Tuesday, June 28, 2011 PHYS 1443-001, Summer 2011 Dr. Jaehoon Yu 1 PHYS 1443 – Section 001 Lecture #13 Tuesday, June 28, 2011 Dr. Jaehoon Yu • Collisions • Center of Mass • Rotational Motion • Rotational Kinematics • Relationship Between Angular and Linear quantitiesTuesday, June 28, 2011 2 Announcements • Reading Assignment – CH9.10 • Quiz #3 tomorrow, Wednesday, June 29 – Beginning of the class – Covers CH8.1 through CH9.9 • Planetarium Show extra credit – Must obtain the signature of the “Star Instructor” AFTER watching the show on the ticket stub – Tape one side of the ticket stubs on a sheet of paper with your name on it – Submit it on the last class Thursday, July 7 • Late submissions will not be accepted!!! PHYS 1443-001, Summer 2011 Dr. Jaehoon YuTuesday, June 28, 2011 PHYS 1443-001, Summer 2011 Dr. Jaehoon Yu 3 Valid Planetarium Shows • Regular shows – TX star gazing; Nanocam; Ice Worlds • Private shows for a group of 15 or more – Bad Astronomy; Black Holes; IBEX; Magnificent Sun – Microcosm; Stars of the Pharaohs; Time Space – Two Small Pieces of Glass; SOFIA – Violent Universe; Wonders of the Universe • Please watch the show and obtain the signature on the back of the ticket stubTuesday, June 28, 2011 PHYS 1443-001, Summer 2011 Dr. Jaehoon Yu 4 Extra-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 8 of this lecture note in a far greater detail than in the note. – 20 points extra credit • Show mathematically what happens to the final velocities if m1=m2 and explain in detail in words the resulting motion. – 5 point extra credit • NO Credit will be given if the process is too close to the note! • Due: Start of the class Tuesday, July 5Extra Credit: Two Dimensional Collisions • Proton #1 with a speed 5.0x106 m/s collides elastically with proton #2 initially at rest. After the collision, proton #1 moves at an angle of 37o to the horizontal axis and proton #2 deflects at an angle φ to the same axis. Find the final speeds of the two protons and the scattering angle of proton #2, φ. This must be done in much more detail than the book or on page 13 of this lecture note. • 10 points • Due beginning of the class Wednesday, July 6 Tuesday, June 28, 2011 5 PHYS 1443-001, Summer 2011 Dr. Jaehoon YuTuesday, June 28, 2011 PHYS 1443-001, Summer 2011 Dr. Jaehoon Yu 6 Collisions 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 on a microscopic scale. t F F12 F21 Assuming 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 Using Newton’s 3rd law we obtain So the momentum change of the system in a collision is 0, and the momentum is conserved d p2 d p = −d p1 = d p1+ d p2 psystem = p1+ p2Tuesday, June 28, 2011 PHYS 1443-001, Summer 2011 Dr. Jaehoon Yu 7 Elastic and Inelastic Collisions Collisions are classified as elastic or inelastic based on whether the total 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 Collision Two 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 Collision A 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.Tuesday, June 28, 2011 PHYS 1443-001, Summer 2011 Dr. Jaehoon Yu 8 Elastic and Perfectly Inelastic Collisions In perfectly inelastic collisions, the objects stick together after the collision, moving together. Momentum is conserved in this collision, so the final velocity of the stuck system is How about elastic collisions? In elastic collisions, both the momentum and the kinetic energy are conserved. Therefore, the final speeds in an elastic collision can be obtained in terms of initial speeds as m1v1i− v1 f( )= m2v2i− v2 f( )v1 f=m1− m2m1+ m2⎛⎝⎜⎞⎠⎟v1i+2m2m1+ m2⎛⎝⎜⎞⎠⎟v2im1v1i− v1 f( )v1i+ v1 f( )= m2v2i− v2 f( )v2i+ v2 f( )From momentum conservation above v2 f=2m1m1+ m2⎛⎝⎜⎞⎠⎟v1i+m1− m2m1+ m2⎛⎝⎜⎞⎠⎟v2iWhat happens when the two masses are the same?Tuesday, June 28, 2011 PHYS 1443-001, Summer 2011 Dr. Jaehoon Yu 9 Example for Collisions A car of mass 1800kg stopped at a traffic light is rear-ended by a 900kg car, and the two become entangled. If the lighter car was moving at 20.0m/s before the collision what is the velocity of the entangled cars after the collision? piThe momenta before and after the collision are What can we learn from these equations on the direction and magnitude of the velocity before and after the collision? m1 20.0m/s m2 vf m1 m2 Since momentum of the system must be conserved pi= pfThe cars are moving in the same direction as the lighter car’s original direction to conserve momentum. The magnitude is inversely proportional to its own mass. Before collision After collision = m1v1i+ m2v2i = 0 + m2v2i pf = m1v1 f+ m2v2 f = m1+ m2( )vf m1+ m2( )vf = m2v2i vf =m2v2im1+ m2( ) =900 × 20.0900 + 1800= 6.67m / sTuesday, June 28, 2011 PHYS 1443-001, Summer 2011 Dr. Jaehoon Yu 10 The mass of a block of wood is 2.50-kg and the mass of the bullet is 0.0100-kg. The block swings to a maximum height of 0.650 m above the initial position. Find the initial speed of the bullet. Ex.9 – 11: A Ballistic Pendulum m1vf 1+ m2vf 2= m1+ m2( ) v01=What
View Full Document
Unlocking...