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Impulse; Momentunm; and Conservation of Momentum

Impulse; Momentunm; and Conservation of Momentum. Intro: Which Train has more momentum?. While stopped? When moving at the same velocity?. Both have no velocity= no momentum. The larger has more mass= more momentum.

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Impulse; Momentunm; and Conservation of Momentum

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  1. Impulse; Momentunm; and Conservation of Momentum

  2. Intro: Which Train has more momentum? • While stopped? • When moving at the same velocity? Both have no velocity= no momentum The larger has more mass= more momentum

  3. Momentum (ρ)- (inertia in motion) the product of mass and velocity of an object • Momentum equation • ρ = mv • Momentum = mass x velocity • The SI unit for momentum is kg·m/s • Change in momentum equation Δρ = mΔv or Δρ = m(vf – vo)

  4. Example A: An airplane is launched from an aircraft carrier. The plane is going from south to north. If the airplanes launch velocity is 70 m/s in the direction the ship was sailing and its mass is 2.5 x 104 kg, what is its momentum immediately after the launch (include direction since momentum is a vector). GIVEN: EQUATION: SOLVE: v = 70 m/s p = mv p = 1,750,000 kg m/s m = 25,000 kg UNKNOWN: SUBSTITUTE: p = (25,000 kg) (70 m/s) p = ?

  5. Example B: A 0.060 kg tennis ball traveling at 10.0 m/s is returned in the opposite direction with a speed of 36.0 m/s. What is the change in momentum of the ball? GIVEN: EQUATION: SOLVE: p = - 2.76 kg m/s p = mv m = 0.060 kg vi = 10.0 m/s p = m(vf – vi) vf = -36.0 m/s SUBSTITUTE: p = (0.060 kg) (-36.0 m/s – 10 m/s) UNKNOWN: p = ? p = (0.060 kg) (-46.0 m/s)

  6. A moving object can have a large momentum if it has a large mass, a lot of speed, or both. A rollerskate traveling the same velocity of a truck would have less momentum.

  7. Impulse (J) is a force applied over a period of time • The SI unit for impulse is N·s Impulse = FΔt The man is applying an impulse to the car

  8. Example C: What is the impulse when a force of 35 N is applied for 1.2 seconds? GIVEN: EQUATION: J = Ft F = 35 N t = 1.2 s SUBSTITUTE: J = (35 N)(1.2 s) UNKNOWN: J = ? SOLVE: J = 42 N·s

  9. An impulse causes a change in momentum hence, Impulse = change in momentum • (remember F = ma) so The unit for impulse and momentum are equivalent • N·s = kg·m/s The man in the picture is causing an impulse and changing the cars momentum

  10. To increase the momentum of an object the most, you would want the greatest force possible over the longest time possible • FΔt = mΔv

  11. Two cars of equal mass are traveling the same speed. What do we know about their momentum? It’s the same for both cars P = mv 10 m/s A 500kg 10 m/s 500kg B

  12. Look at the equation and determine what this means: FΔt = mΔv Which car is going to take less time to stop Same for both cars stops in less time 10 m/s A 500kg 10 m/s 500kg B

  13. Which car is going to apply more force during the crash? with the same momentum Ft = mv less time = more force t = mv t F F A more time = less force = mv t t F F B

  14. Back to Newtons 2nd Law F=ma • If there is a greater force on the same object you will get a greater acceleration, or deceleration. • Force causes acceleration

  15. Example D: A 0.060 kg tennis ball traveling at 10.0 m/s is returned in the opposite direction with a speed of 36.0 m/s. If the ball is in contact with the racket for 0.02 s, with what average force is the ball hit? EQUATION: GIVEN: SOLVE: m = 0.060 kg vi = 10.0 m/s vf = -36.0 m/s t = 0.02s SUBSTITUTE: UNKNOWN: F = ?

  16. Example E: Two identical cars (same mass), each traveling 20 m/s, are brought to a stop. Car A stops by applying its breaks the normal way. Car B stops as a result of running into an unmovable concrete wall. Which of the following statements is TRUE? (explain why the incorrect statements are false) J = Ft = p = mv a. Car A has the greatest change in momentum. False, both have the same p (both have same mass and change in velocity) b. Car B experiences the greatest impulse. False, remember J = p if they both have same change in momentum, then they both have the same impulse. c. Car B has the greatest change in momentum. False, same as answer a d. Car B has the greatest force applied to it. F t = mv True, less time gives a greater force if p is the same.

  17. Example #1 Bernie, whose mass is 70.0 kg, leaves a ski jump with the velocity of 21.0 m/s. What is Bernie’s momentum as he leaves the ski jump? GIVEN: EQUATION: p = mv m = 70.0 kg v = 21.0 m/s SUBSTITUTE: UNKNOWN: p = (70.0 kg) (21.0 m/s) p = ? SOLVE: p = 1,470 kg m/s

  18. Example #2 Mark squishes a spider by applying a 20N force for 0.1s. What is the impulse of this action? GIVEN: EQUATION: J = Ft F = 20 N t = 0.1 s SUBSTITUTE: UNKNOWN: J = (20 N) (0.1 s) J = ? SOLVE: J = 2 N s

  19. Example #3 Ethel hits a 0.20 kg ball at rest causing it to go 20 m/s. What average force is applied if the ball is in contact for 0.4 s? SOLVE: GIVEN: EQUATION: m = 0.20 kg vi = 0 m/s vf = 20 m/s t = 0.4 s SUBSTITUTE: UNKNOWN: F = ?

  20. Bouncing • The impulse needed to bring an object to a stop and “throw it back again” is greater than the impulse required to just bring an object to a stop. • To produce a stop you reduce momentum to 0 since v=0 • To bounce you need a negative momentum since the direction of velocity changed

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