A white billiard ball with mass m_w = 1.6 kg is moving directly to the right wit

Question

A white billiard ball with mass m_w = 1.6 kg is moving directly to the right with a speed of v = 2.97 m/s and collides elastically with a black billiard ball with the same mass mb = 1.6 kg that is initially at rest. The two collide elastically and the white ball ends up moving at an angle above the horizontal of theta_W = 46degree and the black ball ends up moving at an angle below the horizontal of theta_b = 44degree. What is the final speed of the white ball? What is the final speed 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

by conservation of momentum

initial horizontal momentum = final horizontal momentum

mw * v + 0 = mw * v1 * cos(46) + mb * v2 * cos(44)

v = v1 * cos(46) + v2 * cos(44)

2.97= v1 * cos(46) + v2 * cos(44)

initial vertical momentum = final vertical momentum

0 = mw * v1 * sin(46) - mb * v2 * sin(44)

0 = v1 * sin(46) - v2 * sin(44)

on solving we'll get

v1 = 2.06 m/s

v2 = 2.14m/s

after collision velocity of white ball = 2.06m/s

after collision velocity of black ball = 2.14 m/s

final momentum magnitude = initial momentum = mw*vw = 1.6*2.97 = 4.752 Kgm/s

toatl energy final = energy initial = 1/2*mw*v^2 = 1/2*1.6*2.97^2 = 7.05672 J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.