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3 years ago

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A spacecraft flies away from the earth with a speed of 4.80×106m/s relative to the earth and then returns at the same speed. The

spacecraft carries an atomic clock that has been carefully synchronized with an identical clock that remains at rest on earth. The spacecraft returns to its starting point 365 days (1 year) later, as measured by the clock that remained on earth. What is the difference in elapsed time on the two clocks,measured in hour?

1 answer:

marta [7]3 years ago

3 0

Answer:

1.1215 h

Explanation:

Δt=Δt_o/√(1-u^2/c^2)

(Δt° is the proper time in the rest frame,

Δt is the time intent measured in the second frame of reference u is the speed of the second frame with respect to the rest frame c is the speed of light )

a) the proper time is the time on spacecraft (rest frame);

Δt = 365 days = 8760 h

Δt=Δt_o/√(1-u^2/c^2)= 8761.1215 h

the difference = 8761.1215 h — 8760 h = 1.1215 h

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Generally the coefficient of performance of the air condition is mathematically represented as

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So it implies that the air condition removes $\frac{T_i}{T_o - T_i}$ heat with 1 unit of electricity

Now from the question we are told that the rate at which heat enters an air conditioned building is often roughly proportional to the difference in temperature between inside and outside. This can be mathematically represented as

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E unit of electricity will remove $Q= k (T_o - T_i)$

So

$E = \frac{k(T_o - T_i)}{\frac{T_i}{ T_h - T_i} }$

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=> $E \ \alpha \ (T_o - T_i)^2$

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Considering the second question

Assuming that $T_i = 30 ^oC$

and $T_o = 40 ^oC$

Hence

$E = K (T_o - T_i)^2$

Here K stand for a constant

So

$E = K (40 - 30)^2$

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Now if the $T_i = 20 ^oC$

Then

$E = K (40 - 20)^2$

=> $E = 400 \ K$

So from this see that the electricity require (cost of powering and operating the air conditioner)when the inside temperature is low is much higher than the electricity required when the inside temperature is higher

Considering the third question

Now in the case where the heat that enters the building is at a rate proportional to the square-root of the temperature difference between inside and outside

We have that

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Assuming $\frac{k}{T_i}$ is a constant

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