2. Two balls of equal mass m =1kg collide and stick together as shown in the fig

Question

2.       Two balls of equal mass m =1kg collide and stick together as shown in the figure. The initial velocity of ball B is 12 m/s and that of ball A is 6 m/s.

Two balls of equal mass m =1kg collide and stick together as shown in the figure. The initial velocity of ball B is 12 m/s and that of ball A is 6 m/s. Calculate the velocity (magnitude and direction) of the motion of mass A + B after the collision. 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?

Explanation / Answer

1)applying conservation of momentum equations in x and y directions we have

m1u1 x cosA + m2u2 x cosB = (m1 + m2) x V x cosC ----------(1)

and m1u1 x sinA + m2u2 x sinB = (m1 + m2) x V x sinC -------------(2)

where m1 = m2 = 1 kg,u1 = 6 m/s,u2 = 12 m/s,A = 120o and B = 240o,V is the common velocity of the combined mass after collision and C is the angle made by the mass

solving equations (1) and (2) for V and C

2)the ratio is

(Ef/Ei) = [(1/2) x (m1 + m2) x V^2/(1/2) x m1u1^2 + (1/2) x m2u2^2)]

the collision is inelastic,as the two masses stick together after the collision

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