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

The gradient of the momentum versus time graph represents the average net force acting on the object.

Impulse can be calculated using the change in momentum:

$ext{Impulse} = riangle p = p_{final} - p_{initial}$

From the graph:

• At $t = 10$ s, momentum $p_{initial} = 120 ext{ kg m s}^{-1}$
• At $t = 30$ s, momentum $p_{final} = -40 ext{ kg m s}^{-1}$

Thus,

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

The average net force can be calculated using the impulse and the time interval:

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

The time interval from $t = 10 ext{s}$ to $t = 30 ext{s}$ is $20 ext{s}$:

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

To find the momentum of object Y after the collision, we can use the law of conservation of momentum, which states that the total momentum before the collision equals the total momentum after the collision:

$p_{initial} = p_{final}$

The momentum of object X before the collision at $t = 30$ s is $-40 ext{ kg m s}^{-1}$, and object Y has a momentum of $50 ext{ kg m s}^{-1}$. Thus:

$p_{total} = p_{X} + p_{Y} = -40 + 50 = 10 ext{ kg m s}^{-1}$

Therefore, the momentum of object Y after the collision can be derived from:

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

The physics principle used is the law of conservation of momentum, which states that the total linear momentum of a closed system remains constant unless acted upon by an external force.