8.2 – Investigating Conservation of Momentum (Leaving Cert Physics): Revision Notes

8.2 – Investigating Conservation of Momentum

Introduction and aim

This experiment investigates one of the most fundamental principles in physics - the conservation of momentum. You will measure the velocity of a trolley before and after it collides with another trolley, then calculate the momentum values to verify that the total momentum remains constant during the collision.

The principle states that in any collision where no external forces act on the system, the total momentum before the collision equals the total momentum after the collision.

Equipment required

To carry out this investigation, you will need:

• A runway with two trolleys of known masses (e.g. 250g, 500g, and 1000g)
• A ticker timer with ticker tape and power supply
• Two magnets that can be mounted on the fronts of the trolleys
• A box for safe trolley collection
• A balance for measuring masses accurately

Experimental method

Follow these steps carefully to ensure accurate results:

Setup procedure

1. Use the equipment as shown in the diagram above
2. Raise one end of the runway so that trolley 1 (with ticker tape attached) will move down the runway at constant speed when given a gentle push and released
3. Place trolley 1 at the upper end of the runway and trolley 2 about halfway down
4. Turn on the ticker timer and give trolley 1 a gentle push so it moves down the runway and collides with trolley 2

Data collection

5. Stop the timer at the end of the runway and remove the ticker tape
6. The tape should show dots before the collision and dots after the collision, similar to the pattern shown below:

Velocity before ••••••••••• Velocity after

7. Repeat the experiment with different masses on each trolley and with the trolleys travelling at different speeds
8. Record all results in a data table

Measurements and calculations

9. Calculate the velocity of trolley 1 before (u) and after (v) the collision using the ticker tape method
10. Use a balance to find the mass of trolley 1 (m₁) and trolley 2 (m₂)
11. Calculate the momentum before the collision (m₁u) and the momentum after the collision ((m₁ + m₂)v)

Data collection and calculations

Use the following table structure to record your measurements:

Before collision			After collision
Velocity from ticker tape	Mass	Momentum	Velocity from ticker tape	Mass	Momentum
S₁ = number of spaces (n) in length S₁	m₁	m₁u	S₂ = number of spaces (n) in length S₂	m₂	(m₁ + m₂)v
u = S₁/(n/50)			v = S₂/(n/50)

Key formulas

• Velocity calculation: $u = \frac{S_1}{n/50}$ and $v = \frac{S_2}{n/50}$
• Momentum before collision: $p_{before} = m_1u$
• Momentum after collision: $p_{after} = (m_1 + m_2)v$

Expected results

The momentum before the collision should equal the momentum after the collision: $m_1u = (m_1 + m_2)v$

This demonstrates the conservation of momentum principle - the total momentum of the system remains constant when no external forces act upon it.

Sources of error

To ensure accurate results, be aware of these potential sources of error:

Systematic errors

• Friction: Both air resistance and rolling friction can affect the trolleys, which is why you must ensure no net external force acts on the bodies
• Runway alignment: Ensure the trolleys can roll freely and the runway is properly levelled
• Measurement precision: Select as large a distance as possible when measuring velocities to improve accuracy

Random errors

• Ticker tape measurements: Avoid parallax errors when measuring distances on the tape
• Timing variations: Ensure consistent ticker timer frequency (50Hz)
• Mass measurements: Use an accurate balance and record masses precisely

Important considerations

Understanding why certain aspects of this experiment work is crucial for accurate results.

Why use magnets?

If magnets are used in this experiment, the forces they exert do not change the total momentum of the system because they are internal forces - one magnet pulls on the other with equal and opposite force, so the net external force acting on the trolley system is zero.

Precautions for accurate results

• Lubricate trolley wheels if necessary to minimise friction
• Ensure the runway surface is clean and level
• Take multiple readings and calculate average values
• Use appropriate scales when measuring distances and masses

Remember!