- Books Name
- Science Made Easy Science Book
- Publication
- Science Made Easy
- Course
- CBSE Class 9
- Subject
- Science
Law of Conservation of Momentum
→ When two (or more) bodies act upon one another, their total momentum remains constant (or conserved) provided no external forces are acting.
• Initial momentum = Final momentum
Suppose, two objects A and B each of mass m1 and mass m2 are moving initially with velocities u1 and u2, strike each other after time t and start moving with velocities v1 and v2 respectively.
Now, Initial momentum of object A = m1u1
Initial momentum of object B = m2u2
Final momentum of object A = m1v1
Final momentum of object B = m2v2
So, Rate of change of momentum in A,
F1 = (m1v1 - m1u1)t = m1(v1 - u1)/t ....(i)
Rate of change of momentum in B,
F2 = (m2v2 – m2u2)t = m2(v2 - u2)/t ....(ii)
We know from 3rd law of motion,
F1 = −F2
So, m1(v1 - u1)/t = - m2(v2 - u2)/t
⇒ m1v1 – m1u1 = -m2v2 + m2u2
⇒ m1u1 + m2u2 = m1v1 + m2v2
Thus, Initial momentum = Final momentum
Example 1: A bullet of mass 20 g is fired horizontally with a velocity of 150 m/s from a pistol of mass 2 kg. Find the recoil velocity of the pistol.
Solution
Given, Mass (m1) of bullet = 20 g = 0.02 kg
Mass (m2) of pistol = 2 kg
Initially bullet is inside the gun and it is not moving.
∵ Mass = m1+m2 = (0.02 + 2) kg = 2.02 kg
and u1 = 0
∴ Initial momentum = 2.02 × 0 = 0 ....(i)
Let the velocity of pistol be v2 and v1 for bullet = 150
∴ Final momentum = m1v1 + m2v2 = 0.02×150 + 2v2 ...(ii)
We know that,
Initial momentum = Final momentum
∴ (0.02×150)/100 + 2v2 = 0 [From equations (i) and (ii)]
⇒ 3 + 2v2 = 0
⇒ 2v2 = −3
⇒ v2 = −1.5 m/s
(−)ve sign indicates that gun recoils in direction opposite to that of the bullet.
Example 2: Two hockey players viz A of mass 50 kg is moving with a velocity of 4 m/s and another one B belonging to opposite team with mass 60 kg is moving with 3 m/s, get entangled while chasing and fall down. Find the velocity with which they fall down and in which direction?
Solution
Given,
mA = 50 kg, uA = 4 m/s
mB = 60 kg, uB = 3 m/s
Initial momentum A = mAuA = 50 × 4 = 200 kgm/s
Initial momentum B = MBuB = 60 × 3 = 180 kgm/s
∴ Total initial momentum = 200 + 180 = 380 kgm/s ....(i)
Final momentum = (mA + mB)v = (50 + 60)v = 110v ....(ii)
According to the law of conservation of momentum,
380 = 110v
⇒ v = 380/110 = 3.454 m/s