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 momentum
B)Car Z
C)Car Y
D)Car X

Answer 1

A-They all have the same amount of momentum

Step-by-step explanation:

Mx > My > Mz

But

The net force exerted on each car is identical

That is

Fx = Fy = Fy

According the newton second law of motion

Force is directly proportional to the rate of change of momentum

F=m(v-u) / t

Ft= m(v-u)

But u=0 i.e fron rest

Ft=mv

Ft=mv(momentum)

But they all moved for 10secs

F x 10 =momentum

Momentum= 10Fx = 10Fy = 10Fz = 10F

Since Fx=Fy=Fz=F

So therefore the momentum are of the car x,y, z are similar despite having different mass but identical net force.

So we can conclude that They all have the same amount of momentum

Answer 2

They all have same amount of momentum which is equal to 10 times of net force exerted on each car.

Step-by-step explanation:

Given that

`M_(x) > M_(y) > M_(z)`

From Newton's 2nd law of motion:

`F = Ma` ---- (1)

`a = (F)/(M)` --- (2)

Velocity is related to acceleration by:

`v= at`

substituting (2) in above

`v=(Ft)/(M)` --- (3)

Momentum is given as:

`p= Mv`

`p_(x) = M_(x)v \\p_(y) =M_(y) v \\ p_(z) = M_(z)v`

Using (3) in above

`p_(x) = M_(x)(Ft)/(M_(x)), p_(y) =M_(y) (Ft)/(M_(y)), p_(z) = M_(z)(Ft)/(M_(z))`

`p_(x) = p_{y] = p_(z) = Ft`

We have to find momentum after 10 sec which is equal to 10 times of net force F exerted on each car.