Question

Croquet ball A moving at 8.3 m/s makes a head on collision with ball B of equal mass and initially at rest. Immediately after the collision ball B moves forward at 6.4 m/s .

What fraction of the initial kinetic energy is lost in the collision?

Answer 1

Answer:

0.25

Explanation:

That is the right answer.

Answer 2

The fraction of the initial kinetic energy is lost in the collision is 35.3%.

The given parameters:

• Initial velocity of ball A = 8.3 m/s
• Initial velocity of ball B = 0
• Final velocity of ball B = 6.4 m/s

The initial kinetic energy of the system collision is calculated as follows;

$K.E_i = \frac{1}{2} mv_1_i^2 + \frac{1}{2} mv_2_i^2\\\\K.E_i = \frac{1}{2} (m)(8.3)^2 + \frac{1}{2} (m) (0)^2\\\\K.E_i = 34.445 m$

The final velocity of ball A after collision is calculated as follows;

$u_1 + v_1 = u_2 + v_2\\\\8.3 + v_1 = 0 + 6.4\\\\v_1 = 6.4 - 8.3\\\\v_1 = -1.9 \ m/s$

The final kinetic energy of the system after collision is calculated as follows;

$K.E_f = \frac{1}{2} m(-1.9)^2 + \frac{1}{2} m(6.4)^2\\\\K.E_f = 22.285 \ m$

The fraction of the initial kinetic energy is lost in the collision is calculated as follows;

$= \frac{K_i - K_f}{K_i} \\\\= \frac{34.445 - 22.285}{34.445} \\\\= 0.353\\\\= 35.3\%$

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