Billiards Balls
Collision between two billiard balls speeds?
Two billiard balls, of equal mass, collide as shown in the figure below. Ball 1 is initially traveling along x with a speed of 14 m/s, and ball 2 is at rest. After the collision, ball 1 moves away with a speed of 7.0 m/s at an angle = 59.
What is the speed of ball 2 after the collision?
What is the angle made with the positive x axis, measured counterclockwise?
Well the important thing you need to know is that momentum is conserved because the collision is considered to be elastic.
The initial momentum in the x direction is the mass M of the first ball times 14 m/s. The momentum in the x direction after the collision must be the same. It can be calculated by adding the momentum of the two balls in the x direction. M * 7 cos 59 + M * V(Velocity of mall 2) cos (Theta)(angle of ball 2)
Similarly the momentum in the y direction is conserved which is zero because ball 1 is moving solely in the y direction. M * 7 sin (59) + M * V sin (theta) =0.
Now there are two equations and two unknowns(V & Theta)
The equations are:
M * 7 cos(59) + M * V cos(theta) = M * 14
M * 7 sin (59) + M * V sin(theta) = 0
solve equation 1 to get:
Equation 3
V cos(theta) = 14 – 7 cos (59)
solve equation 2 to get:
Equation 4
V sin (theta) = -7 sin (59)
Divide equation 4 by equation 3 to remove one of the two variables(V) to get:
Equation 5
Tan (theta) = ((-7 * sin (59))/ (14 – 7 cos (59))
theta = arc tan (((-7 * sin (59))/ (14 – 7 cos (59)))
Back substituting theta into equation 4
V = (-7 * sin(59))/ (sin (theta))
Stevie star regurgitation.. billiard ball, and goldfish!
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