PHY100H1 Lecture Notes - Lecture 5: Inertial Frame Of Reference, Special Relativity

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6 Oct 2018

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PHY100H1 Lecture Notes - Lecture 4: Special Relativity

PHY100H1 Lecture Notes - Lecture 5: Inertial Frame Of Reference, Special Relativity

PHY100H1 Lecture Notes - Lecture 6: Michael Faraday, Popular Science

Document Summary

Inertial frame: anything that is moving at constant velocity or at rest. Imagine if there was a light shone on one side of the room with two people. The person closer to the light is walking towards the light when it is shone. The speed of light that the person moving feels, would seem faster. One twin remains on earth (twin 1) while the other hops on a rocket to space (twin 2) They each have a clock that measures time where they are. To the twin on earth, looking at the twin in space, the twin in space seems to have a slower moving clock. So according to the twin on earth, the time for the twin in space is dilated (slower). When the twin in the rocket looks at the other twin, he will think that he is going backwards at velocity v (because he is moving in the opposite direction - away from him)

Related Questions

Learning Goal: To understand length contraction and timedilation.

An inertial frame of reference is one in which Newton's laws hold.Any frame of reference that moves at a constant speed relative toan inertial frame of reference is also an inertial frame. Theproper length l_0 of an object is defined to be the length of theobject as measured in the object's rest frame. If the length of theobject is measured in any other inertial frame, moving with speed urelative to the object's rest frame (in a direction parallel tol_0), the resulting length l is given by the length contractionequation

l = l_0\sqrt{1-\frac{u^2}{c^2}} ,

where c is the speed of light. Similarly, if two events occur atthe same spatial point in a particular reference frame, and anobserver at rest in this frame measures the time interval betweenthese two events, the time interval so measured is defined to bethe proper time Delta t_0. When the time interval is measured inany other inertial frame, again moving with speed u relative to thefirst frame, the resulting time interval Delta t is given by thetime dilation equation

\Delta t = \frac{\Delta t_0}{\sqrt{1-\frac{u^2}{c^2}}} .

a. Suppose that you measure the length of a spaceship, at restrelative to you, to be 400 \rm m. How long will you measure it tobe if it flies past you at a speed of u = 0.75c?
Express the length l in meters to three significant figures.

b. The spaceship from Part A has a large clock attached to itsside. This clock ran at the same rate as your watch when you werein the same reference frame. How much time Delta t will pass onyour watch as 80 \rm s passes on the clock attached to theship?
Express your answer in seconds to three significant figures.

c. Two spaceships, named A and B, are flying toward each other withrelative speed 0.800c. If the captain of ship A fires a missile,counts 10.0 \rm s on his watch, and then fires a second missile,how much time Delta t will the captain of ship B measure to havepassed between the firing of the two missiles?
Express your answer in seconds to three significant figures.

d. The captain of ship B knows that ship A uses 2-m-long missiles.She measures the length of the first missile, once it has finishedaccelerating, and finds it to be only 0.872 \rm m long. What is thespeed u of the missile, relative to ship B?
Express your answer in meters per second to three significantfigures. Use c = 3 \times 10^8 \; \rm m/s.

Please answer fully... thank you

x.Hmo general consequences of relativity: moving clocks run slow,and moving lengths contract (although you need to carefully applythe definitions of proper time and proper length to avoid gettingyourself stuck in an infinite thought loop).

Please look at the problem below and explain, carefully, how the"moving clocks run slow" and "moving lengths contract" rules applyto parts a, b, and c. That is, why are you not surprised at thesizes of your answers in these three parts?

An interstellar space probe is launched from Earth. After a briefperiod of acceleration it moves with a constant velocity, 72.0% ofthe speed of light. Its nuclear-powered batteries supply the energyto keep its data transmitter active continuously. The batterieshave a lifetime of 15.9 years as measured in a restframe.

(a) How long do the batteries on the space probe last as measuredby mission control on Earth?

yr

(b) How far is the probe from Earth when its batteries fail, asmeasured by mission control?

There two general consequences of relativity: moving clocksrunslow, and moving lengths contract (although you need tocarefullyapply the definitions of proper time and proper length toavoidgetting yourself stuck in an infinite thought loop).

Please look at the problem below and explain, carefully, howthe"moving clocks run slow" and "moving lengths contract" rulesapplyto parts a, b, and c. That is, why are you not surprised atthesizes of your answers in these three parts?

Aninterstellar space probe is launched from Earth. After abriefperiod of acceleration it moves with a constantvelocity, 72.0%of the speed of light. Its nuclear-poweredbatteries supply theenergy to keep its data transmitter activecontinuously. Thebatteries have a lifetime of 15.9 years as measured in a restframe.

(a) How long dothe batteries on the space probe last as measured bymissioncontrol on Earth?

yr
(b) How far is the probe from Earth when its batteries fail,asmeasured by mission control?

ly
(c) How far is the probe from Earth, as measured by itsbuilt-intrip odometer; when its batteries fail?

ly
(d) For what total time after launch is data received from theprobeby mission control? Note that radio waves travel at the speedoflight and fill the space between the probe and Earth at the timethebattery fails.