Question

Three cars, car X, car Y and car Z, begin accelerating from rest,at the same time. Car X is more massive than car Y, which is moremassive than car Z. The net force exerted on each car is identical.After 10 seconds, which car has the most amount of momentum?A) They all have the same amount of momentumB)Car ZC)Car YD)Car X

Answer 1

Answer:

A) They all have the same amount of momentum

Explanation:

Newton's second law of motion gives an operational definition of force as the rate of change in momentum. It states that the rate of change in momentum of a body  is directly proportional to the applied force.

This is expressed as follows mathematically;

$F=\frac{m(v-u)}{t}................. (1)$

We can further simplify (1) above as follows;

$Ft=m(v-u)................(2)$

if initial velocity u = 0, then equation (2) becomes

$Ft=mv...............(3)$

This implies that change in momentum is equal to the impulse experienced by the body.

According to the problem stated, all the cars X, Y and Z are subjected to the same magnitude of force for the same time interval, hence irrespective of their masses they will all experience the same magnitude of change in momentum. Also, since they all began from rest, their velocities may differ as a result of their differences in mass, however their instantaneous momenta at end of the 10s will be the same.

The condition that would have warranted different momenta for them is if they had different initial velocities.

When different masses with a common initial velocity are subjected to the same magnitude of force for the same time interval, they will experience the same momentum at the end of the time interval although with different velocities. The smallest mass will have the highest velocity while the largest will have the lowest velocity at the end of the time interval.