# Percent Length Contraction (check solution)

• Quelsita
In summary, the percent length contraction of an aircraft traveling at Mach 2 is approximately 1%. This is because the speed of the aircraft is much slower compared to the speed of light, resulting in a small number when calculating the percentage. It is important to double check calculations and use a calculator to get an accurate result.
Quelsita
Question:
What is the percent length contraction of an aircraft traveling at Mach 2?

So, we know that Mach 2= 680.58 m/s
and that L'=L$$\sqrt{1-(v/c)^2}$$

If you divide over the L to get:

L'/L=$$\sqrt{1-(v/c)^2}$$=% length contraction

Plug-n-chug from here to get:

L'/L=$$\sqrt{1-(680.58/c)^2}$$
=$$\sqrt{1-(5.15X10^-12)}$$
=$$\sqrt{1}$$
=1

Is this correct? It only contracts 1%?

I'd recheck your calculation and be careful in taking your square root.

680/300,000 is what you were intending I trust?

LowlyPion said:
680/300,000 is what you were intending I trust?

Yep. That's why I thought it was off because it's such a small number that you'll have 1 under the radical...

Or is the percent contraction supposed to be very small since the aircraft, compared to the speed of light, is going extremely slow?

Yes it is a small number.

And when you take the square root it gets closer to 1.

Use a calculator, and don't approximate or round until you have an expression for the percentage.

LowlyPion said:
I'd recheck your calculation and be careful in taking your square root.

680/300,000 is what you were intending I trust?

c = 300,000,000 m/s

## 1. What is percent length contraction?

Percent length contraction is a concept in physics that describes the decrease in length of an object as it approaches the speed of light. This phenomenon is described by the theory of relativity, and is a result of time and space being relative to the observer's frame of reference.

## 2. How is percent length contraction calculated?

Percent length contraction can be calculated using the formula: L' = L√(1-(v^2/c^2)), where L' is the contracted length, L is the original length, v is the velocity of the object, and c is the speed of light. This formula shows that as the velocity of an object approaches the speed of light, the contracted length approaches zero.

## 3. What is the significance of percent length contraction?

Percent length contraction is significant because it helps explain the apparent discrepancy in the measurement of an object's length when observed from different frames of reference. It also helps to reconcile the laws of physics with the observed phenomena of time and space. Additionally, it is a crucial aspect of the theory of relativity and has been confirmed through numerous experiments and observations.

## 4. Does percent length contraction only apply to objects approaching the speed of light?

Yes, percent length contraction only applies to objects that are moving at extremely high velocities, close to the speed of light. At slower speeds, the effects of length contraction are negligible and cannot be observed.

## 5. Are there any practical applications of percent length contraction?

While percent length contraction is primarily a theoretical concept, it has some practical applications in modern technology. For example, it is taken into consideration in the design of particle accelerators and GPS satellites. It also helps to explain the behavior of subatomic particles and the effects of high-speed collisions.

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