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UT Arlington PHYS 1441 - Lecture Notes

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PHYS 1441 – Section 002 Lecture #17AnnouncementsSlide 3Slide 4Reminder: Special ProjectReminder: Special Project IIExtra-Credit Special ProjectMore on Conservation of Linear Momentum in a Two Body SystemHow do we apply momentum conservation?Ex. Ice SkatersCollisionsElastic and Inelastic CollisionsElastic and Perfectly Inelastic CollisionsEx. A Ballistic PendulumEx. A Ballistic Pendulum, cnt’dTwo dimensional CollisionsExample for Two Dimensional CollisionsMonday, Nov. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu1PHYS 1441 – Section 002Lecture #17Monday, Nov. 15, 2010Dr. Jaehoon Yu•Linear Momentum Conservation•Collisions•Center of Mass•Fundamentals of Rotational MotionToday’s homework is homework #10, due 10pm, Tuesday, Nov. 23!!Announcements•Quiz #5–Beginning of the class this Wednesday, Nov. 17–Covers: CH 6.5 – CH 7.8•Two colloquia this week–One at 4pm Wednesday, Nov. 17–Another at 4pm Friday, Nov. 19Monday, Nov. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu2Reminder: Special Project1. A ball of mass M at rest is dropped from the height h above the ground onto a spring on the ground, whose spring constant is k. Neglecting air resistance and assuming that the spring is in its equilibrium, express, in terms of the quantities given in this problem and the gravitational acceleration g, the distance x of which the spring is pressed down when the ball completely loses its energy. (10 points)2. Find the x above if the ball’s initial speed is vi. (10 points)3. Due for the project is this Wednesday, Nov. 17.4. You must show the detail of your OWN work in order to obtain any credit.Monday, Nov. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu5Monday, Nov. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu6Reminder: Special Project IIA ball of mass m is attached to a light cord of length L, making up a pendulum. The ball is released from rest when the cord makes an angle θA with the vertical, and the pivoting point P is frictionless. A) Find the speed of the ball when it is at the lowest point, B, in terms of the quantities given above.B) Determine the tension T at point B in terms of the quantities given above. Each of these problem is 10 point. The due date is this Wednesday, Nov. 17.mgmmθALTh{BPMonday, Nov. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu7Extra-Credit Special Project•Derive the formula for the final velocity of two objects which underwent an elastic collision as a function of known quantities m1, m2, v01 and v02 in page 13 of this lecture note in a far greater detail than the note.–20 points extra credit•Show mathematically what happens to the final velocities if m1=m2 and describe in words the resulting motion.–5 point extra credit•Due: Start of the class Monday, Nov. 29Monday, Nov. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu8More on Conservation of Linear Momentum in a Two Body SystemWhat does this mean?As in the case of energy conservation, this means that the total vector sum of all momenta in the system is the same before and after any interactionsMathematically this statement can be written as Whenever two or more particles in an isolated system interact, the total momentum of the system remains constant. pur=∑From the previous lecture we’ve learned that the total momentum of the system is conserved if no external forces are exerted on the system.2 1i ip p+ =r rThis can be generalized into conservation of linear momentum in many particle systems.systemxfsystemxiPPsystemyfsystemyiPPsystemzfsystemziPP2 1f fp p+r r pur2+pur1=constMonday, Nov. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu9How do we apply momentum conservation?1. Define your system by deciding which objects would be included in it.2. Identify the internal and external forces with respect to the system.3. Verify that the system is isolated.4. Set the final momentum of the system equal to its initial momentum. Remember that momentum is a vector.Monday, Nov. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu10Starting from rest, two skaters push off against each other on ice where friction is negligible. One is a 54-kg woman and one is a 88-kg man. The woman moves away with a speed of +2.5 m/s. Find the recoil velocity of the man.Ex. Ice Skaters=f oP Pr r1 1 2 2f fm v m v+ =2fv =2fv =No net external force  momentum conserved0Solve for Vf21 12fm vm-( ) ( )54 kg 2.5m s1.5m s88 kg+- =-Monday, Nov. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu11Collisions Consider a case of a collision between a proton on a helium ion. The collisions of these ions never involve physical contact because the electromagnetic repulsive force between these two become great as they get closer causing a collision.Generalized collisions must cover not only the physical contact but also the collisions without physical contact such as that of electromagnetic ones in a microscopic scale. Δrp1=rF21ΔttFF12F21Assuming no external forces, the force exerted on particle 1 by particle 2, F21, changes the momentum of particle 1 by Likewise for particle 2 by particle 1 2 12p F tD = DrrUsing Newton’s 3rd law we obtain So the momentum change of the system in the collision is 0, and the momentum is conserved Δpur2 Δpur12F t= Dr21F t=- Dr =−Δpur1 =Δpur1+Δpur2 pursystem =pur1+pur2constant0Monday, Nov. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu12Elastic and Inelastic Collisions Collisions are classified as elastic or inelastic based on whether the kinetic energy is conserved, meaning whether it is the same before and after the collision.A collision in which the total kinetic energy and momentum are the same before and after the collision. Momentum is conserved in any collisions as long as external forces are negligible.Elastic CollisionTwo types of inelastic collisions:Perfectly inelastic and inelastic Perfectly Inelastic: Two objects stick together after the collision, moving together with the same velocity.Inelastic: Colliding objects do not stick together after the collision but some kinetic energy is lost.Inelastic CollisionA collision in which the momentum is the same before and after the collision but not the total kinetic energy .Note: Momentum is constant in all collisions but kinetic energy is only in elastic collisions.Monday, Nov. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu13Elastic and Perfectly Inelastic Collisions In perfectly inelastic collisions, the objects stick together after the


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UT Arlington PHYS 1441 - Lecture Notes

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