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Momentum: Conservation of Momentum: Vocabulary: .Momentum Vocabulary: .Law of conservation of momentum .Impulse .Impulse-Momentum Theorem .Elastic collision .Inelastic collision .Perfectly inelastic collision I can: give examples and compare the momentum of different moving objects. calculate impulse and compare to its change in momentum. discuss how force and time vary in a collision using the impulse-momentum theorem. I can: explain the law of conservation of momentum. recognize when to solve a problem using the law of conservation of momentum. calculate velocities and other variables within a given collision using the law of conservation of momentum. differentiate between elastic, inelastic and perfectly inelastic collisions. Equations: p mv J Ft J p pi p f m1v1i m2v2 i m1v1 f m2v2 f Is it harder to stop the Titanic or a rubber ducky if they are traveling at the same speed? We say that Titanic has more MOMENTUM than the rubber ducky. Momentum is inertia in motion. the product of an object’s mass and velocity. p = mv Vector Formula Units Abbreviations p =m x v kg·m/s = kg x m/s p = momentum m = mass (kg) v = velocity (m/s) The result of force acting on an object for a specific time. Impulse (J): J = FΔt Units: Newton Seconds (N·s) Vector Impulse Example Problems A 500 kg car moving at 10 m/s hits a brick wall and comes to a stop. What is the impulse imparted on the car? It is found that it took the car 0.21 seconds to stop. What is the magnitude of the force exerted on the car? A 1.5 kg superball is moving to the right with a velocity of 20 m/s when it strikes a wall and bounces back to the left with a speed of 15 m/s. What is the impulse on the ball? How much force is exerted on the ball if it is in contact with the wall for a time of 0.02 seconds? A 1000 kg car moving at 30 m/s (p = 30,000 kg*m/s) can be stopped by 30,000 N of force acting for 1.0 s (a crash!) or by 3000 N of force acting for 10.0 s (normal stop) Impulse is the area under a Force vs. Time Graph Impulse = change in momentum Can be written as: J = Δp OR F Δ t = mΔv The units must be the same also! N·s= kg·m/s MOMENTUM Decreasing Momentum: Which would it be more safe to hit in a car ? Ft mv mv Ft In each case, the momentum is decreased by the same amount or impulse (force x time) Hitting the haystack extends the impact time (the time in which the momentum is brought to zero). The longer impact time reduces the force of impact and decreases the deceleration. Whenever it is desired to decrease the force of impact, extend the time of impact ! Example 1 What is the momentum of a 2.9 kg seagull which is flying at a velocity of 19.1 m/s to the west? p mv p (2.9kg)(19.1 m ) s p 55.4kg m s Example 2 A 2.7 kg soccer ball approaches a player with a velocity of 3.8 m/s to the North. The player strikes the ball and causes it to move toward the south with a speed of 20 m/s. What impulse was delivered to the ball by the player? Assume North is Positive and South is Negative. J p v v f vi J mv p (2.7kg)( 20 m 3.8 m ) s s p 64.3kg m s Example 3 A 620 kg car driven by Toonces the cat predictably flies off a cliff and collides with the ground at a speed of 33 m/s. If the car crumples during the collision for 0.7 s before coming to a complete stop, what is the magnitude of the average force experienced during the impact? J p Ft mv v v f vi F (0.7 s) (620kg)(33 m 0 m ) s s F (0.7 s) 20460kg m s F 29228.6N