3.1 Define the term momentum - NSC Technical Sciences - Question 3 - 2024 - Paper 1

The physical quantity represented by the gradient of the momentum versus time graph is the average net force acting on the object.

Impulse is defined as the change in momentum of an object. Therefore, to calculate the impulse object X experiences between t = 10 s and t = 30 s, we use:

$ext{Impulse} = ext{Change in momentum} = p_{final} - p_{initial}$

From the graph, at t = 10 s, the momentum is $p_{initial} = 120 ext{ kg m s}^{-1}$, and at t = 30 s, $p_{final} = -40 ext{ kg m s}^{-1}$.

Therefore:

$ext{Impulse} = -40 ext{ kg m s}^{-1} - 120 ext{ kg m s}^{-1} = -160 ext{ kg m s}^{-1}$

The average net force can be calculated using the impulse-momentum theorem:

F_{net} = rac{ ext{Impulse}}{ ext{time interval}}

The time interval is from 10 s to 30 s, which is 20 seconds. Therefore:

F_{net} = rac{-160 ext{ kg m s}^{-1}}{20 ext{ s}} = -8 ext{ N}

Thus, the average net force acting on object X is $8 ext{ N}$ to the left.

To find the momentum of object Y after the collision, we apply the principle of conservation of momentum, which states that the total momentum before the collision equals the total momentum after the collision. From the graph, the momentum of object X before the collision is $-40 ext{ kg m s}^{-1}$ and the momentum of object Y is $50 ext{ kg m s}^{-1}$. Thus:

$p_{X, initial} + p_{Y, initial} = p_{X, final} + p_{Y, final}$

Plugging in:

$(-40) + 50 = -40 + p_{Y, final}$

Solving for $p_{Y, final}$ gives:

$p_{Y, final} = 50 - 40 = 10 ext{ kg m s}^{-1}$

The physics principle used to answer QUESTION 3.4.1 is the conservation of momentum, which states that in an isolated system, the total linear momentum remains constant before and after a collision, provided no external forces act on the system.