A white billiard ball with mass m w = 1.25 kg is moving directly to the right wi

Question

A white billiard ball with mass mw = 1.25 kg is moving directly to the right with a speed of v = 3.21 m/s and collides elastically with a black billiard ball with the same mass mb = 1.25 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 = 30 A white billiard ball with mass mw = 1.25 kg is moving directly to the right with a speed of v = 3.21 m/s and collides elastically with a black billiard ball with the same mass mb = 1.25 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 = 30 A white billiard ball with mass mw = 1.25 kg is moving directly to the right with a speed of v = 3.21 m/s and collides elastically with a black billiard ball with the same mass mb = 1.25 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 = 30 degree and the black ball ends up moving at an angle below the horizontal of ?b = 60 degree . What is the final speed of the white ball? What is the final speed of the black ball? What is the final total energy of the system?

Explanation / Answer

Let the final speed of white bal be vw and black ball be vb

so vw (vector ) = vwcos 30 i^ + vw sin 30 j^
= 0.5 * vw * root(3) i^ + 0.5*vw j^

vb ( vector ) = vb cos 60 i^ - vw sin 60 j^
= 0.5*vbi^ - 0.5*vb root(3) j^

conserving momentum aloing y direction
0.5*vw - 0.5*vb root(3) = 0

so... vb = vw / root(3)

conserving momentum along x direction

1.25 * 3.21 = 1.25 * ( 0.5 * vw * root(3) ) + 1.25 * ( 0.5*vb )

so.. vw root(3) + vw / root(3) = 6.42

so... 4 vw = 6.42 * root(3)

so vw = 2.7799 m/sec

so.. a) final speed of white ball = 2.7799 m/sec

b) final speed of black ball = vw / root(3) = 2.7799/root(3) = 1.605 m/sec

c) final total energy of the system
= 0.5*1.25*( 2.7799^2 + 1.605^2 ) = 6.4399 J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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