Loss in Kinetic Energy during Perfectly Inelastic Collision – Rankers Physics
Topic: Center of Mass , Momentum and Collision
Subtopic: Collision

Loss in Kinetic Energy during Perfectly Inelastic Collision

A metal ball of mass $2\text{ kg}$ moving with speed of $36\text{ km/h}$ has a head on collision with a stationary ball of mass $3\text{ kg}$. If after collision, both the balls move as a single mass, then the loss in K.E. due to collision is:

(1997)

$100\text{ J}$
$140\text{ J}$
$40\text{ J}$
$60\text{ J}$

Solution:

Initial kinetic energy $K_i = \frac{1}{2}m_1 u_1^2 = 100\text{ J}$ (with $u_1 = 10\text{ m/s}$). Final velocity $v = \frac{m_1 u_1}{m_1+m_2} = 4\text{ m/s}$, and final kinetic energy $K_f = \frac{1}{2}(m_1+m_2)v^2 = 40\text{ J}$. Loss in K.E. = $100 - 40 = 60\text{ J}$.

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