A white billiard ball with mass m_w = 1.38 kg is moving directly to the right wi

Question

A white billiard ball with mass m_w = 1.38 kg is moving directly to the right with a speed of v = 3.17 m/s and collides elastically with a black billiard ball with the same mass nib = 1 -38 kg that is initially at rest. The two collide elastically and the white ball ends up moving at an angle above the horizontal of 0W = 57 degree and the black ball ends up moving at an angle below the horizontal of theta_b = 33 degree. What is the final speed of the white ball? What is the final need of the black ball? What is the magnitude of the final total momentum of the system? What is the final total energy of the system?

Explanation / Answer

let after collision velocity of white ball = Vw

let after collision velocity of black ball = Vb

as there is no external force in horizontal direction so momentume will conserve

Pi = Pf

as mass of both ball is same = m = 1.38 kg

m ( 3.17 ) = m ( Vw cos57 + Vb cos33)

Vw cos57 + Vb cos33 = 3.17

Vw = (5.82 - 1.54Vb) .........................(1)

energy conservation

KEi = KEf

1/2 m (3.17)2 = 1/2 m (Vb)2 + 1/2 m (Vw)2

(Vb)2 + (Vw)2 = (3.17)2

from eq 1 put Vw = (5.82 - 1.54Vb)

so (Vb)2 + ( (5.82 - 1.54Vb) )2 = (3.17)2

3.37Vb2 - 17.92 + 23.82 =0

Vb = 2.68 m/s ..............ans2

so Vw = (5.82 - 1.54Vb)

Vw = 1.69 m/s    ............ans 1

3) final total momentum = mVw + mVb

Pf= 1.38 ( 2.68 + 1.69)

Pf= 6.03 kg m/s

4) KEf = 1/2 m (Vb)2 + 1/2 m (Vw)2

= 1/2 * 1.38 *{ (Vb)2 + (Vw)2}

=1/2 * 1.38 * (3.17)2

= 6.93 J

answer

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