Question

two railway trucks of masses m and 3m move towards each other in opposite direction with speeds 2v and v respectively . these trucks collide and stick together . what is the speed of the truck after the collision ?

Answer 1

We know that According to Law of Conservation of Momentum :

The Momentum in a closed system remains constant before and after collision.

Let us calculate the Railway trucks system momentum before the collision :

Let us consider the truck with mass 'm' is coming from the left with velocity '2v'

⇒ The momentum of the truck coming from left = m × 2v = 2mv

Let us consider the truck with mass '3m' is coming from the right side with veloctiy 'v'

⇒ The momentum of the truck coming from right = 3m × (-v)

The negative sign should be considered because the truck coming from the right is moving in the opposite direction to that of truck coming from the left.

Total momentum of Railway truck system before collision = 2mv - 3mv = -mv

Now let us calculate the momentum of this system after the collision :

As both the truck's stick together after the collision, the total mass of the Railway truck system = m + 3m = 4m

But we don't know the velocity with which this combined truck system is moving.

Let us consider the velocity of the combined truck system as : v(don't know)

Momentum of this combined truck system = 4m × v(don't know)

Momentum before collision = Momentum after collision

⇒ mv = 4m × v(don't know)

⇒ v(don't know) = v/4 = 0.25v

Hence the speed of the combined truck system after collison = 0.25v

Answer 2

Concept

A collision is any situation in which two or more objects exert pressures on one another quickly.

Given

speeds given are  2v and v

Find

We need to find the speed of the truck after the colllision  

Solution

By applying equation of collision.

m1u1 + m2u2 = v(m1+m2).

The second object is moving in opposite direction so its momentum is negative. So, we have.

V= m1u1 + (-m2u2)/ m1 + m2

By imputing the data we have;

V = m×2v + (-3m×v)/ m+3m

V= 2mv - 3mv/ 4m

V = -mV/4m

V= -v/4

Hence The speed of the truck after collision is -v/4

#SPJ2