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Physics 114A - Mechanics Lecture 7 (Walker: 3.6) Relative Motion January 16, 2014. John G. Cramer Professor Emeritus, Department of Physics B451 PAB email@example.com. Announcements.
Physics 114A - MechanicsLecture 7 (Walker: 3.6)Relative MotionJanuary 16, 2014 John G. Cramer Professor Emeritus, Department of Physics B451 PAB firstname.lastname@example.org
Announcements • Homework Assignments #1-3 are now available on WebAssign. Assignment #1 is due at 11:59 PM tonight (Thursday, January 16). Be sure to do the “A” homework (not “B”). So far 216/218 students have registered for 114A on WebAssign. Everyone MUST register on WebAssign before Exam 1. • Obtain a H-iTT clicker from the University Bookstore. RF Clickers should be set to Channel 01. Register your clicker using the “Clicker” link on the Physics 114A Syllabus page. So far 202/218 students have registered their clickers. • If you are disabled and plan to take the 114A exams at the DRS Office in Mary Gates Hall, see me as soon as possible to make arrangements. • The 117 labs start this week. By 8:00 AM on the day of your lab, you must have completed the Pre-Lab exam on WebAssign. Physics 114A - Lecture 7
Lecture Schedule (Part 1) We are here. Physics 114A - Lecture 7
Finding v(t) and a(t) from r(t) Suppose we have an equation in powers of t that gives the position r of an object vs. time. How can we find the velocity v and acceleration a? Physics 114A - Lecture 7
Vector Motion withConstant Acceleration Average velocity: Velocity as a function of time: Position as a function of time: Physics 114A - Lecture 7
Graphs of x-y and v-t Physics 114A - Lecture 7
Clicker Question 1 Which of the blue position vs.time graphs goes with this greenvelocity vs. time graph? Theparticle’s position at ti = 0 s isxi= -10 m. Physics 114A - Lecture 7
Relative Motion Definition: An Inertial Reference Frame is any coordinate system (or frame of reference) that is either at rest or moving in some direction with a constant velocity. Example: a train or airplane moving forward with a constant speed. Physics 114A - Lecture 7
Relative Motion The speed of the passenger with respect to the ground depends on the relative directions of the passenger’s and train’s speeds: vgnd = 16.2 m/s vgnd = 13.8 m/s Physics 114A - Lecture 7
Relative Motion This also works in two dimensions: Physics 114A - Lecture 7
Relative Motion Amy, Bill, and Carlos all measure the velocity of the runner and the acceleration of the jet plane. The green velocity vectors are shown in Amy’s reference frame. What is the runner’s velocity? It depends on the frame of the observer. Amy: vR = 5 m/s Bill: vR = 0 m/s Carlos: vR =-10 m/s What about aplane? Physics 114A - Lecture 7
Relative Position The position depends on the frame. A set of position observations in one frame can be transformed to get equivalent observations in another frame. Physics 114A - Lecture 7
z’ B y’ x’ Relative Velocity The velocity also depends on the frame. A set of velocity observations in one frame can be transformed to get equivalent observations in another frame. z vpA A y vAB x Physics 114A - Lecture 7
Example: Flying a Plane A pilot wishes to fly a plane due north relative to the ground. The airspeed of the plane is 200 km/h, and the wind is blowing from west to east at 90 km/h.(a) In which direction should the plane head?(b) What will be the ground speed of the plane? Physics 114A - Lecture 7
Example: Crossing a River You are riding in a boat with a speed relative to the water of vbw = 6.1 m/s. The boat points at an angle of q = 25° upstream on a river flowing at vwg = 1.4 m/s. (a) What is your speed vbgand angle qbg relative to the ground? Physics 114A - Lecture 7
Example: A Ball Toss • Mike throws a ball upward at a 630 angle with a speed of 22 m/s. Nancy rides past Mike on her bicycle at 10 m/s at the instant he releases the ball. • What trajectory does Mike see? • What trajectory does Nancy see? Physics 114A - Lecture 7
The Object and FrameVelocities Add Vectorially Physics 114A - Lecture 7
Galilean Relativity Consider how the acceleration transforms from frame Sto frame S’, an inertial frame that is moving with constant velocity V relative to S. An “inertial frame” is defined to be any reference frame that is at rest or moving with a constant velocity. Velocities add, so Galilean Relativity: While position and velocity are frame-dependent, acceleration is observed to be the same in all inertial reference frames. Physics 114A - Lecture 7
Galileo vs. Einstein The laser beam moves along the x axis away from Tom at the speed of light, vx = 3 x 108 m/s. Sue flies by in her space ship, moving along the x axis at Vx =2 x 108 m/s. From her point of view, how fast is the laser beam moving? Galileo:vx’ = vx – Vx= 1 x 108 m/s Einstein:vx’ = vx = 3 x 108 m/s Velocity transformations are valid in all inertial reference frames. The speed of light is the same in all inertial reference frames. Physics 114A - Lecture 7
Before the next lecture on Friday, read Walker, Chapter 4.1 and 4.2 • Homework Assignments #1 is due at11:59 PM on Thursday, January 16 (tonight!). Homework Assignments #2 is due at 11:59 PM on Thursday, January 23. • No class on Monday due to the MLK Holiday. We will have Exam 1 on Friday, January 24. Send seat requests, if you have not already done so. End of Lecture 7