Question

Two objects of masses 100g and 200g are moving along the same line and direction with velocities of 2mf 1 and

·1ms-

1 respectively. They collide and after the collision, the first object moves at a velocity of 1.67mf1

. Determine

the velocity of the second object. ​

Answer 1

Given :

• Mass of object 1 = 100 g = 0.1 kg
• Mass of object 2 = 200 g = 0.2 kg
• Velocity of object 1 = 2 m/s
• Velocity of object 2 = 1 m/s
• After collision velocity of object 1 = 1.67 m/s

To find :

• Velocity of object 2 after collision

According to the question,

➞ Momentum of first object (Before collision) = Mass of first object × Velocity of first object

➞ p = m × v

➞ p = 0.1 kg × 2 m/s

➞ p = 0.2 kg m/s

So,the momentum of first object before collision is 0.2 kg m/s.

➞ Momentum of second object (Before collision) = Mass of second object × Velocity of second object

➞ p = m × v

➞ p = 0.2 kg × 1 m/s

➞ p = 0.2 kg m/s

So,the momentum of second object before collision is 0.2 kg m/s.

➞ Total momentum before collision = 0.2 + 0.2

➞ Total momentum before collision = 0.4 kg m/s

➞ Momentum of first object (After collision) = Mass of first object × Velocity of first object

➞ p = m × v

➞ p = 0.1 kg × 1.67 m/s

➞ p = 0.167 kg m/s

So,the momentum of first object after collision is 0.167 kg m/s.

➞ Momentum of second object (After collision) = Mass of second object × Velocity of second object

➞ p = m × v

➞ p = 0.2 kg × v

➞ p = 0.2v kg m/s

So,the momentum of second object after collision is 0.2v kg m/s.

According to law of conservation of momentum,

➞ Total momentum before collision = Total momentum after collision

➞ 0.4 = 0.167 + 0.2v

➞ 0.2v = 0.4 - 0.167

➞ 0.2v = 0.233

➞ v = 0.233 ÷ 0.2

➞ v = 1.165 m/s

So,the velocity of second object after collision is 1.165 m/s.