The 1kg cart starts rolling without friction from rest at position and subsequently strikes the 3kg block as shown in Figure. Block B is connected to point O with a light rigid rod, which can rotate around O. The coefficient of restitution for the collision is e = 0.7, determine approximately the speed of block (in m/s) when it is at a height of 1.1 m above the ground. Neglect friction.

Engineering

Physics

Conservation of Energy

SHM of Simple Pendulum

Collision

Question

The 1kg cart starts rolling without friction from rest at position and subsequently strikes the 3kg block as shown in Figure. Block B is connected to point O with a light rigid rod, which can rotate around O. The coefficient of restitution for the collision is e = 0.7, determine approximately the speed of block (in m/s) when it is at a height of 1.1 m above the ground. Neglect friction.

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$\frac{1}{2} \times 1 \times u^{2} = 1 \times 10 \times 7 .2$

⇒ u = 12 m/s

1 × 12 + 3 × 0 = 1 × v₁ + 3 × v₂

$\frac{v_{2} - v_{1}}{12} = 0 .7 \Rightarrow v_{2} - v_{1} = 8 .4$

12 = 4v₂ 8.4 ⇒ v₂ = 5.10 m/s

$\frac{1}{2} m (5 .1)^{2} - mg (1 .1) = \frac{1}{2} {mv}^{2} \Rightarrow v = 2 m / s$