A 4 kg mass is projected towards 1 kg mass with a velocity 10 m/s. All collisions are elastic and all surfaces are smooth. How many total collisions occur between the two blocks?

Engineering

Physics

Collision

Question

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4 × 10 = 4v₄ + v₁

$1 = \frac{v_{1} - v_{4}}{10}$

–(v₁ – v₄ = 10)
v₁ + 4v₄ = 40

__________________

5v₄ = 30
v₄ = 6 m/s
v₁ = 16 m/s
4 × 6 – 16 × 1 = 4v₄ + 1v₁

$e = 1 = \frac{v_{1} - v_{4}}{22}$

8 = 4v₄ + v₁
4 × 22 = v₁ – v₄
v₁ = 19.2 ⇒ v₄ = –2.8

$e = \frac{v_{4} - v_{1}}{16 .4} = 1$

4 × 2.8 + 1 × 19.2 = 4v₄ + 1v₁
30.4 = 4v₄ + v₁
16.4 = v₄ – v₁
_________________
46.8 = 5v₄
v₄ = 9.36 m/s
v₁ = –7.04 m/s

Total 3 collisions.