In an experiment to verify the principle of conservation of momentum, a body A was set in motion with a constant velocity - Leaving Cert Physics - Question 1 - 2005

The time interval of 0.2 s was measured using a ticker tape timer. The setup was as follows:

1. A ticker tape with 10 dots representing time intervals of 0.02 s.
2. Two light gates connected to a data logger on the trolley.
3. The time between the dots was calculated as 0.2 s, derived from the equation: time = number of dots × 0.02 s.

(i) Before the collision: Using the formula $v = \frac{d}{t} = \frac{10.1\, \text{cm}}{0.2\, \text{s}} = 50.5\, \text{cm/s} = 0.505\, \text{m/s}$

(ii) After the collision: Using the displacement after collision: $v = \frac{d}{t} = \frac{5.1\, \text{cm}}{0.2\, \text{s}} = 25.5\, \text{cm/s} = 0.255\, \text{m/s}$

To verify the conservation of momentum, we analyze the momentum before and after the collision:

• Momentum before: $p = mv$ For body A: $p_A = (0.5201\, \text{kg}) \times (0.505\, \text{m/s}) = 0.263\, \text{kg m/s}$ For body B (initially at rest): $p_B = 0\, \text{kg m/s}$ Total momentum before: $p_{total, before} = p_A + p_B = 0.263\, \text{kg m/s}$

• Momentum after:

• After collision, the combined bodies move with a common velocity 0.255 m/s: $p_{total, after} = (0.5201 + 0.490) \times 0.255 = 0.263\, \text{kg m/s}$

This confirms that momentum before the collision equals momentum after, thereby verifying conservation of momentum.

Several methods were employed to minimize the effects of friction and gravity:

1. Air cushion was used to separate surfaces, reducing friction.
2. Smooth runway: The air track was designed to be almost frictionless.
3. Low resistance wheels: The trolley wheels were designed to reduce rolling resistance.
4. The inclination was adjusted so that gravitational effects on momentum were minimal.