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Impulse-Momentum January 6, 2009 Newton’s 3rd law • Equal and opposite forces – what does this mean? – 4 conceptual questions 3rd law demos • Tug of war • Tug of war on roller skates Momentum • Momentum: mass in motion • p = mv • Momentum: mass in motion • p = mv • Change momentum by exerting a force over a period of time (impulse) Impulse-Momentum • Impulse = Ft • Impulse = m∆v Examples of Impulse-Momentum • Determine the direction of the impulse – Cart on a track – Projectile motion – Circular Motion • Determine the direction of momentum change – Cart on a track – Projectile motion – Circular Motion Impulse-Momentum • Impulse and momentum change are the same thing!!! • Impulse is always in the same direction as the force (so is momentum change) – Impulse is a vector (it has direction) Happy/sad balls • If I drop two identical balls from the same height, which will exert the larger force on the ground: the one that bounces or the one that does not bounce? Why? • Impulse = F*t • Impulse = m∆v Rank the impulse from most positive to most negative (negative numbers are smaller than positive) 10 m/s 20 m/s 20 m/s 20 m/s 30 m/s 20 m/s 10 m/s 0 m/s 10 m/s -10 m/s -10 m/s -20 m/s Rank the change in momentum from most positive to most negative (negative numbers are smaller than positive) 10 m/s 20 m/s 20 m/s 20 m/s 30 m/s 20 m/s 10 m/s 0 m/s 10 m/s -10 m/s -10 m/s -20 m/s Rank the following situations in order of greatest to least momentum change V = 2m/s V = 4m/s C A V = -2m/s V = -4m/s V = 2m/s V = 4m/s B D V =0 V=0 Rank the following situations in order of greatest to least impulse V = 2m/s V = 4m/s C A V = -2m/s V = -4m/s V = 2m/s V = 4m/s B D V =0 V=0 Impulse Investigation • A cart holding a force sensor is pulled from rest across a frictionless surface. – If we want to determine the impulse the person will experience, what measurements should we take? What equation will you use? Impulse Investigation • A person holding a force sensor is pulled from rest across a frictionless surface. – If we want to determine the impulse the person will experience, what measurements should we take? What equation will you use? – Is there more than one answer to the previous question? Force-time Graphs • Jumping on a force plate Two methods of determining impulse • Force Sensor – area under curve • Motion sensor – m∆v Impulse from Multiple Forces • Ex – book sitting on a table Impulse from multiple forces • A man weighing 800 N gets in an elevator. As the elevator is accelerating upward, the scale reads 850 N. – Draw a FBD of the man – Determine the net impulse he experiences during the first 2 seconds of motion. – How fast is the man moving after 2 seconds? Conservation of momentum • Equal and opposite impulses (just like equal and opposite forces) • Yesterday’s collision simulation Calculating final velocity (inelastic collisions) mava + mbvb = (ma + mb) v’ Example • A car with a mass of .5 kg and a velocity of .5 m/s collides with a car of mass 1 kg and velocity -.25 m/s. Determine the final velocity of the carts after they collide, assuming they stick together after the collision. Thursday, January 14 • Conservation of momentum principles What do you think will happen to the speed of the cart when a mass is dropped on top of it? Conservation of momentum • http://www.physicsclassroom.com/mmedia/ momentum/cbb.cfm • http://www.physicsclassroom.com/mmedia/ momentum/fcb.cfm • http://www.physicsclassroom.com/mmedia/ momentum/creti.cfm “reverse” collisions • When you shoot a gun, why does it “recoil”? Explain using the law of conservation of momentum. Hint: • When objects START together and separate (shooting a gun, throwing a baseball, pushing off from someone on ice skates) simply flip the conservation of momentum equation (ma + mb) v = mava + mbvb Practice • A 15-kg medicine ball is thrown at a velocity of 20 m/s to a 60-kg person who is at rest on ice. The person catches the ball and subsequently slides with the ball across the ice. Determine the velocity of the person and the ball after the collision. • Suppose that you have joined NASA and are enjoying your first space walk. You are outside the space shuttle when your fellow astronaut of approximately equal mass is moving towards you at 2 m/s (with respect to the shuttle). If she collides with you and holds onto you, then how fast (with respect to the shuttle do you both move after the collision? • http://www.physicsclassroom.com/mmedia/ momentum/ast.cfm Tomorrow’s lab • Predict what velocity-time graphs will look like for: – Two cars pushed toward each other, sticking together after the collision – Two carts pushed toward each other, bouncing off of each other after the collision – One cart initially at rest, while the other is pushed toward it. The carts stick together. – One cart initially at rest, while the other is pushed toward it. The carts bounce off of one another. Tuesday, January 19, 2010 • TEST tomorrow! • Go over last week’s homework • On the test: – Impulse (m∆v, Ft, change in momentum) – Direction of impulse = direction of force – Force-time graphs – Conservation of momentum Describing the motion…. “reverse” collisions (explosions) • You are standing at rest on a frictionless sheet of ice. You throw a .25-kg baseball forward at a speed of 18 m/s. If you have a mass of 55 kg, at what speed (and in what direction) are you moving after you throw the baseball?
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