Elastic and Inelastic Collisions

1. Elastic and Inelastic Collisions

2. Conservation of Momentum • If a system is isolated (no external forces) and a collision occurs, momentum is conserved • Collisions may involve direct contact or actions at a distance (e.g., electric fields)

3. Conservation of Momentum • As a result changes in momentum are equal and opposite: or

4. Conservation Of Momentum Momentum is conserved in all three types of collisions • Elastic: Collide and separate; KE conserved • Inelastic: Collide then separate deformed KE is not conserved Perfectly Inelastic: Collide and stick together, then move with common velocity. KE is not conserved

5. ELASTIC COLLISION Momentum & KE conserved v2i v1i Before collision m1 m2 Objects “bounce off each other” v2f v1f m2 After collision m2 m1 CHANGES IN MOMEMTUM ARE EQUAL AND OPPOSITE

6. Elastic Collisions

7. The animation below portrays the elastic collision between a 3000-kg truck and a 1000-kg car. The before- and after-collision velocities and momentum are shown in the data tables.

8. Elastic Collisions • pi= pf(Conservation of Momentum) • Momentum before collision = momentum after • the collision • KEi = KEf(Conservation of Kinetic Energy)

9. Elastic Collision Hockey player A has a mass of 115 kg and a velocity of 3.35 m/s. Hockey player B has a mass of 105 kg and a velocity of 2.35 m/s. The two players collide and player A ends up with a velocity of 0.500 m/s. What is player B’s velocity after the collision? How much kinetic energy is lost during the collision? (Assume the motion is in 1 dimension)

10. pBefore = p After Player A mA = 115 kg vA = 3.35 m/s vA = 0.50 m/s Player BmB = 105 kg vB = -2.35 m/s vB = ? Important! You must apply the correct sign to velocity of the object (115 kg)(3.35m/s)1i + (105kg)(-2.35m/s)2i = (115kg)(0.50m/s)1f + (105kg)(vB)2f VB= 1.32 m/s

11. Inelastic Collision Two objects collide and bounce off each other just as an elastic collision BUT the objects deform during the collision so that the total kinetic energy decreases. MOST REAL LIFE COLLISIONS THIS TYPE.

12. Perfectly Inelastic Collisions Colliding objects stick together and move with a common velocity. They become deformed, generate heat, during the collision. Become tangled or coupled together. Conservation of Momentum but NOT KE

13. Perfectly Inelastic Collision

14. The animation below portrays the inelastic collision between a very massive diesel and a less massive flatcar. The diesel has four times the mass of the freight car. After the collision, both the diesel and the flatcar move together with the same velocity.

15. Perfectly Inelastic Collision A shark grabs a motionless swimmer They stay together as one body. If the 24 kg shark is traveling 6.7 m/s when it grabs the swimmer of mass 45 kg, What is the velocity just after the shark grabs the swimmer? How much kinetic energy is lost?

16. Perfectly Inelastic Collisions Momentum Shark + Momentum Swimmer = Momentum of Shark & Swimmer Conservation of Momentum but NOT KE

17. Mass shark m1= 24kgVelocity of shark v1=6.7m/sMass swimmer m2 = 45kgVelocity swimmer = 0 m/sfinal velocity of shark and swimmer Vf = ? (24kg)(6.7m/s) + (45kg)(0) = (24kg+ 45kg) vf Vf= 2.33 m/s

18. KE perfectly inelastic collision KE before collision = ½ (m1v1)2i + ½ (m2v2)2i = ½ (24kg)(6.7m/s)2 + ½(45kg)(0m/s)2 = 539 J = ½ (m1 m2)vf2 KE after collision ½ (24kg + 45kg)(2.33m/s)2 = 187 J ΔKE = 539 J - 187 J = 352 J

19. How is KE Lost? In the Inelastic collisions some of the kinetic energy is converted into internal energy of the objects when they deform. Heat produced from friction Sound

20. Glancing Collisions (2-D) • Conservation of Momentum in two dimensions • Conservation of Energy onlyif elasticcollision m2

21. Conservation of Momentum (2-D) x-components: y-components: