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Chapter 3: Conservation Laws Interviewer: “So did you see which train crashed into which train first?” 15-year-old: “No, they both ran into each other at the same time.” –BBC Radio 4 2 3.1 Newton’s Third Law and Momentum • Use Newton’s third law to explain various situations. • Explain the relationship between Newton’s third law and momentum conservation. • Solve recoil problems. 3 Newton’s Third Law • “For every action, there is an equal and opposite reaction.” • Forces come in pairs. Bodies always exert equal forces on each other, but that doesn’t mean the acceleration is the same; acceleration also depends on mass. 4 Newton’s Third Law • “For every action force, there is a reaction force equal in strength and opposite in direction” – page 59 in your textbook. • Unlike Newton’s 1st and 2nd laws, which focus on one object, the 3rd law involves the mutual interaction between two objects. Does the moon exert just as much force on the earth as the earth does on the moon? 5 Balanced Forces • Be careful, balanced forces acting on a single object is not an example of Newton’s 3rd law! • Fnet = ma = 0 • Therefore, Normal equals Weight (mg) • Not because of Newton’s 3rd Law! • Both these forces act on the same object, the book! 6 Action – Reaction Pairs Force of table on book, “Normal” Force of earth of book, W=mg Force of book on table Force of book on earth Remember that the two forces in an action-reaction pair never act on the same object! 7 8 Momentum • Remember the inertia of an object indicated the object’s resistance to change, but both skaters have the same mass, and same inertia. • So which skater will be harder to stop, both have the same inertia, but different momentum. 9 Momentum • Momentum is a vector so direction matters! • Why doesn’t a massive object at rest have momentum? 10 Impulse • An “impulse” is given to an object, for example the tennis ball, when a force acts on the object over a time interval. • Impulse = Force * time 11 Impulse-Momentum Theorem If an impulse is given to an object, that impulse will change the object’s momentum! 12 Conservation of Momentum • • • Two objects (boy and ball) each exert equal forces on each other as the boy throws the ball. The two objects will be in contact for the same amount of time. Therefore the impulses on each object will be the same (but in opposite directions). If the impulse on each object is the same, so is the change in momentum (again in an opposite direction). If interacting objects in a system are not acted on by outside forces, the total amount of momentum in the system cannot change. mAvA1 mBvB1 mAvA2 mBvB 2 13 14 Class Problems • An astronaut floating in space throws a 2 kg hammer to the left at 15 m/sec. If the astronaut’s mass is 60 kg, how fast does the astronaut move to the right after throwing the hammer? mAvA1 mBvB1 mAvA2 mBvB 2 • A group of playful astronauts, each with a bag full of balls, form a circle in outer space. Describe what happens when they begin tossing balls simultaneously to one another. 15 3.2 Energy and Its Conservation • • • • Describe work and energy. Calculate potential energy. Calculate kinetic energy. Apply the law of conservation of energy to explain the motion of an object acted on by gravity. 16 What is Energy? • We have talked about energy many times, page 65 is a good summary. • Energy is a quantity that measures the ability to cause change in a physical system. • The metric unit for energy is named after the English physicist James Joule (1818–1889). 17 What is Work? • We say work is done on an object when a force acts to move that object in the direction of the force. • Work done on an object transfers energy to that object. • An object (or system) with energy has the ability to do work. • Work is also measured in Joules (J). 18 Force and Distance • The work done on an object can be positive or negative: positive if it adds energy to the object, negative if the object loses energy! • Forces acting 90o to the motion do not do work. • Remember W = F*d, so if there is no motion (distance) no work is done. Force is at 90o to distance => no work box moving to the right No distance => no work Negative work done – Box loses energy! Positive work done – energy is added to the box 19 Potential Energy • Potential energy is energy due to the position of an object in a system. • An object some height above the ground has potential energy due to the earth’s gravity. • There are other forms of potential energy such as elastic and electrical. 20 Kinetic Energy • Energy of motion is called kinetic energy. • Kinetic energy depends on both an object’s speed and its mass. – Double the mass of a moving object and the KE will double. – Double the speed and the KE will quadruple, since KE ~ v2. 21 Class Problems • Work: You are on the track team working out by pushing a “sled” with a force of 50 lbs (F = 2250 N) half a football field (d = 50 m), how much work do you do? • Potential Energy: How much do you have on the roller coaster shown if you and the coaster have a combined mass of 80 kg and are 4 meters off the ground? • Kinetic Energy: How much kinetic energy does a bullet of mass = 40 grams moving at 300 m/s have? 22 Law of Conservation of Energy • An important conservation law in physics: “Energy can never be created or destroyed, just converted from one form into another.” • The diver initially has useful PE which converts to KE on the way down. Ultimately the energy turns into useless heat energy, but the total energy for the “system” in constant. 