Two balls of equal mass collide and stick together as shown in the figure. The i
ID: 1902221 • Letter: T
Question
Two balls of equal mass collide and stick together as shown in the figure. The initial velocity of ball B is twice that of ball A. (Take ? = 48?.) (a) Calculate the angle above the horizontal of the motion of mass A + B after the collision. (b) What is the ratio of the final velocity of the mass A + B to the initial velocity of ball A, vf/vA? (c) What is the ratio of the final energy of the system to the initial energy of the system, Ef/Ei? Is the collision elastic or inelastic? elastic inelastic
Explanation / Answer
(a) x: mvAx+m2vAx = 2mvfx 3vAx=2vfx, vfx = 3/2 vAx y: -mvAy+m2vAy = 2mvfy vfy = 1/2 vAy tangents give needed ratios of y components over x components tan thetaf = vfy/vfx = 1/3 vAy/vAx tan theta = vAy/vAx thetaf = tan-1 ( 1/3 tan (56) ) = 26.3deg (b) vfy = vf sin thetaf vAy = vA sin thetai vf/vA = vfy/vAy sin(thetai)/sin(thetaf) = 1/2 sin(56)/sin(26.3) = 0.94 (c) Ef/Ei = (1/2 * (2m) * (vf)^2) / [ (1/2 * m * (vA)^2) + 1/2*m*(2vA)^2) ] 2vf^2 / 5vA^2 = 0.35