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Setler79 [48]
3 years ago
12

How fast must an object move before its length appears to be contracted to one-fourth its proper length? (Give your answer in te

rms of c.)
Physics
1 answer:
Tresset [83]3 years ago
3 0

Answer:

<em>0.97c</em>

<em></em>

Explanation:

From the relativistic equation for length contraction, we have

l = l_{0}\sqrt{1 - \beta }

where

l is the final length of the object

l_{0} is the original length of the object before contraction

β = v^{2} /c^2

where v is the speed of the object

c is the speed of light in free space = 3 x 10^8 m/s

The equation can be re-written as

l/l_{0} = \sqrt{1 - \beta }

For the length to contract to one-fourth of the proper length, then

l/l_{0} = 1/4

substituting into the equation, we'll have

1/4 = \sqrt{1 - \beta }

substituting for β, we'll have

1/4 = \sqrt{1 - v^2/c^2 }

squaring both side of the equation, we'll have

1/16 = 1 - v^2/c^2

v^2/c^2 = 1 - 1/16

v^2/c^2 = 15/16

square root both sides of the equation, we have

v/c = 0.968

v = <em>0.97c</em>

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What is the wavelength associated with 0.113kg ball traveling with velocity of 43 m/s?
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Answer:

2.73×10¯³⁴ m.

Explanation:

The following data were obtained from the question:

Mass (m) = 0.113 Kg

Velocity (v) = 43 m/s

Wavelength (λ) =?

Next, we shall determine the energy of the ball. This can be obtained as follow:

Mass (m) = 0.113 Kg

Velocity (v) = 43 m/s

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Next, we shall determine the frequency. This can be obtained as follow:

Energy (E) = 104.4685 J

Planck's constant (h) = 6.63×10¯³⁴ Js

Frequency (f) =?

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104.4685 = 6.63×10¯³⁴ × f

Divide both side by 6.63×10¯³⁴

f = 104.4685 / 6.63×10¯³⁴

f = 15.76×10³⁴ Hz

Finally, we shall determine the wavelength of the ball. This can be obtained as follow:

Velocity (v) = 43 m/s

Frequency (f) = 15.76×10³⁴ Hz

Wavelength (λ) =?

v = λf

43 = λ × 15.76×10³⁴

Divide both side by 15.76×10³⁴

λ = 43 / 15.76×10³⁴

λ = 2.73×10¯³⁴ m

Therefore, the wavelength of the ball is 2.73×10¯³⁴ m.

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