A particle A of mass is moving on a perfectly smooth horizontal table with speed…

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

Problem

A particle A of mass

m

is moving on a perfectly smooth horizontal table with speed

u

along the positive

x

-axis. It collides elastically with an identical particle B that is initially at rest at the origin of the coordinate system fixed on the table. Immediately after the impact the two particles move away making angles

\theta

and

\phi

respectively with the original direction of motion of A. (i) Obtain the two independent scalar equations that relate the components of linear momentum of the system before and after the collision. (ii) Using the result of part (i) together with the fact that the collision is elastic, prove that

\theta+\phi=90^{\circ}

. (iii) Derive expressions for the magnitudes

v_1

and

v_2

of the velocities of particles A and B after the collision in terms of

u

only. (iv) If particle A is observed to scatter through

30^{\circ}

to the original line of motion, calculate the numerical values of

v_1

and

v_2

. (Leave the answers in terms of

u

if necessary.)

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