Length Contraction Calculator, Formula and Sample Problems

Length Contraction Calculator :

Enter the length contraction calculator to discover that length is relative to the point of view, and you get the calculator check it.

Length Contraction Calculator

Length Contraction Formula :

Length contraction Formula is L(m) is equal to the length of an object at rest L0(m)  in meter and multiply the root of  square velocity of the object v2 (m/s) and divided by square of  velocity of the object c2(m/s) in meter per second. Hence the formula of length contraction can be written as

L(m)=L0(m) *√1-v2 (m/s)/ c2(m/s)

L → length of an object with is in relativistic speed in m

L0→ length of an object at rest in m

C→ velocity of light in m/s

V→ velocity of the object in m/s

Sample Problems :

Example1 :

Calculate the contracted length of an object whose initial length 20 m and travel with a velocity 0.80c?

Solution :

Given parameters are

L0=20m

V=0.80c

C=speed of light (3.0 ×108 m/s)

The formula for length contraction is

L=L0√1-v2 / c2

L=20√1-0.80c2/ c2

L=20×√1-(0.80)2

L=20×√0.36

L=12m

Example2 :

Calculate the contracted length of an object whose initial length 40 m and travel with a velocity 0.50c?

Solution :

Given parameters are

L0=40m

V=0.50c

C=speed of light (3.0 ×108 m/s)

The formula for length contraction is

L=L0√1-v2 / c2

L=40√1-0.50c2/ c2

L=40×√1-(0.50)2

L=40×√0.75

L=34.64m

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