Momentum Revisited Momentum "Mass in Motion" p = mv. p > momentum (kgm/s) m > mass (kg) v > velocity (m/s) Change in Momentum.

Transcription

1 Momentum Revisited Momentum "Mass in Motion" p = mv p > momentum (kgm/s) m > mass (kg) v > velocity (m/s) Change in Momentum p = p f p i p = mv f mv i p = m v 1

2 Unit 1 Section 4 Collisions/Explosions 2

3 Conservation of Momentum For any collision between objects in a closed and isolated system, the total momentum before the collision is equal to the total momentum after the collision. The Law of Conservation of Momentum p A + p B = p A ' + p B ' m A v A + m B v B = m A v A ' + m B v B ' 3

4 Types of Collisions/Explosions Collisions/Explosions 1D 2D Elastic Inelastic 4

5 1D Collisions/Explosions Example: When a car of mass 2.0 x 10 3 kg moving at 9.0 m/s collides head on with a second car having a mass of 1.5 x 10 3 kg, the cars lock and come to rest at the point of collision. What was the velocity of the second car before the collision? 5

6 Example: A 6500 kg train travelling at 2.5 m/s collides with a stationary 8000 kg train. If they interlock upon collision, find their velocity after the collision. j

7 Example: A shell having a mass of 25.0 kg is fired horizontally eastward from a cannon with a velocity of 500 m/s. If the mass of the cannon is 1000 kg, what is the magnitude and direction of the recoil velocity? 7

8 Example: A kg hockey puck moving at 48 m/s is caught by a 75 kg goalie at rest. With what velocity does the goalie slide on the ice after the puck is caught? 8

9 Elastic Collisions An elastic collision is a collision in which both momentum and kinetic energy are conserved. Reminder: E k = 1 mv 2 2 E k > kinetic energy (energy of motion) [J] m > mass [kg] v > speed [m/s] kgm 2 = J s 2 No collision at the macroscopic level is perfectly elastic. Perfectly elastic collisions only occur at the atomic or subatomic levels. This is because collisions at the macroscopic level involve energy transformations in which kinetic energy is converted into thermal energy, sound energy, etc. 9

10 If you are told that a collision is elastic, you may need to use both conservation of momentum equations and conservation of energy equations. Example Elastic Collision: Sphere A with mass 12 kg moving at 2.4 m/s east makes an elastic head on collision with Sphere B, mass 36 kg, which is at rest. Find the velocities of the two spheres after the collision. Assume all motion is in one dimension. (v A = 1.2 m/s, v B = 1.2 m/s) m A BEFORE m B m A AFTER m B m A = 12 kg m B = 36 kg v A = +2.4 m/s v B = 0 m/s v A =? v B =? 10

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12 Inelastic Collisions An inelastic collision results when kinetic energy is not conserved. A perfectly inelastic or completely inelastic collision results when objects lock or stick together upon collision. 12

13 Example Inelastic Collision: In an accident due to slippery roads, a compact car, mass 575 kg moving at +15 m/s, smashes head on into the rear of a car with a mass of 1575 kg originally moving at +5.0 m/s. They lock together and slide forward. a) What is the final velocity of the wrecked cars? (7.7 m/s) b) How much kinetic energy was lost? (2.1 x 10 4 J lost) 13

14 Two Dimensional (2D) Collisions/Explosions In order to solve two dimensional collision/explosion problems, write a conservation of momentum equation for the horizontal components of the momenta and a conservation of momentum equation for the vertical components of the momenta. lab 14

15 Example: A 1325 kg car moving north at 27.0 m/s collides with a 2165 kg car moving east at 17.0 m/s. They stick together. In what direction and with what speed do they move after the collision? (14.7 m/s, 44.2 o N of E) 15

16 Example: A 1200 kg car is moving east at 30.0 m/s and collides with a 3600 kg car moving at 20.0 m/s in a direction 60.0 o N of E. The vehicles interlock and move off together. Find their common velocity. (19.8 m/s, 40.9 o N of E) 16

17 Example: A 6.0 kg object, A, moving at a velocity of 3.0 m/s east collides with a 6.0 kg object, B, at rest. After the collision, A moves off in a direction 40.0 o to the left of its original direction. B moves off in a direction 50.0 o to the right of A's original direction. What is the magnitude of the velocity of each object after the collision? ' ' (v A = 2.3 m/s, v B = 1.9 m/s) 17

18 Attachments p12 lad 2d collision.jpg p12 lad 2d collision 2.jpg p12 lad 2d collision 3.jpg