Two spherical balls of the same size are traveling toward each other along the s

Question

Two spherical balls of the same size are traveling toward each other along the same straight line with the velocities indicated. The mass of ball A is ma -9.0 kg and the mass of ball B is 14.0 kg. Treat the balls as point particles and neglect the effects of friction and drag while answering the following questions. Also, be sure to include the proper sign in your answers to indicate the appropriate direction of velocity. Plane of Contact VA-7.0 m/s VB-11.0 m/s Line of Impact Part A: Assuming the collision between balls A and B is perfectly elastic (e-1) calculate the final velocity of each ball. How much energy is lost during the collision in [J] Gjoules)?

Explanation / Answer

given data

u1 = 7 m/s

u2 = -11 m/s

a) from the relations

final speed of the objects are

v1 = (m1-m2/m1+m2)u1+2m2u2/(m1+m2)

v1 = (9-14/9+14)7-2*14*11/(9+14)

v1 = -14.9 m/s

v2 = (m2-m1)u2/(m1+m2)+2m1u1/(m1+m2)

v2 = -(14-9)*11/23+2*9*7/23

v2 = 3.09 m/s

b) initial kinetic energy

ki = 1/2m1u1^2+1/2m2u2^2 = 1/2*9*7^2+1/2*14*11^2 = 1067.5 J

final kinetic enegy

kf = 1/2m1v1^2+1/2m2v2^2 = 1/2*9*14.9^2+1/2*14*3.09^2 = 1066 J

in an elestic collison energy and momentum are also conserved

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