A white billiard ball with mass m w = 1.3 kg is moving directly to the right wit

Question

A white billiard ball with mass mw = 1.3 kg is moving directly to the right with a speed of v = 3.44 m/s and collides elastically with a black billiard ball with the same mass mb = 1.3 kg that is initially at rest. The two collide elastically and the white ball ends up moving at an angle above the horizontal of ?w = 62° and the black ball ends up moving at an angle below the horizontal of ?b = 28°.

1)

What is the final speed of the white ball?

2)

What is the final speed of the black ball?

3)

What is the magnitude of the final total momentum of the system?

4)

What is the final total energy of the system?

Explanation / Answer

here,

mw = 1.3 kg

initial speed of white ball , uw = 3.44 m/s

mb = 1.3 kg

theta w = 62 degree

thetab = 28 degree

let the final speed of the white ball be vw and the blck ball be vb

uisng conservation of momentum in x direction

mw* uw = mw*vw*cos(thetaw) + mb*vb*cos(thetab)

3.44 = vw*cos(62) + vb*cos(28) ......(1)

using conservation of momentum in y direction

mw*vw*sin(thetaw) - mb*vb*sin(thetab) = 0

vw*sin(62) - vb*sin(28) = 0 ...(2)

vw = 1.61 m/s

vb = 3.04 m/s

1)

the final speed of the white ball is 1.61 m/s

2)

the final speed of the black ball is 3.04 m/s

3)

final total momentum Pf = Pi = mw * uw

Pi = 4.47 kg.m/s

the final momentum is 4.47 kg.m/s

4)

final total energy , KEf = KEi = 0.5 * mw*uw^2

KEf = 7.69 J

the final total energy of the system is 7.69 J

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