Conservation of Momentum

Transcription

1 Conservation of Momentum Momentum is a vector quantity that is always conserved. If J = 0, p i = p f The total momentum of an isolated system is constant.

2 Conservation of Energy Energy is a scalar quantity that is always conserved. If W net = 0, E i = E f The total energy of an isolated system is constant.

3 2 m/s 0 m/s System: Both cars (m car = 0.25 kg) Initial: Instant before collision (v 1i = 2 m/s, v 2i = 0 m/s) Final: Instant after they collide and stick together a) Determine the final velocity of the two cars. What physics concept did you use? b) Calculate the total kinetic energy of the twocar system before and right after the collision. c) Draw an energy bar chart for the collision.

4 2 m/s 0 m/s

5 Perfectly Inelastic Collision A collision in which two objects stick together (have the same velocity after they collide). A large fraction of the system s kinetic energy is converted into internal energy. Examples: Catching a football, cars colliding and sticking together, running and hugging a friend

6 Is it possible to have a collision in which the kinetic energy stays constant? 2 m/s 2 m/s 0 m/s 0 m/s

7 Perfectly Elastic Collisions Both the momentum and total kinetic energy of the system are constant. The internal energy of the system does not change. The colliding objects do not stick together or become deformed. No sound is produced. There are no perfectly elastic collisions in nature, although collisions between very rigid objects (such as billiard balls) come close. Collisions between atoms or subatomic particles are almost perfectly elastic.

8 All collisions cause vibrations which lead to an increase in internal energy.

9 In a collision between two objects, regardless of what type of collision, the total momentum of the two-object system is always constant.

10 However, if the collision is inelastic or perfectly inelastic, the total kinetic energy of the system will decrease (internal energy will increase). SK sys = 1 2 mv mv2 SK sys = 0 DU int > 0

11 Spiderman is climbing up a building when he spots Mary Jane 10 m below, standing on a platform which is about to explode. Spiderman swings down and grabs Mary Jane, hoping to swing up with her to a terrace, 5 m above the platform, where they would be safe. Will they make it?

12 Let s break the process into three parts: i. Spiderman s swing from the first building down to Mary Jane (before they join together) ii. their brief impact, an inelastic collision (because they are traveling together after the impact); iii. their swing together until they stop on the terrace.

13 i. Spiderman s swing from the first building down to Mary Jane (before they join together) System: Spiderman and Earth Initial state: Instant of release at max height Final state: Instant before colliding with MJ We can solve for his speed right before colliding with MJ.

14 ii. their brief impact, an inelastic collision System: Spiderman and Mary Jane Initial state: Instant before collision (h = 0) Final state: Instant after collision (h = 0) We can solve for their speed right after colliding.

15 ii. their swing together to the new max height. System: Spiderman, Mary Jane and Earth Initial state: Instant after collision (h = 0) Final state: Maximum height of swing (v f = 0) We can solve for their max height swinging up together.

16 Why can t they make it?

17 Mechanical Energy Kinetic energy, gravitational potential energy, and elastic potential energy

18 Perfectly Inelastic Collision K = 5J K = 5J Although total energy is a conserved quantity, mechanical energy is not a conserved quantity. K = 0J U int = +10J In an inelastic collision, mechanical energy is converted into internal energy.

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20 When two of the spheres (each of mass m) in the Newton s Cradle are dropped, they collide with an initial speed v with the spheres waiting below. a) Use Conservation of Momentum to determine 2 possibilities for the result of the collision. b) For each possibility, determine the amount of kinetic energy before and after the collision in terms of m and v.

21 The collision between steel marbles is elastic (but not quite perfectly so).

22 In reality, most collisions are partially inelastic (not perfectly elastic or perfectly inelastic).

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