COLLEGE PHYSICS
COLLEGE PHYSICS
2nd Edition
ISBN: 9781711470832
Author: OpenStax
Publisher: XANEDU
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Chapter 8, Problem 38TP
To determine

Initial and final momentum and kinetic energy, and to check whether momentum is conserved or not, and whether the collision is elastic or inelastic.

Expert Solution & Answer
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Answer to Problem 38TP

Initial momentum of body is 5.0kgm/s.

Final momentum of body is 5.0kgm/s.

Initial kinetic energy is 4.165J.

Final kinetic energy is 4.165J.

The momentum is conserved.

The collision is elastic.

Explanation of Solution

Given:

The positions of two objects before and after collision are depicted in the following figure.

  COLLEGE PHYSICS, Chapter 8, Problem 38TP

  Figure (1)

Mass of object A, m1=1.0kg.

Mass of object B, m2=3.0kg.

Formula used:

Velocity of object from the figure is calculated as,

  v=s2s1t2t1

Initial momentum is calculated as,

  pi=maua+mbub

Final Momentum is calculated as,

  pf=mava+mbvb

Initial kinetic energy is calculated as,

  K.Ei=12ma(ua)2+12mb(ub)2

Final kinetic energy is calculated as,

  K.Ef=12ma(va)2+12mb(vb)2

Change in momentum is calculated as,

  Δp=pfpi

Change in kinetic energy is calculated as,

  ΔK.E=K.EfK.Ei

Calculation:

Initial velocity of object A, ua is calculated as,

  ua=s2s1t2t1=1.5m0m0.6s0s=2.5m/s

Initial velocity of object B, ub is calculated as,

  ub=s2s1t2t1=2.01.5m0.60s=0.83m/s

Final velocity of object A, va is calculated as,

  va=s2s1t2t1=1.50m1.20.6s=2.5m/s

Final velocity of object B, vb is calculated as,

  vb=s2s1t2t1=2.0m1.5m1.2s0.6s=0.83m/s

Initial momentum is calculated as,

  pi=maua+mbub=(1.0kg)(2.5m/s)+(3.0kg)(0.83m/s)=(2.5+2.5)kgm/s=5.0kgm/s

Final Momentum is calculated as,

  pf=mava+mbvb=(1.0kg)(2.5m/s)+(3.0kg)(0.83m/s)=(2.5+2.5)kgm/s=5.0kgm/s

Initial kinetic energy is calculated as,

  K.Ei=12ma( u a)2+12mb( u b)2=12(1.0kg)(2.5m/s)2+12(3.0kg)(0.83m/s)2=3.125+1.04J=4.165J

Final kinetic energy is calculated as,

  K.Ef=12ma( v a)2+12mb( v b)2=12(1.0kg)(2.5m/s)2+12(3.0kg)(0.83m/s)2=3.125+1.04J=4.165J

Change in momentum is calculated as,

  Δp=pfpi=(5.0kgm/s)(5.0kgm/s)=0

Change in kinetic energy is calculated as,

  ΔK.E=K.EfK.Ei=(4.165J)(4.165J)=0

Conclusion:

Initial momentum of body is 5.0kgm/s.

Final momentum of body is 5.0kgm/s.

Initial kinetic energy is 4.165J.

Final kinetic energy is 4.165J.

The change in initial and final momentum is zero. Therefore, the momentum is conserved.

The change in initial and final kinetic energy is zero. Therefore, the collision is elastic in nature.

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