Question

Two carts are involved in an inelastic collision. Cart A with mass 0.900 kg hits cart B with mass 0.550 kg (initially at rest). The two carts stick together after the collision and continue to move along together. Cart A has an initial velocity of 0.19 m/s
What is the final velocity of the two-cart system?

What is the initial kinetic energy of cart A?

What is the initial kinetic energy of cart B?

What is the final kinetic energy of the system?

Is kinetic energy conserved for inelastic collisions? yes or no

Is momentum conserved for inelastic collisions? yes or no

Answer 1

Answer:

a) $v = 0.118 \frac{m}{s}$, b) $K_{A} = 0.016 J$, c) $K_{B} = 0 J$, d) $K = 0.010 J$, e) No, f) Yes.

Explanation:

a) Final velocity of the two-cart system:

The final velocity can be derived of the momemtum equation associated with the system:

$m_{A} \cdot v_{A} + m_{B} \cdot v_{B} = (m_{A} + m_{B})\cdot v$

$v = \frac{m_{A}\cdot v_{A} + m_{B}\cdot v_{B}}{m_{A}+m_{B}}$

$v = \frac{(0.9 kg)\cdot (0.19 \frac{m}{s} )+(0.550 kg)\cdot (0 \frac{m}{s} )}{0.9 kg + 0.55 kg}$

$v = 0.118 \frac{m}{s}$

b) Initial kinetic energy of cart A:

The kinetic energy is:

$K_{A} = \frac{1}{2} \cdot m_{A} \cdot v_{A}^{2}$

$K_{A} = \frac{1}{2} \cdot (0.9 kg) \cdot (0.19 \frac{m}{s} )^{2}$

$K_{A} = 0.016 J$

c) Initial kinetic energy of cart B:

As the cart B is initially at rest, the kinetic energy is:

$K_{B} = 0 J$

d) Final kinetic energy of the system:

The kinetic energy is

$K = \frac{1}{2}\cdot (m_{A} + m_{B})\cdot v^{2}$

$K = \frac{1}{2} \cdot (0.9 kg + 0.55 kg)\cdot (0.118 \frac{m}{s} )^{2}$

$K = 0.010 J$

e) No. The kinetic energy is not conserved for inelastic collisions since some of the energy is dissipated during the collision.

f) Yes. The momentum for inelastic collisions is conserved due to the absence of external forces.