ASTR BC 1754y Lecture Notes - Lecture 12: Length Contraction, Time Dilation, Special Relativity

16 views1 pages

apricotsalmon916

26 Aug 2016

School

Barnard College

Department

Physics and Astronomy

Course

ASTR BC 1754y

Professor

Jacquelinevan Gorkom

For unlimited access to Class Notes, a Class+ subscription is required.

Document Summary

Speed of light is the same in the direction of the motion of earth and perpendicular to it. No information can travel faster than the speed of light, and no material can reach the speed of light. If you observe anyone or anything moving by you at a speed close to the sol you will conclude time runs more slowly for that person or object. If you measure the size of something moving by you close to the speed of light you will find that it s length is shorter than if it were not moving. If you measure the mass of something moving close to the speed of light, you will find it to have a greater mass than at rest. The laws of nature are the same for everyone. The speed of light is the same for everyone. The speed of light is the same in all reference frames.

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

ASTR BC 1754y Lecture Notes - Lecture 12: Length Contraction, Time Dilation, Special Relativity

Document Summary

Get access

Related textbook solutions

Physics: Principles with Applications

Related Documents

ASTRO 142 Chapter Notes - Chapter 7: Lorentz Transformation, Galilean Transformation, Galilean Invariance

ASTR 1210 Chapter Notes - Chapter S2: Thought Experiment, Green Flash, Length Contraction

AST201H1 Chapter Notes - Chapter S2: Infinite Mass, Time Dilation, Length Contraction

Related Questions