A 0.850 kg air-track glider moving at 1.75 m/s bumps into a 1.45 kg glider initially at rest. Find the total kinetic energy after an inelastic collision and an elastic collision.

Answer 1

In both cases (inelastic and elastic) you have conservation of momentum as long as the external net force is zero.

With an elastic collision, kinetic energy is also conserved, meaning that the total kinetic energy is the same as it was before the collision.

This means that KE_elastic = m_a*v_a² / 2 + m_b*v_b² / 2, with v_b = 0 m/s (before the collision), so only the first glider contributes to the total KE (before the collision).

In the case of an inelastic collision, KE is NOT conserved, some of it has transferred to another form of energy (bonding, heat, sound, deformation,...).

To be able to put a number on it with the data we have, I will assume it is a perfect inelastic collision (they stick together after colliding).

In that case, we'll use conservation of momentum to calculate the velocity of both gliders after the collision:

p_after = p_before (note that momentum and velocity are vector quantities, KE is a scalar quantity)

(m_a + m_b)v_a+b = m_av_a + m_bv_b, again with v_b = 0 m/s.

KE_inelastic = (m_a + m_b)v_a+b² / 2

With v_a+b = m_av_a / (m_a + m_b)

KE_inelastic = m_a²v_a² / (m_a + m_b)