College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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To understand length contraction and time dilation.

An inertial frame of reference is one in which Newton's laws hold. Any frame of reference that moves at a constant speed relative to an inertial frame of reference is also an inertial frame. The proper length l0 of an object is defined to be the length of the object as measured in the object's rest frame. If the length of the object is measured in any other inertial frame, moving with speed u relative to the object's rest frame (in a direction parallel to l0), the resulting length lll is given by the length contraction equation

l= l0 *sqrt(1-u^2/ c^2)

where c is the speed of light. Similarly, if two events occur at the same spatial point in a particular reference frame, and an observer at rest in this frame measures the time interval between these two events, the time interval so measured is defined to be the proper time Δt0. When the time interval is measured in any other inertial frame, again moving with speed uuu relative to the first frame, the resulting time interval Δt t is given by the time dilation equation

Δt= Δt0/ sqrt(1-u^2/ c^2)

Part A: Suppose that you measure the length of a spaceship, at rest relative to you, to be 400 m. How long will you measure it to be if it flies past you at a speed of u=0.75c?

Part B: The spaceship from Part A has a large clock attached to its side. This clock ran at the same rate as your watch when you were in the same reference frame. How much time Δt t will pass on your watch as 80s passes on the clock attached to the ship?

 

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