Two objects undergo a perfectly inelastic collision. Using conservation of momen

Question

Two objects undergo a perfectly inelastic collision. Using conservation of momentum, derive an expression for the velocity after collision, in terms of the masses and initial velocities (assume that, except collision forces, all other interactions are negligible). Using expression from part (a), calculate the final velocity, if the masses and initial velocities are a follows: m_1 = 3.2 kg, m_2 = 2.5 kg; v_1 = 1.1 m/s, V_2 = -0.85 m/s. Recalculate the final velocity, if V_2 = 0, i.e. the second object is motionless before collision.

Explanation / Answer

elastic collision in one dimension

m1v1+m2v2=m1v'1+m2v'2

m1(v1-v'1)=m2(v2-v'2)

collision is elastic ,kinetic energy would be conserved

1/2m1v12+1/2m2v22=1/2m1v'12+1/2m2v'22

m1(v12-v'12)=m2(v22-v'22)

dividing below equation by above equation

v1+v1'=v2'+v2

for perfectly inelastic collision

final velocity of particle after collision remains the same

let v be the commom velocity after collision

m1v1+m2v2=(m1+m2)v

v=(m1v1+m2v2)/(m1+m2)

PART 2

final Velocity(v)=(3.2*1.1-2.5*.85)/5.7

calculating

1.395/5.7=.2447 m/s

v=.2447m/s

PART3

V2=0

m1=3.2

v1=1.1m/s

calculating

(3.2*1.1)/5.7=

.6175 m/s

v=.6175m/s

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