23 Conservation of Energy Problems • We can use the idea of conservation of energy to solve problems. • Consider the diagram to the right: first you might have to use a winch to do work lifting the block… now complete the description… • We could find the speed (velocity) of the block right as it hits the stake using conservation of energy! 24 Conservation of Energy Problems • Remember in Chapter 2 we solved free fall problems. Can you recall how to find the maximum height if the initial velocity is 40 m/s? • How many seconds does it take to get to the highest point? • What’s the average velocity? • What the distance (or height)? • We could also use conservation of energy to solve for h. 1 mv2 mgh 2 25 “Using” vs. “Conserving” Energy • You turn on a light in your study, assume the energy ultimately came for a hydroelectric power plant. Describe the what is going on… • In what sense do you use energy up? • Is energy really destroyed? • What is being used up? Energy can never be created or destroyed, just converted from one form into another 26 Conservation of Mechanical Energy Mechanical Energy = Kinetic Energy + Potential Energy 27 3.3 Collisions • Distinguish between elastic and inelastic collisions. • Use momentum conservation to solve collision problems. • Explain how momentum, impulse, force, and time are related. 28 Elastic and Inelastic Collisions • A collision occurs when two or more objects hit each other. • When a perfectly elastic collision occurs, objects bounce off each other with no loss in the total kinetic energy. • In an inelastic collision, objects change shape or stick together, and the total kinetic energy of the system decreases. • During any collision, momentum is always conserved. 29 One Dimensional Collision • When two (or more) objects collide, momentum is conserved. But for the system of objects, not for any one individual object. • That is the total momentum before equals the total momentum after the collision. • m1v1 + m2v2 = m1v1 + m2v2 30 Trains “Coupling” after Collision • Both trains share a common final velocity! • m1v1 + m2v2 = (m1 + m2)v 31 Momentum as a Vector When the firecracker bursts, the vector sum of the momenta of its fragments add up to the firecracker’s momentum just before bursting. 32 Forces in Collisions & Bouncing • The impulse equals the change in momentum, so… • …the bigger the change in momentum, the greater the impulse and force… • Changing directions usually means a bigger change in momentum! A “Pelton Wheel” has curved paddles instead of flat ones – causing the water to “bounce” away creating more force! http://www.youtube.com/watch?v=3eE9NVKCipQ 33 Both cars have the same momentum to begin with – and both have the same momentum at the end (zero!) – so the change in momentum is the same, and therefore the impulse on the cars is the same…. But would you rather stop with a large force in a short time, or with a smaller force over a longer time interval? 34 Car Crash Safety • Remember the impulse on an object equals its change in momentum. • But for a given impulse, you can decrease the force by increasing the time! Seat belts and air bags both help extend time. 35 Class Problems • A 75 kg crash dummy traveling at 22 m/s (~50 mph) stops in 0.01 seconds. What is the force on the driver? What is the acceleration? How could we increase the time to lessen the force and acceleration? What if the time to stop was 0.15 seconds? • An 8,000-kg train car moves to the right at 10 m/sec. It collides with a 2,000-kg parked train car. The cars get stuck together and roll along the track. How fast do they move after the collision? 36 Rockets: Out of This World Travel Robert H. Goddard (1882 – 1945) New York Times editorial: "Professor Goddard . . . does not know the relation of action to reaction, and of the need to have something better than a vacuum against which to react… seems to lack the knowledge ladled out daily in high schools." July 1969 - Further investigation and experimentation have confirmed the findings of Isaac Newton in the 17th Century and it is now definitely established that a rocket can function in a vacuum as well as in an atmosphere. The Times regrets the error. 37 Rockets: Out of This World Travel • Think back to Newton’s 3rd Law! • Momentum is conserved so that the momentum of the rocket equals the momentum of the gas. • Remember momentum is a vector! The two ice skaters have zero momentum initially, after pushing off of each other one acquires momentum to the right, the other the same amount of momentum to the left? Who has the greater velocity? 38 Chapter 3 Review 1) 2) 3) 4) 5) 6) When swimming, you push the water backwards – call this action. What is the reaction force? (a) Which has the greater mass, a heavy truck at rest or a rolling skateboard? (b) Which has a greater momentum? Does impulse equal momentum, or a change in momentum? You can’t throw a raw egg against a wall without breaking it, but you can throw it at the same speed into a sagging sheet without breaking it. Comic-strip hero Superman meets an asteroid in outer space and hurls it at 100 m/s, as fast as a bullet. The asteroid is a thousand times more massive than Superman. In the strip, Superman is seen at rest after the throw. Taking physics into account, what would be his recoil speed? Most Earth satellites follow an oval shaped (elliptical) path rather than a circular path around the Earth. The PE increases when the satellite moves farther from the Earth. According to the law of energy conservation, does a satellite have its greatest speed when it is closest to or farthest from Earth? 39