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Inertia and Momentum

Inertia and Momentum. Definition: Inertia: Measures an object’s tendency to remain at rest or stay in constant motion. A measure of the inertia of an object is its mass . Galileo used this term to describe how easy or difficult it is to change an object’s motion.

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Inertia and Momentum

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  1. Inertia and Momentum

  2. Definition: • Inertia: Measures an object’s tendency to remain at rest or stay in constant motion. A measure of the inertia of an object is its mass. • Galileo used this term to describe how easy or difficult it is to change an object’s motion. • Reminder: Mass is the quantity of matter, with units in kilogram.

  3. Example: Arrange the following from high to low inertia: • - Bowling ball -Mosquito - Ms. Irani - 18- wheeler • Answer: 18-wheeler, Ms.Irani, Bowling ball, Mosquito

  4. Momentum can be defined as "mass in motion." • All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion. • The amount of momentum which an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. Momentum depends upon the variables mass and velocity.

  5. In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object. Momentum = mass • velocity • In physics, the symbol for the quantity momentum is the lower case "p". Thus, the above equation can be rewritten as p = m • v • where m is the mass and v is the velocity.

  6. The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity. • Momentum does not have a standard unit. What units can you use? Kg.m/s; g.m/s; kg.km/h

  7. Example: Consider the following diagram:

  8. Which case has greatest velocity change? • a. The velocity change is greatest in case B. The velocity changes from +30 m/s to -28 m/s. This is a change of 58 m/s (-) and is greater than in case A (-15 m/s).

  9. Which case has greatest acceleration change? • b. The acceleration is greatest in case B. Acceleration depends on velocity change and the velocity change is greatest in case B

  10. Which case has greatest Momentum change? • The momentum change is greatest in case B. Momentum change depends on velocity change and the velocity change is greatest in case B.

  11. Question 1. Determine the momentum of a .. • a. 60-kg halfback moving eastward at 9 m/s. • p = m*v = 60 kg*9 m/s p = 540 kg•m/s, east • b. 1000-kg car moving northward at 20 m/s. • p = m*v = 1000 kg*20 m/s • p = 20 000 kg•m/s, north

  12. c. 40-kg freshman moving southward at 2 m/s. • p = m*v = 40 kg*2 m/s • p = 80 kg•m/s, south

  13. 2. A car possesses 20 000 units of momentum. What would be the car's new momentum if ... • a. its velocity were doubled. • p = 40 000 units (doubling the velocity will double the momentum)

  14. b. its velocity were tripled. • p = 60 000 units (tripling the velocity will triple the momentum) • c. its mass were doubled (by adding more passengers and a greater load) • p = 40 000 units (doubling the mass will double the momentum)

  15. d. both its velocity were doubled and its mass were doubled. • p = 80 000 units (doubling the velocity will double the momentum and doubling the mass will also double the momentum;

  16. Conservation of Momentum • For a collision occurring between object 1 and object 2 in an isolated system (a system that only includes 2 objects and is free from external forces such as friction) , the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by object 1 is equal to the momentum gained by object 2.

  17. Example1: Describe in physics and in word why the momentum of the system is conserved on Figure 11-12 (pg 313)? • System: 2 balls • Right Before collision PA = 0 & PB= 0.2 kg.m/s PTotal= 0+0.2 = 0.2 kg.m/s Right after collision PA = 0.15 & PB= 0.05 kg.m/s PTotal= 0.15+0.05 = 0.2 kg.m/s • If one object slows down, it’s because it hit another object. The object then moves faster. The one object lost just as much momentum as the other one gained, so there is no change overall.

  18. Example 2: Describe why the momentum of the system is conserved on Figure 11-13? • System= Student + skateboard • Right before jump: P student + P skateboard = m. v + m. v= 0 ( because v=0 ) • Right after jump: P student + P skateboard = m. (-v) + m. (+v) = 0 ( because momentums are equal but in different directions so they cancel one another)

  19. Question 1: Using physics language predict what will happen to a ball if it bounces off the bumper of an approaching car. • The ball with gain some momentum because some of the car’s momentum will be transferred to the ball.

  20. a-Two trains of equal mass are coupled in a train yard. To begin, the cars are located some distance apart on the track. The first car is pushed toward the second car that is sitting at rest. If the first car is moving at 2 m/s when it bumps into the stationary car, what happens after the cars are coupled? (What is their velocity after they’re coupled?) • m1=m2 ; v1= 2 ; v2=0 • Right Before collision ;  Ptotal=P1 + P2= 2m1 + 0= 2m1 • Right after collision ; Ptotal=P1 + P2 = m1 v1 +m1 v2 Based on conservation of momentum: momentum before collision = momentum after collision 2m1 = (m1+m1)v2 2= 2v2 They continue moving in the same direction but half the speed ( 1 m/s)

  21. b-What happens if the first car is empty and the second car is twice as heavy? (What is their velocity after they’re coupled?) • m1 ; m2= 2 m1 ; v1= 2 ; v2=0 • Right Before collision ;  Ptotal =m1 v1 +m2 v2 Ptotal= 2m1 + 0 • Right after collision ; Ptotal = (m1 +m2)v 2m1 = (m1 +2 m1)v 2= 3 v v=0.67 m/s

  22. Warm Up • One skater weights 25 kg and is traveling at 2 m/s. Another weights 75 kg and is traveling at -3 m/s. They collide but manage to hold onto each other and keep their footing. What is their velocity after the collision? • Momentum before hitting= momentum after hitting (25* 2) + ( 75 * -3) = (25+ 75) V -175 = 100 v V= -1.75 • Answer : - 1.75 m/sec

  23. p. 315 HW 1-You should have the same momentum: • P lineman = 140 * 10 = 1400 kg. km/hr • P you = 50 * V = 1400 • V you= 28 km/hr 2- No the balls could be moving either way 3- the dust comes from all different directions. 1 mil kg is much less than earth’s mass. 4-total momentum before collision = total momentum after collision 5-3 = -2 + PB PB= 4 kg.m/s

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