Physics 114A - Mechanics Lecture 22 (Walker: Ch. 9.6-8) Collisions and C.M. February 21, 2014

Physics 114A - MechanicsLecture 22 (Walker: Ch. 9.6-8)Collisions and C.M.February 21, 2014 John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw.edu

Announcements • Exam 2 was returned yesterday: Av.= 64.23, StD=17.62 .If you did not get yours, see Susan Miller in room C136 PAB. • Check your Exam 2 section scores on WebAssign to make sure you have credit for both sections. The Exam 2 Solutions are available from the Physics 114A Course Schedule by clicking on “Exam 2”. Regrade requests may be turned in to Susan Miller until 4 PM on Monday, February 24. • My office hours are 12:30-1:20 PM on Tuesdays and 2:30-3:20 PM on Thursdays, both in the “114” area of the Physics Study Center on the Mezzanine floor of PAB A (this building). Physics 114A - Lecture 22

Lecture Schedule (Part 3) We are here. Physics 114A - Lecture 22

Elastic Collisions In elastic collisions, both kinetic energy and momentum are conserved. One-dimensional elastic collision: Physics 114A - Lecture 22

Momentum Conservation Energy Conservation Speed of approach = Speed of separation Elastic Collisions in 1D Physics 114A - Lecture 22

Elastic Collisions with v2i = 0 If v1i=v0 and v2i=0, we have two equations (conservation of momentum and conservation of kinetic energy) and two unknowns (the final speeds). Solving for the final speeds, we get: Physics 114A - Lecture 22

Three Elastic Collisions Equal masses. Big on Small. Small on Big. Physics 114A - Lecture 22

Example:Elastic Collision of Two Blocks A 4.0 kg block moving to the right at 6.0 m/s undergoes an elastic head-on collision with a 2.0 kg block moving to the right at 3.0 m/s. Find their final velocities. Physics 114A - Lecture 22

Example: Elastic Collision of a Neutron and a Nucleus A neutron of mass mn and speed vniundergoes a head-on elastic collisionwith a carbon nucleus of mass mC initially at rest. (a) What are the final velocities of both particles?(b) What fraction of its initial kinetic energy does the neutron lose? Physics 114A - Lecture 22

2D Elastic Collisions Two-dimensional collisions can only be solved if some of the final information is known, such as the final velocity of one object: Physics 114A - Lecture 22

Clicker Question 1 A juggler performs a series of juggling tricks with three steel balls while standing on a bathroom scale. Usually two of the balls are in the air, and he is handling the third one. How does the average scale reading while he is juggling compare with the reading while he is holding the balls at rest? • The average weight reading is lower while he is juggling. • The average weight reading is the same. • The average weight reading is larger while he is juggling Physics 114A - Lecture 22

Center of Mass The center of mass of a system is the point where the system can be balanced in a uniform gravitational field. Physics 114A - Lecture 22

Center of Mass For two objects: The center of mass is closer to the more massive object. Note that we can also apply this relation to the velocities and accelerations of the objects and their center of mass. Physics 114A - Lecture 22

Center of Mass The center of mass need not be within the object: Physics 114A - Lecture 22

Center of Mass The center of mass is the point on (or near) an extended object that moves as if all the mass of the object were concentrated at that point. xcm = (m1x1 + m2x2)/(m1 + m2) Physics 114A - Lecture 22

Example: Exploding Projectile A projectile is fired into the air over level ground in a trajectory that would result in its landing 55 m away. However, at its highest point it explodes into two fragments of equal mass. Immediately after the explosion, one fragment has a momentary speed of zero and then falls straight down. Where does the other fragment land? Physics 114A - Lecture 22

Example:Changing Places in a Rowboat Pete (mass 80 kg) and Dave (mass 120 kg) are in a rowboat (mass 60 kg) on a calm lake. Dave is near the bow of the boat, rowing, and Pete is at the stern, 2.0 m from the center. Dave gets tired and stops rowing. Pete offers to row, so after the boat comes to rest they change places. How far does the boat move when they change places? Since there are no external forces, the system CM does not move. Physics 114A - Lecture 22

Motion of the Center of Mass Motion of the center of mass: Physics 114A - Lecture 22

Center of Mass The total mass multiplied by the acceleration of the center of mass is equal to the net external force: The center of mass accelerates just as though it were a point particle of mass M acted on by Physics 114A - Lecture 22

Rocket Science A rocket engine burns fuel and expels it from its exhaust as hot gases. The rocket+gas system is isolated and will have no change in momentum: pR + pG = 0 Therefore, the rocket gains momentum in the upward direction by giving momentum to the “fuel packet” that moves away at high velocity in the downward direction. Physics 114A - Lecture 22

Systems with Changing Mass:Rocket Propulsion If a mass of fuel Δm is ejected from a rocket with speed v, the change in momentum of the rocket is: The force, or thrust, is Physics 114A - Lecture 22

End of Lecture 22 • Before Monday, read Walker, Ch. 10.1 to 10.3. • Exam 2 was returned yesterday. If you did not get yours, see Susan Miller in room C136 PAB. • Check your Exam 2 section scores on WebAssign to make sure you have credit for both sections. The Exam 2 Solutions are available from the Physics 114A Course Schedule by clicking on “Exam 2”. Regrade requests may be turned in to Susan Miller until 4 PM on Monday, February 24. • My office hours are 12:30-1:20 PM on Tuesdays and 2:30-3:20 PM on Thursdays, both in the “114” area of the Physics Study Center on the Mezzanine floor of PAB A (this building). Physics 114A - Lecture 22

Physics 114A - Mechanics Lecture 22 (Walker: Ch. 9.6-8) Collisions and C.M. February 21, 2014