Answer the following questions related to collisions in one dimension:

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

Problem

Answer the following questions related to collisions in one dimension: (i) Define a perfectly inelastic collision. (ii) Two bodies of masses

m_1

and

m_2

move with velocities

v_{1i}

and

v_{2i}

along the same straight line and stick together after impact. Derive an expression for their common velocity

v_f

just after the collision in terms of

m_1, m_2, v_{1i}

and

v_{2i}

. (iii) Using the result of part (ii), show that the loss in kinetic energy during such a collision is

\Delta K=\frac{m_1m_2\,(v_{1i}-v_{2i})^{2}}{2\,(m_1+m_2)}.

Explain briefly why this loss must always be positive for

v_{1i}\neq v_{2i}