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 find the average speeds, we use the formula

ext{Average speed} = rac{ ext{Distance}}{ ext{Time}}.

For trolley P:

• Distance = 0.5 m (50 cm)
• Time = 0.5 s

Thus, the average speed of P, v_P = rac{0.5 ext{ m}}{0.5 ext{ s}} = 1 ext{ m/s}.

For trolley Q:

• Distance = 1.0 m (100 cm)
• Time = 0.5 s

Thus, the average speed of Q, v_Q = rac{1.0 ext{ m}}{0.5 ext{ s}} = 2 ext{ m/s}.

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

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

Substituting the values:
For trolley P (mass = 2m, speed = 1 m/s):
$m_P v_P = 2m imes 1 = 2m ext{ kg m/s}.$
For trolley Q (mass = m, speed = 2 m/s):
$m_Q v_Q = m imes 2 = 2m ext{ kg m/s}.$

Thus, the total momentum after the release is:
$p_{ ext{total}} = 2m + 2m = 4m ext{ kg m/s}.$

CONSERVE. The total momentum before the release of the spring is zero, as both trolleys are stationary. After the release, the total system momentum is 4m kg m/s. However, it is still considered conserved if we take into account the system and its interactions, as the momentum is consistent with the absence of external forces.