Phy 101 Week 5 Lecture Notes
Phy 101 Week 5 Lecture Notes PHY 101 - M001
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This 4 page Class Notes was uploaded by Bryce Caplan on Thursday October 1, 2015. The Class Notes belongs to PHY 101 - M001 at Syracuse University taught by K. Foster in Fall 2015. Since its upload, it has received 28 views. For similar materials see Major Concepts of Physics I in Physics 2 at Syracuse University.
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Date Created: 10/01/15
Phy 101 Lecture 8 Sept 28 2015 Section 77 was added and 66 68 were taken off of this test Drawings will be asked of you on the test A conservation law for a vector quantity Conservation laws are useful because they simplify analysis of a large problem and are supported by a large amount of scientific effort If a quantity is conserved then no matter how complicated the situation we can set the value of the conserved quantity at one time equal to its value at a later time More simply what you put in is what you get out The conservation law allows for simple before and after scenarios Linear momentum is a vector defined by p gt mv gt The arrow comes after a vector Momentum is conserved in an isolated system Recall the medicine ball demonstration The momentum was conserved when the ball was thrown to and from the cart ImpulseMomentum Theorem When a force acts upon an object its change in momentum is equal to the product of the force and the time interval In an equation Ap gt 2F gt At 2 means the sum of all Change in momentum is also called impulse Note that this same equation can be written as mvf gt mv gt 2F gt At or mvf gt mv gt 2F gt At or mvf gt mv gt ma gt At or other ways These are just a few ways to integrate a few formulas Graphically Calculating Impulse lmpulse can be figured out in a force by time graph The impulse because it s equal to force times time is calculated by finding the area underneath the curve The average force can be found fairly easily if you know the total impulse lmpulse has units of Nsec and if you want to find the average amount of force just divide the impulse by the time NsecsecN Simple enough A restatement of Newton s Second Law The relationship between impulse and momentum provides us with a new way to understand Newton s second law Originally it was written as 2F gt LAA7 Conservation laws only work within a closed system Demo of inelastic collisions and absorption of impacts Two carts are put on a track with a sonic ranger taking their position and velocity One cart is pushed and hits into the other cart which is stationary and they stick together The cart that was pushed had its initial velocity about halved when it attached to the other cart The two carts then continued rolling in the same direction as the first cart was initially pushed but at half the velocity This is repeated but the stationary cart has a weight added to it that doubles the weight of the cart When the first cart is pushed into the stationary cart they stick together and have a final velocity of one third the first cart had when it was pushed Infrared collisions An infrared camera is pointed at a slab of wood This wood has a relatively low temperature This wood is then hit with a large hammer The place where the hammer hit the wood looks a little warmer in through the infrared camera To find out the final velocity of two objects that stick together in an elastic collision the equation for the conservation of momentum can be used 219 pr which can be turned into m1V1initialm2V2initialm1Vfinalm2vfinal Wthh can be turned Into m1v1mmalm2v2mitialm1m2v nal which can be turned Into m1V1initialm2v2initialm1m2vfinal Elastic collision demo Two carts of equal weight are pushed toward each other They bounce off of each other and have the same velocity moving away from each other This is repeated a few times and is consistent each time A weight is then added to one cart doubling that cart s weight When the two bounce off of each other the weighted cart always ends up with half of the velocity of the unweighted cart Conservation of Momentum would be satisfied by any combination of final velocities that added up to the sum of its initial velocities v nalvinitial Kinetic energy in an elastic collision there is no loss of kinetic energy KE12mv2 Z KEKE1KE2etc Kinetic energy basically just means energy of movement Energy Energy is a concept needed to explain collisions When energy stays in the same form ie no heat light sound etc is produced it is called elastic When two objects stick together it is considered perfectly inelastic Phy 101 Lecture 9 Sept 30 2015 Rockets They re different from cars in that they lose mass as time goes on to push it forward which it expels fuel Cars lose gas very very very slowly in fact for our purposes negligibly and that doesn t push it fonNard the ground does At some time t the momentum of a rocket and its remaining fuel is MA mv where v is the speed relative to the earth They are excellent examples of the conservation of momentum because they show how the effects of them pushing the gas out in a negative direction causes the vehicle to move in a positive direction in order to conserve the initial momentum of O lmpulse is FvA mAt so thrust is equal to veA mAt where ve is the velocity of the exhaust Conservation of Linear Momentum If the net external force acting on a system is zero then the momentum is conserved Basically if things fly apart the overall momentum doesn t change until something that wasn t originally there pushes on one of the things that flew apart If a squid fills a sac with water and shoots out that water to move itself fonNard how fast is it going to move Well we start with a squid floating at rest so it and its water have a total momentum of 0 But it suddenly decides to shoot out its water We can figure out how quickly the squid moves fonNard if we know the mass of the squid the mass of the water it shoots out and the speed at which it is shot out After that it becomes very simple We know that the initial momentum was 0 so in our formula of pipf we know that pi is 0 so Opf and pf is the total momentum of the system So we have vaWmsvsO where anything with a subscript of w relates to the water and anything with a subscript of s relates to the squid Then it s simple algebra If we want to find vs we first need to subtract vaW from both sides then divide both sides by ms This gives us m v v W W which we can then plug numbers into in order to get an exact answer Note 8 m S that the negative in front is because v8 and vW are vectors and they face in the opposite direction If as a random number you got 4239ms that just means that it s going 4239ms in the opposite direction of the water Recall Inelastic collisions They happen when the two masses that collide become one unit or move together as one unit effectively combining their masses Recall elastic collisions Two masses bounce off of each other and their momentum is totaled as a system In both inelastic and elastic collisions as long as no outside force is applied the momentum before the collision is the same as that after the collision Make drawings always draw it can never hurt Make sure the sum of the momenta are equal before and after or make pipf MAke sure you know what type of collision occurs and make sure you know what you re solving for Energy and Work Various types of energy include thermal kinetic gravitational potential spring potential chemical potential nuclear potential etc Heavy pendulum demo A pendulum swinging back and forth will have potential energy at the top of its swing which will convert into kinetic energy as it goes to the bottom of its swing until it s all kinetic energy at the bottom of the swing As the ball moves back up the kinetic energy turns back into gravitational energy The person holding the heavy ball in front of hisher face will be okay because all of the kinetic energy of the ball is turned into potential energy at the top of its swing some of which is lost due to friction Energy Energy is always conserved and summative The energy in a system is always conserved Some of the energy in the demonstration was lost to the environment but if we think of the part that supplies the friction the air and friction at the top of the string as part of the system we notice that no energy is lost Whatever energy is not converted back into potential energy is turned into heat light and sound energy or kinetic energy of the air surrounding the pendulum That little loss of energy was enough to keep the person s face from being bashed by a large ball Work Work is the change in energy WAE Work requires motion so even if you hold a really heavy object up you re not doing any work Work is also defined as force times displacement Kinetic energy is the energy that a moving object has that can do work The notes from the lecture show how the equation for kinetic energy is derived Ekin1l2mv2 This is an equation that needs to be memorized
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