Consider two particles of masses and confined to a horizontal frictionless plane

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

Consider two particles of masses

m_1

and

m_2

confined to a horizontal frictionless plane. Particle 1, with initial speed

u

, moves along the

+x

-direction and strikes particle 2 which is initially at rest. The collision is perfectly elastic. (a) Derive the expressions for the components of the final velocities

v_{1x}

v_{1y}

v_{2x}

, and

v_{2y}

in terms of

m_1

m_2

, and

u

. (b) Hence, derive expressions for the scattering angles

\theta

(for particle 1) and

\phi

(for particle 2) measured from the

+x

-axis. (c) Show that

\tan\theta\,\tan\phi = \frac{m_2}{m_1}

. (d) Using the results of part (a), prove explicitly that the total kinetic energy is conserved during the collision.

Related theory

Collisions
Linear momentum
Elastic and inelastic collisions
Collisions in two dimensions
Work, Energy and Power

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