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3 years ago

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An interstellar space probe is launched from Earth. After a brief period of acceleration it moves with a constant velocity, 70.0

% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 15.9 years as measured in a rest frame. (a) How long do the batteries on the space probe last as measured by mission control on Earth?
yr
(b) How far is the probe from Earth when its batteries fail, as measured by mission control?
ly
(c) How far is the probe from Earth, as measured by its built-in trip odometer; when its batteries fail?
ly

1 answer:

sleet_krkn [62]3 years ago

3 0

Answer:

22.26 years

, 15.585 light years , 11.13 light years

Explanation:

a)

$t' = t/(\sqrt{1-(v/(c*v)/c)}$

= $15.9/\sqrt{(1-0.7*0.7)}$

= 22.26 years

b)

0.7*c*22.26 years

=15.585 light years

c)

0.7*c*15.9

=11.13 light years

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3 years ago

PLEASE HELP ME 45 POINTS

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Answer:

a) We kindly invite you to see the explanation and the image attached below.

b) The acceleration of the masses is 4.203 meters per square second.

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a) At first we assume that pulley and cord are both ideal, that is, masses are negligible and include the free body diagrams of each mass and the pulley in the image attached below.

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The acceleration of the masses is 4.203 meters per square second.

c) From (2) we get the following expression for the tension force in the cord:

$T = m_{B}\cdot (a+g)$

If we know that $m_{B} = 2\,kg$ , $g = 9.807\,\frac{m}{s^{2}}$ and $a = 4.203\,\frac{m}{s^{2}}$ , then the tension force in the cord:

$T = (2\,kg)\cdot \left(4.203\,\frac{m}{s^{2}}+9.807\,\frac{m}{s^{2}} \right)$

$T = 28.02\,N$

The tension force in the cord is 28.02 newtons.

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$\Delta y = \frac{1}{2}\cdot a\cdot t^{2}$ (3)

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$t = \sqrt{\frac{2\cdot \Delta y}{a} }$

$t = \sqrt{\frac{2\cdot (1.5\,m)}{4.203\,\frac{m}{s^{2}} } }$

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$v = \left(4.203\,\frac{m}{s^{2}} \right)\cdot (0.845\,s)$

$v = 3.551\,\frac{m}{s}$

The final speed of the system is 3.551 meters per second.

8 0

2 years ago