Class 11 Physics Laws of Motion Collision of Bodies

Collision of Bodies

Let the two bodies 1 & 2 have momentum p1 & p2 before they collided with each other. After collision their momentum are p1’ and p2’ respectively.

By Newton’s Second law,

F = dp/dt

For 1:  F12 = (p1’ – p1) /∆t

For 2:   F21 = (p2’ – p2) /∆t

By Newton’s Third law,

F 12 = - F21

(p1’ – p1)/∆t = (p2’ – p2) /∆t

(p1’ – p1) = (p2’ – p2)

p1’ + p2’ = p1 + p2

Conclusion: Final momentum of the system = Initial momentum of the system

Problem: A railway truck A of mass 3 * 104 kg travelling at 0.6 m/s collides with another truck B of half its mass moving in the opposite direction with a velocity of 0.4 m/s. If the trucks couple automatically on collision, find the common velocity with which they move.

Solution.

m1 = 3 * 104 kg

m2 = ½ of mass of A = 1.5 * 104 kg

u1 = 0.6 m/s

u2 = -0.4 m/s

Before collision: m1u1 + m2u2 = 3 * 10* 0.6 + 1.5 * 104 * (-0.4)

= 1.2 * 104 kg m/s

After collision: (m1 + m2) v = 4.5 * 104 v kg m/s

As per conservation of momentum,

1.2 * 104   =  4.5 * 104 v

V = 1.2/ 4.5 = 0.27 m/s

Therefore, the common velocity is 0.27m/s

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