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Conservation of momentum – Example

Consider two clay balls moving towards each other. The first ball has a mass of 100 gm and a velocity of 15 cm/s moving. The second ball has a mass of 150 gm and a velocity of 20 cm/s moving. On collision, the two balls stick to each other and become one object. In which direction and with what velocity will the combined lump move after collision?

Solution:

We have derived the conservation of momentum equation for two objects colliding with each other. It is given as:

m1v1 + m2v2 = m1u1 + m2u2

Total momentum after the collision = Total momentum before the collision

In our frame of reference, we will consider the right side as positive and the left as negative. Also, we will assume that the first ball is moving towards the left and the second towards the right.

The data that we have is as below:

m1 = 100gm u1 = 15 cm/s

m1 = 150gm u1 = −20 cm/s (The negative sign is because the ball is moving towards the left.)

Since after collision, the two balls become one, the velocity at which they will move after the collision will be the same.

Hence,

v1 = v2 = v

So, we can write the law of momentum equation for the two balls as:

m1v + m2v = m1u1 + m2u2 Substituting the values of m1, m2, u1 and u2 in the above equation gives:

100v + 150v = (100 X 15) + (150 X −20)

Here ‘v’ is the velocity at which the lump moves.

Solving the equation gives:

250v = 1500 – 3000

250v = −1500

v = −6

The value of ‘v’ is −6 cm/s or −0.06m/s. The negative sign tells us that the combined lump will move in

the direction of the second ball at a velocity of 0.06 m/s.