Two identical balls A and B lie on a smooth horizontal surface, which gradually merges into a curve to a height 3.2 m. Ball A is given a velocity of 10 m/s, it collides head-on with ball B, which then takes up the curved path. The minimum cofficient of restitution e for the collision between A and B, in order that ball B reaches the highest point C of the curve is (g = 10 m/s2) :

Engineering

Physics

Conservation of Energy

Collision

Question

Two identical balls A and B lie on a smooth horizontal surface, which gradually merges into a curve to a height 3.2 m. Ball A is given a velocity of 10 m/s, it collides head-on with ball B, which then takes up the curved path. The minimum cofficient of restitution e for the collision between A and B, in order that ball B reaches the highest point C of the curve is (g = 10 m/s²) :

$\frac{3}{4}$

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{3}{5}$

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$\frac{1}{2} {mV}_{2}^{2} = mgh \Rightarrow V_{2} = \sqrt{2 gh} = \sqrt{2 \times 10 \times 3.2} = 8 m / s$

m × 10 + m × 0 = m × V₁ + mV₂
V₁ = 2 m/s

$e = \frac{V_{2} - V_{1}}{10 - 0} = 0.6$ .