3.1 On a railway shunting line a locomotive is coupling with a stationary carriage of a mass of 2 500 kg - NSC Technical Sciences - Question 3 - 2021 - Paper 1

To calculate the momentum of the locomotive before the collision, we use the formula for momentum:

$p = mv$

Here, the mass (m) of the locomotive is 5 800 kg and its velocity (v) is 1,5 m·s⁻¹. Plugging in these values:

$p = 5800 imes 1.5 = 8 700 ext{ kg·m·s}^{-1}$

Thus, the momentum of the locomotive before the collision is 8 700 kg·m·s⁻¹ due west.

Since the locomotive and carriage couple together, we can apply the law of conservation of momentum. The total momentum before the collision equals the total momentum after the collision.

The total mass after the coupling is:

$m_{total} = m_{locomotive} + m_{carriage} = 5800 + 2500 = 8 300 ext{ kg}$

The total momentum before the collision is 8 700 kg·m·s⁻¹, and we can find the velocity (v') of the combined system:

$8700 = 8300 imes v'$

Solving for v':

v' = rac{8700}{8300} ≈ 1.05 ext{ m·s}^{-1}

Thus, the velocity of the locomotive-carriage combination after the collision is approximately 1.05 m·s⁻¹ due west.

Elastic collisions are those in which both momentum and kinetic energy are conserved. In such collisions, the objects bounce off each other without any loss in kinetic energy.

Inelastic collisions, on the other hand, are those in which momentum is conserved, but kinetic energy is not. Inelastic collisions often result in objects sticking together or deforming, leading to a loss of kinetic energy in the form of heat or sound.

Seatbelts save lives during a collision by providing a force that restrains the occupants of a vehicle, preventing them from being thrown forward into the dashboard or windshield. They work on the principle of inertia, which states that an object in motion will remain in motion unless acted upon by a force. When a vehicle comes to a sudden stop during a collision, the seatbelt exerts a force on the occupant to decelerate them gradually, reducing the risk of serious injuries.

Impulse is defined as the change in momentum of an object, which can be expressed mathematically as:

$J = riangle p = F imes riangle t$

where J is the impulse, F is the force, and * riangle t* is the change in time.

Initially, the car has a momentum of 24 300 kg·m·s⁻¹. After hitting the wall and coming to rest, its final momentum is 0. Therefore, the impulse experienced by the car is:

$J = 0 - 24300 = -24300 ext{ kg·m·s}^{-1}$

This negative sign indicates that the impulse acts in the opposite direction of the initial momentum.

To determine if the wall can withstand the impact, we'll first calculate the average force exerted on the wall by the car. Given that the impulse is -24 300 kg·m·s⁻¹ and the time taken to come to rest is 1.2 s, we can use the impulse-momentum theorem: