Question

12.Two objects, each of mass 1 kg, are moving in the same straight line but in opposite directions. The velocity of each object is 1 ms-1 before the collision during which they stick together. What will be the velocity of the combined object after collision?
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Answer 1

Working out:

In the above question, we have find the final velocity of the combined objects when we are providing with their mass and initial velocities. This can be done by conservation of momentum law.

According to Law of conservation of momentum:

It states that the momentum of an isolated system remains constant. It means initial momentum = Final momentum.

Let us see the parameters given:

• Mass of object 1 before collision = 1 kg
• Mass of object 2 moving in opposite direction before collision = 1 kg
• Velocity of object 1 before collision = 1 m s-¹
• Velocity of object 2 moving in opposite direction before collision = -1 m s-¹

After collision,

❒ Object 1 sticks to object 2

So, the total mass of the objects = m1 + m2

⇛ Total mass = 1 kg + 1 kg

⇛ Total mass = 2 kg

So,

Let us consider that the velocity of the combination becomes v. Then, according to the law of conservation of momentum,

• Total momentum before collision = Total momentum after collision

This can be written as,

⇛ m1v1 + m2v2 = (m1 + m2)v

⇛ 1 kg × 1 m/s + 1 kg × -1 m/s = 2 kg × v

⇛ 1 kg m/s - 1 kg m/s = 2 kg × v

⇛ 0 kg m/s = 2 kg × v

Flipping it,

⇛ v = 0 kg m/s / 2 kg

⇛ v = 0 m/s

So, the final velocity of the objects sticking with each other after collision would be:

$\huge{ \boxed{ \bf{ \red{0 \: m {s}^{ - 1} }}}}$

It is because they are having equal mass and same initial velocity which are opposite to each other.

And we are done !!

Answer 2

Answer:

✒Here we Go !

✒Given:-

•Equal mass of two objects(m1 and m2)

which are moving in same line but in

opposite directions is=2.5kg

•Equal initial velocity(u1 and u2) of the

objects=4.5m/s

✒To find:-

•Velocity of the combined object after

collision.

✒Solution:-

In this case,we can see that the objects are moving in opposite directions. So if we take u1 as +ve,we have to take u2 as -ve.

Thus,u1= +4.5m/s

u2= -4.5m/s

Let the velocity of the combined object after

collision be v.

$\red{ \sf{By \: using \: Law \: of \: Conservation \: of \: momentum \: we \: get:-}}</p><p>$

=>m1u1+m2u2 = (m1+m2)v

=>2.5(4.5)+2.5(-4.5) = (2.5+2.5)v

=>0=5v

=>v=0/5

=>v=0

So, the final velocity of the objects sticking with each other after collision would be:

0ms-1

It is because they are having equal mass and same initial velocity which are opposite to each other.

Thus,velocity of the combined object after collision is 0. It means after collision,both the masses will come to rest.