Grade 12 learners are investigating the principle of conservation of linear momentum for an isolated system - NSC Technical Sciences - Question 3 - 2023 - Paper 1

Given that trolley P has a mass of 2m and moves 50 mm in 0.5 seconds, the average speed of trolley P can be calculated as:

$v_P = \frac{\Delta x}{\Delta t} = \frac{0.05 \, m}{0.5 \, s} = 0.1 \, m/s$

For trolley Q with mass m, moving 100 mm:

$v_Q = \frac{\Delta x}{\Delta t} = \frac{0.1 \, m}{0.5 \, s} = 0.2 \, m/s$

The total momentum after the release of the spring can be calculated using:

$p_{total} = m_P v_P + m_Q v_Q$

Substituting the masses:

$p_{total} = (2m)(0.1) + (m)(0.2) = 0.2m + 0.2m = 0.4m \, kg \, m/s$

CONSERVE

The total momentum is conserved because the system is isolated and no external forces act on it. Thus, the total momentum before and after the collision remains equal.

Impulse is defined as the change in momentum of an object when a net force is applied over a period of time. It is mathematically expressed as:

$J = F_{net} \Delta t$.

The change in momentum for the ball can be calculated as:

$\Delta p = m(v_{final} - v_{initial}) = (0.6 \, kg)(10 \, m/s - (-15 \, m/s)) = 300 \, kg \, m/s$

The net force can be calculated using the impulse formula:

$F_{net} = \frac{\Delta p}{\Delta t} = \frac{300 \, kg \, m/s}{0.05 \, s} = 6000 \, N$

1. Airbags: These deploy quickly to cushion passengers during a collision, reducing impact forces.

2. Crumple zones: These are designed to deform during a crash, absorbing energy and limiting the force transmitted to occupants.

3. Seat belts: These secure occupants in place, preventing them from being thrown forward in a collision and reducing the risk of injury.