A white billiard ball with mass mw = 1.37 kg is moving directly to the right wit
ID: 1459590 • Letter: A
Question
A white billiard ball with mass mw = 1.37 kg is moving directly to the right with a speed of v = 3.12 m/s and collides elastically with a black billiard ball with the same mass mb = 1.37 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 = 50° and the black ball ends up moving at an angle below the horizontal of b = 40°. What is the final speed of the white ball? What is the final speed of the black ball? What is the final speed of the black ball? What is the final total energy of the system?
Explanation / Answer
mw =1.37 kg , u1x =3.12 m/s,u1y =0, mb =1.37 kg, u2 =0
w = 50°, b = 40°
v1x =v1 cos(50) = 0.643 v1
v1y =v1 sin(50) = 0.766 v1
v2x =v2 cos(40) = 0.766 v2
v2y = -v2 sin(40) = -0.643 v2
From conservation of momentum along x-direction
m1u1+m2u2 =m1v1x+m2v2x
u1 =v1x+v2x
3.12 = 0.643v1+0.766v2 ..(1)
From conservation of momentum along y-direction
m1uy+m2uy =m1v1y+m2v2y
0 =v1y+v2y
0 = 0.766v1 -0.643v2 ...(2)
By solving (1) and (2) we get
Final speed of white ball v1 = 2 m/s
Final speed of black ball v2 = 2.4 m/s
In elastic collision Kf =Ki
Kf = (1/2)m1u1^2+(1/2)m2u2^2
Kf = (1/2)(1.37*3.12*3.12) +0
Final total energy of system is Kf = 6.67 J
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