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VI. Conservation of Energy and Momentum C. Momentum 12. 13. 14. 15. The Nature of Momentum The Conservation of Momentum Inelastic Collisions Elastic Collisions Why is a bullet that is thrown not as dangerous as a bullet that is fired from a rifle? _______________________________________________________________________________ Momentum is ________________ in motion. _________________________ is the product of the mass of a moving body and its velocity. momentum () = m v SI Unit for momentum: ______________ Example 1: Determine the momentum of an F 150 truck moving northward at 45 mph. Assume a weight 5000 pounds 1 mile = 1.6 km 1 kg = 2.2 pounds Example 2: How fast (in mph) would a Mini Cooper (2500 pounds) need to be traveling to have the same momentum as the truck in Example 1? Example 3: Calculate the momentum of the Titanic, of mass 4.2 x 107 kg, moving at 14 knots (1 knot = 1.852 km/h). Momentum of an object can be changed by __________________. This requires a ___________. The result is not instantaneous, but requires _____________. Sauder/jschulzgov momentum C - page 1 12/2010 _________________________ is the product of a force and the time interval during which it acts. Unlike most of our calculations, impulse is NOT defined by just one variable. Impulse is nothing more than a ____________________ in momentum. impulse (Ft) = m v. SI Unit for momentum: ______________ Impulse-Momentum Theorem : Ft = p In simple terms, a ___________ force acting for a long time can produce the same change in momentum as a large force acting for a ________ time Example 4: A hockey puck has a mass of 0.115 kg and is at rest. A hockey player makes a shot, exerting a constant force of 30.0 N on the puck for 0.16 s. With what speed does it head toward the goal? Example 5: If the momentum of the NASA space shuttle as it leaves the atmosphere is 3.75 x 108 kg m/s, and its mass is 75,000 kg, what is its speed? Example 6: A 2200-kg sport utility vehicle traveling at 26 m/s can be stopped in 21 s by gently applying the brakes, in 5.5 s in a panic stop, or in 0.22 s if it hits a concrete wall. What average force is exerted on the SUV in each of these stops? Sauder/jschulzgov momentum C - page 2 12/2010 Law of Conservation of Momentum A 5.0 kg bowling ball with a velocity of 6.0 m/s strikes a 1.5 kg standing pin squarely. If the ball continues on at a velocity of 3.0 m/s what will be the velocity of the pin after the collision? A 5 kg bowling ball is rolling in the gutter towards the pins at 2.4 m/s. A second bowling ball with a mass of 6 kg is thrown in the gutter and rolls at 4.6 m/s. It eventually hits the smaller ball and the 6 kg ball slows to 4.1 m/s. What is the resulting velocity of the 5 kg ball? Two people are practicing curling. The red stone is sliding on the ice towards the west at 5.0 m/s and has a mass of 17.0 kg. The blue stone has a mass of 20.0 kg and is stationary. After the collision, stone A moves east at 1.25 m/s. Calculate the momentum and velocity of the blue stone after the collision. A 50-g golf ball is struck with a club. The force on the ball varies from zero (when contact is made) up to a maximum value (when the ball is deformed) and then back to zero (when the ball leaves the club). Assume that the ball leaves the club’s face with a velocity of +44 m/s. A. Estimate the impulse due to collision. B. Estimate the duration of the collision. C. Estimate the average force on the ball. An inelastic collision between two particles is one in which part of their kinetic energy is transformed to another form of energy. The total amount of energy remains the same. We will consider that the objects that collide do not bounce off each other. An elastic collision between particles is one in which the total kinetic energy of the particles is conserved. We will consider that the objects that collide do bounce off each other. inelastic: m1 v 1 + m2 v 2 = m1+2 v1+2 elastic: m1 v 1 + m2 v 2 = m1Av1A + m2Av2A We will assume energy is conserved. Momentum is directly related to energy. Therefore, momentum is conserved. How does the momentum equation differ from the kinetic energy equation? Sauder/jschulzgov momentum C - page 3 12/2010 Example: A 59-kg physics student jumps off the back of her Laser sailboat, of mass 42 kg. After she jumps, the Laser is found to be traveling at 1.5 m/s. What is the speed of the student? Example: The same physics student jumps off the back of her Laser again, but this time the Laser is already traveling at 3.1 m/s before she jumps. If the physics student jumps off with a speed of 2.1 m/s, how fast is the Laser going after she jumps? Example: The Titanic hit an iceberg estimated to be half of her mass. Before hitting the iceberg, the Titanic was estimated to be going 22 knots (11.3 m/s). After hitting the iceberg, the Titanic was estimated to be going about 6.0 knots (3.1 m/s). How fast was the iceberg going after the collision? Example: A 59 kg physics student is riding her 220 kg Harley at 12 m/s when she has a head-on collision with a 2.1 kg pigeon flying the opposite direction at 44 m/s. The bird is still on the motorcycle after the collision. How fast is the motorcycle going after the collision? Example: A BC Ferry, or mass 13,000,000.0 kg, is traveling at 11 m/s when the engines are put in reverse. The engines produce a force of 1.0 x 106 N for a period of 20.0 seconds. What is the magnitude of the impulse from the engine? What is the new momentum of the ferry? What is the new velocity of the ferry? Sauder/jschulzgov momentum C - page 4 12/2010 References: Trinklein, F. E. Modern Physics (TE). Austin: Holt, Rinehart and Winston, 1992. Chapter 9 of Zitzewitz, P. W. Glencoe Physics: Principles and Problems. New York: Glencoe/McGraw-Hill, 2002. Sauder/jschulzgov momentum C - page 5 12/2010