Question

Suppose two equal mass cars traveling with equal speeds in opposite directions inelasticcollide head on and stick together. What fraction of the energy is dissipated

Answer 1

A collision which is inelastic is one in which the internal energy changes.

All the kinetic energy is dissipated

Reasons:

The given parameters are;

The mass of one car = The mass of the second car in the collision = m

The type of collision = Inelastic collision

The speed of each of the cars in the collision = v and -v

Solution:

In an inelastic collision, we have;

$m_1 \cdot v_{1i} + m_2 \cdot v_{2i} = (m_1 + m_2) \cdot v_f$

Therefore, we get;

$m \cdot v_{i} -m \cdot v_{i} = 0= 2 \cdot m \cdot v_f$

Which gives;

$v_f = 0$

The collision is an example of a perfectly inelastic collision, and the final velocity after the collision is zero.

The change in the energy is $\Delta K.E. = K.E._{final} - K.E._{initial}$

$K.E._{initial}$ = 0.5·m·v² + 0.5·m·v² = m·v²

ΔK.E. = 0.5·(2·m)×0 - 0.5·m·v² + 0.5·m·v² = -m·v²

ΔK.E. = -m·v²

The negative sign stands for energy given out, which gives;

The energy dissipated = m·v² (The total initial kinetic energy)

Therefore, all the kinetic energy is dissipated

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