Two balls of equal mass collide and stick together as shown in the figure. The i

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 ? = 40.)

(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

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 ? = 40½.) (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 theta f = vfy/vfx = 1/3 vAy/vAx tan theta = vAy/vAx theta f = tan-1 ( 1/3 tan (40) ) = 15.6 deg (b) vfy = vf sin thetaf vAy = vA sin thetai vf/vA = vfy/vAy sin(thetai)/sin(thetaf) = 1/2 sin(40)/sin(15.6) = 1.193 (c) Ef/Ei = (1/2 * (2m) * (vf)^2) / [ (1/2 * m * (vA)^2) + 1/2*m*(2vA)^2) ] =2vf^2 / 5vA^2 = 0.5693

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