Consider two bodies of masses and moving along the same straight line with initial…

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Linear Momentum · Linear Momentum

Problem

Consider two bodies of masses

m_1

and

m_2

moving along the same straight line with initial speeds

u_1

and

u_2

, respectively. They collide and stick together. (a) Derive an expression for the loss of kinetic energy

\Delta K

in terms of

m_1

m_2

u_1

and

u_2

for this perfectly inelastic collision. (b) Using the derived expression, calculate the loss of kinetic energy when

m_1 = 1.0\,\text{kg}

m_2 = 2.0\,\text{kg}

u_1 = 6.0\,\text{m s}^{-1}

and

u_2 = 2.0\,\text{m s}^{-1}

, both velocities being along the same direction.