Analyzing Analyzing CollisionsCollisions

Section 11.2 pg. 262-265Section 11.2 pg. 262-265

InelasticInelastic Momentum is conserved.Momentum is conserved. Kinetic energy is lost.Kinetic energy is lost.

AfterBumpers lock m=4000kg vf=8m/s

BeforeCar 1 m=2000 kg vi=16m/sCar 2 m =2000kg vi=0

InelasticInelastic

Is momentum conserved? Is momentum conserved?

Before: 2000kg(16m/s) + 0 = Before: 2000kg(16m/s) + 0 = 32000kgm/s 32000kgm/s

After: 4000kg(8m/s) = 32000kgm/s After: 4000kg(8m/s) = 32000kgm/s 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

YES!

NO it was lost!

ElasticElastic Momentum is conserved.Momentum is conserved. Kinetic energy is conserved.Kinetic energy is conserved.

BeforeCar 1 m=2000 kg vi=16m/sCar 2 m =2000kg vi=0

AfterCar 1 m=2000 kg v f =0 m/sCar 2 m =2000kg vf =16 m/s

ElasticElastic

Is momentum conserved? Is momentum conserved?

Before: 2000kg(16m/s) + 0 = Before: 2000kg(16m/s) + 0 = 32000kgm/s 32000kgm/s

After: 0 + 2000kg(16m/s)= After: 0 + 2000kg(16m/s)= 32000kgm/s 32000kgm/s

YES!

Is energy conserved? Before: ½(2000kg)(16m/s)2 +0 =256 000JAfter: 0 + ½(2000kg)(16m/s)2 = 256 000J

YES!

Practice ProblemPractice ProblemA 6500 kg freight car traveling at 2.5 m/s A 6500 kg freight car traveling at 2.5 m/s

collides with an 8000 kg stationary freight car. collides with an 8000 kg stationary freight car. They interlock upon colliding. What is the They interlock upon colliding. What is the kinetic energy before and after the collision?kinetic energy before and after the collision?

ppBB : (6500 kg)(2.5 m/s) = 16250 kgm/s : (6500 kg)(2.5 m/s) = 16250 kgm/s

Velocity after: 16250kgm/s = (14500)v, v = 1.12 Velocity after: 16250kgm/s = (14500)v, v = 1.12 m/sm/s

Before: ½ (6500 kg)(2.5 m/s)Before: ½ (6500 kg)(2.5 m/s)22 + 0 = 20313 J + 0 = 20313 J

After: ½ (14500 kg)(1.12 m/s)After: ½ (14500 kg)(1.12 m/s)22 = 9094 J = 9094 J

Inelastic or Elastic? Inelastic or Elastic?

Practice Problem #2Practice Problem #2Two lab carts are pushed together with a spring Two lab carts are pushed together with a spring

compressed btwn. them. Upon, release, the compressed btwn. them. Upon, release, the 5.0 kg cart repels one way with a velocity of 5.0 kg cart repels one way with a velocity of 0.12 m/s while the 2.0 kg cart goes in the 0.12 m/s while the 2.0 kg cart goes in the opposite direction. Find the velocity of the opposite direction. Find the velocity of the second car after the collision, and the kinetic second car after the collision, and the kinetic energy before and after the collision:energy before and after the collision:

V: 0 = (5kg)(.12m/s) + (2kg)(-v), v = 3.3 m/sV: 0 = (5kg)(.12m/s) + (2kg)(-v), v = 3.3 m/s

Before: k = 0 Before: k = 0

After: ½ (5 kg)(.12m/s)After: ½ (5 kg)(.12m/s)22 + ½(2kg)(3.3 m/s) + ½(2kg)(3.3 m/s)2 2 = 11 = 11 JJ

Elastic or Inelastic?Elastic or Inelastic?