1. 2D Collisions Physics 12

2. Clip of the day: Minutephysics: What is fire? http://www.youtube.com/watch?v=1pfqIcSyd gE http://www.youtube.com/watch?v=1pfqIcSyd gE

3. Review: Momentum Momentum

4. Review: Conservation of momentum: Momentum is conserved: This is an expression of Newton’s first law: – “An object at rest or in uniform motion will remain at rest or in uniform motion unless acted on by an external force.”

5. Conservation of momentum: In interactions between two bodies/objects, momentum of one object can change, but the total momentum of the system remains constant.

6. Law of Conservation of Momentum (continued…) The total momentum of objects before a collision is the same as the total momentum of the same objects after they collide. The change in momentum in an isolated system is zero. The objects within the system may interact and exchange momentum, but the total momentum does not change!

7. Review: Example Collisions in 1D: A 1.75x10 4 kg boxcar is rolling down a track toward a stationary boxcar that has a mass of 2.50x10 4 kg. Just before the collision the first car is moving east at 5.45m/s. When the boxcars collide, they lock together and continue down the track. What is the velocity of the 2 box cars after the collision? Step 1= draw a diagram!

8. What we know before the collision: m 1 =1750 kg, m 2 =2500 kg, v 1 = 5.45 m/s, v 2 = 0 What we know after the collision: m 1 =1750 kg, m 2 =2500 kg, the 2 cars are now stuck together so they have the same velocity! Velocity is what we are solving for. m 1 v 1 + m 2 v 2 = m 1 v 1 ' + m 2 v 2 ‘ (1750)(5.45) + (2500)(0) = 1750v + 2500v 9537.5 = 4250v 2.24 m/s = v

9. 2D Collisions: In all collisions, momentum is conserved In elastic collisions, energy is also conserved As momentum is a vector, we can break momentum into components (x and y) and employ the conservation of momentum

10. Example: 2D Collision Two cars approach an intersection; the first car is travelling east at a velocity of 15m/s and the car has a mass of 1000.kg. The second car is travelling north at a velocity of 10.m/s and has a mass of 1200.kg. If the cars collide and stick together, determine the following: a. The velocity immediately after the collision b. The direction of motion immediately after the collision

11. Diagram: A B v=15m/s v=10.m/s A B v=?

14. Try it : Page 509 o Questions 35-37

15. EXPLOSIONS! (and energy) Day 2

16. Review Question: Two cars collide at an intersection; if they have the same mass (1200kg) and after the collision they move off at 7.5m/s at 31°, determine the initial velocity of each car assuming one was travelling due north and one was travelling due east.

17. Answer: 7.7m/s north and 13m/s east Physics is such fun!

18. Explosion During an explosion, momentum must be conserved as in a collision We will consider simple problems with a limited number of pieces following the explosion, however this can be applied to any number of particles As with collisions, we need to consider before and after the explosion

19. Example #1: A small firecracker is sitting on a table and explodes into four parts. The initial firecracker has a mass of 50.g and three of the pieces have masses of 12g, 13g, 18g and move off at the following respective velocities; 42m/s, 0.°, 31m/s, 72° and 28m/s, 183°. What is the velocity of the fourth piece?

20. Explosion Problem Before After

23. Elastic vs Inelastic Collisons Elastic = momentum (p) and kinetic energy conserved (E K ) Inelastic = momentum (p) conserved but kinetic energy NOT conserved (E K ) Review: Ek = ½ mv 2

24. Example #2: A 0.0520 kg golf ball is moving east with a velocity of 2.10 m/s when it collides, head on, with a 0.155 kg billiard ball. If the golf ball rolls directly backward with a velocity of –1.04 m/s, was the collision elastic? Reminders: – Momentum is always conserved in a collision. – If the collision is elastic, kinetic energy must also be conserved. – Ek = ½ mv 2

25. Try it : The small firecracker from the previous problem is thrown; when it explodes it is travelling at 25m/s at a 0.° angle. It breaks into the same four pieces but the velocities are now; 61m/s, 0.°, 33m/s, 72° and 15m/s, 183°. What is the velocity of the fourth piece? Page 513 o Question 38 Page 515 o Questions 39-40

26. Explosion Problem Before After