Blocks A and B are moving toward each other on a horizontal, frictionless surfac

Question

Blocks A and B are moving toward each other on a horizontal, frictionless surface. Block A has a mass of 2.7 kg and a velocity of 32 m/s, while B has a mass of 4 kg and a velocity of 25 m/s. They suffer a completely inelastic head-on collision.

(a) What is the total linear momentum of the two-block system after the collision? Indicate the direction with the sign of your answer.
kg•m/s

(b) What is the velocity of the two-block system after the collision? Indicate the direction with the sign of your answer.

Explanation / Answer

a)The momentum of the system remains conserved. So the intial momentum of the system and final are equal.

Pi = Pf

Pi = Ma Va + Mb Vb  

Pi = 2.7 x 32 + 4 x -25 = -13.6 kg-m/s

Hence, Pi = -13.6 kg-m/s

b)from conservation of momentun

Pi = Pf

Ma Va + Mb Vb = (Ma + Mb) Vf

Vf = (Ma Va + Mb Vb)/(Ma + Mb)

Vf = (2.7 x 32 - 4 x 25 )/(2.7 + 4) = -2.03 m/s

Hence, Vf = -2.03 m/s

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