Question

A truck collides with a sports car in a high-speed head-on collision. . The mass of the truck and its contents is 5 times larger than the mass of the car and its contents. Select greater than, less than or equal to. During the collision, the magnitude of the change in momentum of the truck is _____ the magnitude of the change in momentum of the car. A: Greater than B: Less than C: Equal to

Answer 1

The correct option is B

Step-by-step explanation:

This question seeks to test the knowledge of the change in momentum and deep understanding of the Newton's first law of motion which states that a substance will continue to be in a state of rest or constant motion unless acted upon by an external force.

The formula for change in momentum is mass multiplied by change in velocity. where change in velocity is final velocity minus the initial velocity.

The mass of the truck is already said to be 5 times larger, the change in velocity of the car will definitely be negative because the car will pushed back by the truck. For instance, if the initial velocity of the car is 50m/s and the final velocity backwards is 10m/s, the change in velocity will be (-10-50) which will equal (-60)

However, for the truck, the change in velocity will still remain positive for the final velocity because it is expected that the truck will still move forward despite the heads-on collision. Hence, if the initial velocity is 50m/s and the final velocity is 10m/s, the change in velocity will be (10-50) which will equal (-40).

Assuming the mass of the car is 1g. From the formula for change in momentum

The truck will be assumed to be (5 × 1) × -40 = -200

The car will be assumed to be 1 × -60 = -60

Hence, the magnitude of change in momentum of the truck will be lesser than the magnitude of the change in momentum of the car.

Answer 2

A: Greater than

Step-by-step explanation:

Momentum (P) implies product of the mass (m) and velocity (v) of a body.

P = mv

It is measured in kgm/s.

Thus the greater the mass of a body, the more its momentum even when moving at a slower velocity. The change in momentum of an object is called its impulse.

Let the mass of the car be represented by
`m_(c)` and that of the truck be represented by
`m_(T)`.

Thus,

`m_(T)` = 5
`m_(c)`

P of the truck = 5
`m_(c)`v

P of the car =
`m_(c)`v

Thus, during collision, the change in momentum of the truck is greater than that of the car.