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Collisions in One Dimension

Outcomes You will explain, qualitatively, that momentum is conserved in an isolated system You will define, compare and contrast elastic and inelastic collisions, using quantitative examples, in terms of conservation of kinetic energy. You will explain, quantitatively, that momentum is conserved in one- and two- dimensional interactions in an isolated system

Momentum & 1D Collisions Collisions involve both KINETIC ENERGY & MOMENTUM The LAW OF CONSERVATION OF MOMENTUM states that: in an ISOLATED SYSTEM the momentum before the collision will be equal to the momentum following the collision If momentum is gained by one part of the system, an equal amount is lost by the other part of the system.

Kinetic Energy & 1D Collisions Momentum is ALWAYS conserved in collisions, but kinetic energy may or may not be conserved. Some energy may be lost to: Heat Light Sound Deformation

Types of Collisions They’re two types of collisions: ELASTIC & INELASTIC In elastic collisions, BOTH kinetic energy and momentum are conserved (Never seen on a macro scale) Inelastic collisions, momentum is conserved, but kinetic energy is NOT. (Usually on a macro scale)

***ENERGY IS A SCALAR QUANTITY*** Elastic or Inelastic? How do you determine whether a collision is elastic or inelastic? Calculate the kinetic energy of both objects before the collision. Add the kinetic energies before to get the total Ek before. Calculate the kinetic energy of both objects after the collision. Add the kinetic energies before to get the total Ek after. Compare the total Ek before with the total Ek after. If they are the same, the collision is elastic. If they are different, the collision is inelastic. ***ENERGY IS A SCALAR QUANTITY***

Elastic or Inelastic? 𝐸 𝑘𝐵 = 𝐸 𝑘𝐴 𝐸 𝑘𝐵 ≠ 𝐸 𝑘𝐴 Elastic Inelastic

Types OF Problems There are three types of linear problems: Collisions where objects do not stick together after the collision Collisions where objects stick together after the collision Explosions where 1 object separates into 2 or more objects.

Sample Problems A 0.25 kg steel ball is travelling east at a velocity of 4.5 m/s when it collides head on with a 0.30 kg steel ball travelling west at a velocity of 5.0 m/s. After collision the 0.25 kg ball is travelling west at a velocity of 2.0 m/s. What is the velocity of the 0.30 kg ball after the collision? (0.42 m/s E)

Sample Problems A 1.1x103 kg car travelling east at a velocity of 25 km/h collides head on with a 1.3x103 kg car travelling west at a velocity of 15 km/h. During the collision, the two cars lock together. What is the velocity of the locked cars as they move together immediately after collision? (3.3 km/h [E])

Sample Problems A 0.050 kg bullet is fired from a 5.0 kg gun. If the velocity of the bullet is 275 m/s, what is the recoil velocity of the gun? (-2.75 m/s)

Homework CALCULATION QUESTION: p.5 #1-12

Sample Problem (Day 2) A 0.0149-kg bullet from a pistol strikes a 2.0000-kg ballistic pendulum. Upon impact, the pendulum swings forward and rises to a height of 0.219 m. What was the velocity of the bullet immediately before impact? (280 m/s)

Homework CONCEPT QUESTIONS: p. 486 #1-5 DIPLOMA QUESTION: p. 9 & 10