 40 cm) mark on the ruler
2. Use a second cotton loop to hang a mass of 400 g on the other side of the pivot so the metre ruler is balanced. Record this distance as d₂  in the table of results
3. Repeat steps 2 and 3 for d₁ = 30 cm and d₁ = 20 cm

Investigation 2:

1. Use a cotton loop to hang a 200 g mass at the 5 cm (d₁ = 45 cm) mark on the ruler
2. Use a second cotton loop to hang a mass of 600 g on the other side of the pivot so the metre ruler is balanced. Record this distance as d₂  in the table of results
3. Repeat steps 2 and 3 for d₁  = 30 cm and d₁  = 15 cm

Investigation 3:

1. Use a cotton loop to hang an 200 g mass at the 10 cm (d₁ = 40 cm) mark on the ruler
2. Use a second cotton loop to hang a mass of 800 g on the other side of the pivot so the metre ruler is balanced. Record this distance as d₂  in the table of results
3. Repeat steps 2 and 3 for d₁ = 20 cm 

• Now, calculate the clockwise and anticlockwise moments for each step and record in the table of results

An Example Table of Results

A suitable table of results must contain all times for all trials for each number of masses

An Expected Table of Results

Mass /kg	Weight, W1 /N	Distance, d1 /m	Mass /kg	Weight, W2 /N	Distance, d2 /m	Anti-clockwise moment, W1 × d1	Clockwise moment, W2 × d2
0.20	2.0	0.40	0.40	4.0	0.20	0.80	0.80
0.20	2.0	0.30	0.40	4.0	0.15	0.60	0.60
0.20	2.0	0.20	0.40	4.0	0.10	0.40	0.40
0.20	2.0	0.45	0.60	6.0	0.15	0.90	0.90
0.20	2.0	0.30	0.60	6.0	0.10	0.60	0.60
0.20	2.0	0.15	0.60	6.0	0.05	0.30	0.30
0.20	2.0	0.40	0.80	8.0	0.10	0.80	0.80
0.20	2.0	0.20	0.80	8.0	0.05	0.40	0.40

 

Analysis of Results

• The clockwise and anticlockwise moments can be calculated for each mass in each position using the following formula:

M = F × d

• Where:
  • Force = mg in newtons (N)  100 g = 1 N
  • Distance is the distance d₁ or d₂ from the pivot to the mass (cm)
• For each set of results determine if they satisfy the principle of moments
  • Where clockwise moment = anticlockwise moment

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 draught 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 the use of 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