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Analyzing Collisions: Momentum Conservation and Kinetic Energy Loss in Inelastic and Elastic Collisions

This detailed analysis explores the principles of momentum and kinetic energy in both inelastic and elastic collisions. The examples provided illustrate how momentum is conserved, but kinetic energy may be lost in inelastic collisions. By evaluating scenarios involving cars and freight, we illustrate the calculations of before and after collision states. Key questions answered include whether momentum and energy are conserved in different types of collisions, supported by numerical examples. This foundational understanding is crucial in physics and engineering applications.

shannon-christian
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Analyzing Collisions: Momentum Conservation and Kinetic Energy Loss in Inelastic and Elastic Collisions

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  1. Analyzing Collisions Section 11.2 pg. 262-265

  2. Momentum is conserved. Kinetic energy is lost. Inelastic Before Car 1 m=2000 kg vi=16m/s Car 2 m =2000kg vi=0 After Bumpers lock m=4000kg vf=8m/s

  3. Inelastic Is momentum conserved? Before: 2000kg(16m/s) + 0 = 32000kgm/s After: 4000kg(8m/s) = 32000kgm/s YES! Is energy conserved? Before: ½(2000kg)(16m/s)2 +0 =256 000J After: ½(4000kg)(8m/s)2 = 128 000J 128 000J – 256 000J = -128 000J NO it was lost!

  4. Elastic • Momentum is conserved. • Kinetic energy is conserved. Before Car 1 m=2000 kg vi=16m/s Car 2 m =2000kg vi=0 After Car 1 m=2000 kg v f =0 m/s Car 2 m =2000kg vf =16 m/s

  5. Elastic Is momentum conserved? Before: 2000kg(16m/s) + 0 = 32000kgm/s After: 0 + 2000kg(16m/s)= 32000kgm/s YES! Is energy conserved? Before: ½(2000kg)(16m/s)2 +0 =256 000J After: 0 + ½(2000kg)(16m/s)2 = 256 000J YES!

  6. Practice Problem A 6500 kg freight car traveling at 2.5 m/s collides with an 8000 kg stationary freight car. They interlock upon colliding. What is the kinetic energy before and after the collision? pB : (6500 kg)(2.5 m/s) = 16250 kgm/s Velocity after: 16250kgm/s = (14500)v, v = 1.12 m/s Before: ½ (6500 kg)(2.5 m/s)2 + 0 = 20313 J After: ½ (14500 kg)(1.12 m/s)2 = 9094 J Inelastic or Elastic?

  7. Practice Problem #2 Two lab carts are pushed together with a spring compressed btwn. them. Upon, release, the 5.0 kg cart repels one way with a velocity of 0.12 m/s while the 2.0 kg cart goes in the opposite direction. Find the velocity of the second car after the collision, and the kinetic energy before and after the collision: V: 0 = (5kg)(.12m/s) + (2kg)(-v), v = 3.3 m/s Before: k = 0 After: ½ (5 kg)(.12m/s)2 + ½(2kg)(3.3 m/s)2 = 11 J Elastic or Inelastic?

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