4.1 What is meant by an isolated system in physics? 4.2 During an experiment, a rocket of unknown mass is mounted on a toy cart of mass 20 kg - NSC Physical Sciences - Question 4 - 2022 - Paper 1

According to Newton's third law, for every action, there is an equal and opposite reaction. When the rocket is fired, it exerts a force on the toy cart, which in turn exerts an equal and opposite force on the rocket. This interaction causes a change in momentum.

Before firing, the total momentum of the system (cart + rocket) is constant. Upon firing, the momentum of the rocket increases as it moves forward, resulting in a decrease in momentum of the cart, causing it to slow down.

To calculate the mass of the rocket, we can use the principle of conservation of momentum. Before the rocket is fired, the total momentum of the system is:

$P_{initial} = (m_{cart} + m_{rocket})v_{initial}$

After the rocket is fired, the total momentum becomes:

$P_{final} = m_{cart}v_{cart} + m_{rocket}v_{rocket}$

Setting these equal:

$(20 + m_{rocket})(2.5) = 20(0.6) + m_{rocket}(30)$

Simplifying:

$50 + 2.5m_{rocket} = 12 + 30m_{rocket}$

Rearranging the equation gives:

$50 - 12 = 30m_{rocket} - 2.5m_{rocket}$

$38 = 27.5m_{rocket}$

Solving for $m_{rocket}$:

m_{rocket} = rac{38}{27.5} \\ m_{rocket} ext{ approximately equals } 1.38 ext{ kg}