On a smooth billiard table, Ball X (mass ) is struck so that it moves with speed at…

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

Problem

On a smooth billiard table, Ball X (mass

0.20\,\text{kg}

) is struck so that it moves with speed

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

at an angle of

30^{\circ}

above the

+x

-axis. Simultaneously, Ball Y (mass

0.25\,\text{kg}

) moves with speed

1.5\,\text{m\,s}^{-1}

at an angle of

150^{\circ}

measured from the

+x

-axis. The balls collide and afterward are observed moving at the following velocities: • Ball X:

1.0\,\text{m\,s}^{-1}

75^{\circ}

• Ball Y:

1.8\,\text{m\,s}^{-1}

20^{\circ}

(The angles are measured in the same coordinate system; assume the

+x

-axis points to the right and the

+y

-axis points upward.) Neglect rolling resistance and spin effects. (a) Resolve the initial momentum of each ball into

x

and

y

components, and determine the total linear momentum components of the system just before the collision. (b) Repeat the calculations in part (a) for the instant immediately after the collision. Comment quantitatively on whether linear momentum was conserved. (c) Calculate the total kinetic energy of the two-ball system before and after the collision. Determine the percentage change and classify the collision. (d) Provide a brief physical explanation for how kinetic energy could decrease even though the vector sum of momenta remains (to experimental precision) unchanged.

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