PPT Modern Physics

8/10/2019 PPT Modern Physics

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Time Dilation , LengthContraction and Mass Increase

Group 1

Asmah Syafitri

Dian Purnamasari

Yudhistira


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Speed of light is constant


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Our conceptions of space and time has to be

changed.

Facts:

Regardless of speed or direction, observers always

measure the speed of light to be the same value.

Speed of light is maximum possible speed.

Consequences:

The length of an object decreases as its speed

increases

Clocks passing by you run more slowly than do clocks

at rest


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5

Time dilation

Laser bounces up and down from mirror on train.

Joe on ground measures time interval w/ his clock.

Joe watches Janesclock on train as she measuresthe time interval.

Joe sees that these two time intervals are different.

Reference frame

of Janeon train Reference frameof Joeon ground


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Why is this?

Jane on train: light pulse travels distance 2d.

Joe on ground: light pulse travelsfarther Relativity: both Joe and Jane say light travels at c

Joe measures longer travel time of light pulse

This is time dilation

Reference frame of

Janeon train

Reference frame of

Joeon ground


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7

Time dilation, continued

ObserverJaneon train: light pulse travels distance 2d. Time = distance divided by velocity = 2d/c

Time in the frame the events occurred at same location

called the proper time tp

Reference frame of Jane

on train

Reference frame of

Joeon ground


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8

Joe measures a longertime

Time dilation

Time interval in Janes frame

tJane round trip distancespeedof light

2dc

tJoe2 d2 vtJoe /2

2

c

1

1 (v /c)21

tJoe

1

1 (v /c)22d

c

tpd

(vt)/2


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Time Dilation

Events occur in the same location are denoted with the prime frame, S.


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10

The proper time We are concerned with two time intervals.

Intervals between two events.

A single observer compares time intervals measured in

different reference frames.

If the events are at the same spatial location in

one of the frames

The time interval measured in this frame

is called the proper time.

The time interval measured in a frame moving with

respect to this one will be longer by a factor of tother frametproper, 1


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Length contractionAs measured by anEarthling the Earth-to-star distance is Lo, theproper length as measured by an observer atrest with respect to the ends of the ruler, andthe time to make the trip is t. An Astronautmeasures the distance to be L& the time to.

Voyage to a star!

Lo L

u

u u

to

t


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Length Contraction

The Idea :

If the time intervals are different, and speed isthe same, how can distances be the same?

The distances are not the same!Length contraction


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Length Contraction

Spaceship Moving at the 10 % the Speed of Light

Spaceship Moving at the 86.5 % the Speed of Light


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Length Contraction

Spaceship Moving at the 99 % the Speed of Light

Spaceship Moving at the 99.99 % the Speed of Light


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15

Length contraction and proper length

Which one is correct?

Just like time intervals,distances are different in different frames.

There is no preferred frame,so one is no more correct than the other.

The proper length Lpis the length measuredin a frame at rest with respect to objects

Here the objects are Earth and star.

LLp

Lp 1

v 2

c 2

Length in moving

frame

Length in objects

rest frame


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PPT Modern Physics