Relative Motion (a little more than what s in your text, so pay attention)

Transcription

1 Lab Activity

2 Relative Motion (a little more than what s in your tet, so pay attention) Relative motion is something we use everyday, but we don t really think about it. For eample, passing a truck on the highway: 60 mph 70 mph What is your speed relative to the truck? (Or more precisely, what does someone on the truck measure for your speed?) Or: 10 mph 60 mph 70 mph What is the truck s speed relative to you? (Or more precisely, 130 mph what do you measure for the truck s speed? What about velocities?) These questions are pretty easy in 1D, but in 2D, it s better to follow a procedure.

3 Events and Frames of Reference Event: something that happens at a particular place in space at a particular time. Frame S y Event is at point (,y) at time t time t Reference Frame: coordinate systems and clocks to measure position and time of an event. Relative Motion is concerned with how coordinates of events and velocities of objects are related in two frames of reference that are moving relative to each other.

4 S Visualization S V y Space location of event At t=0, the event has the same coordinates in frames S and S, but what about later times when S is moving with constant velocity? (Note the prime in S has nothing do with differentiation) (visualization won t work in a pdf)

5 Frame S y Relative Motion y Frame S event What coordinates and time (?) do observers in S and S measure for the event? Let: Frames S and S coincide at t=0; and and aes be parallel

6 The Galilean Position Transformations S y S y event *interchange primes and unprimes, and From the previous page: Or in component form: Inverse* Who says that the time is the same in the two frames? Wait until PHY192. The Galilean Position Transformations: relates the coordinates of an event in the two frames

7 Relative Velocity Visualization Consider a football as seen from two reference frames. S S V What do observers in frames S and S measure for the velocity of the football? (visualization won t work in a pdf)

8 S S Galilean Velocity Transformations Let: So: The Galilean Position Transformation: Differentiate with respect to time: inverse Or, in component form: Galilean Velocity Transformations. If we know the components of the velocity of an object in one frame, we can calculate them in another frame.

9 Whiteboard Problem 4-5 Steve throws a baseball upward and toward the East at a 63 o angle above the ground with a speed of 22 m/s. Nancy drives East past Steve at 30 m/s at the instant he releases the ball. a) According to Nancy, what is the speed of the ball? (LC) b) According to Nancy, in what direction is the ball travelling? (LC) 22 m/s Note: The most important step in 63 o doing any relative motion problem is to define the frames of reference and draw them. Then define what frames the velocities are relative to. West 30 m/s East

10 Whiteboard Problem 4-6: Driving in the Rain What do you observe when you drive in the rain or snow? When the car is not moving, the rain may be coming straight down, but when you re driving, it appears to be coming at you. Suppose that when you re standing still, you observe that raindrops fall straight down with a speed of 10 mph. When you are driving in your car at a speed of 60 mph, what do you observe for the speed of the raindrops, and what direction (LC) are they coming from?

11 Why are We Being So Picky About This? What we re doing now in PHY191 What we ll do in the Spring in PHY192 (Special Relativity)

12 Whiteboard Problem 4-7: Looking Ahead to PHY192 Two rockets leave the Earth in opposite directions. Rocket A travels at a speed of 0.8c relative to the Earth, and rocket B travels at 0.9c relative to the Earth. (c is the speed of light) v = -0.9c S S B 0.9c A V = 0.8c a) According to the Galilean Velocity Transformations, what do the passengers on Ship A measure for the speed of ship B? (LC) (do it in your head, enter your answer as v/c) b) According to the Lorentz Velocity Transformations, what do the passengers on Ship A measure for the speed of ship B? (LC) Ans: speed = 1.7c Ans: speed = 0.988c