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

To calculate the average speeds, we start by determining the distance traveled by each trolley:

• For trolley P:

  
  \

  Distance = 50 mm = 0.05 m

  Time = 0.5 s

  Average Speed, $v_P = \frac{Distance}{Time} = \frac{0.05 ext{ m}}{0.5 ext{ s}} = 0.1 ext{ m/s}$

• For trolley Q:

  
  \

  Distance = 100 mm = 0.1 m

  Time = 0.5 s

  Average Speed, $v_Q = \frac{Distance}{Time} = \frac{0.1 ext{ m}}{0.5 ext{ s}} = 0.2 ext{ m/s}$

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

Using the formula for momentum, $p = mv$, the total momentum is:

$\text{Total Momentum} = m_P v_P + m_Q v_Q$

Substituting the masses and velocities:

$= (2m)(0.1) + (m)(0.2) = 0.2m + 0.2m = 0.4m$

The total momentum is CONSERVED. In an isolated system where no external forces act on the trolleys, the total momentum before the release of the spring is equal to the total momentum after the release.