A Space Walk An astronaut is taking a space walk near the shuttle when her safety tether breaks. What should the astronaut do to
1 answer:
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Explanation:
Given data:
Area A = 10 cm×2 cm = 20×10⁻⁴ m²
Distance d between the plates = 1 mm = 1×10⁻³m
Voltage of the battery is emf = 100 V
Resistance = 1025 ohm
Solution:
In RC circuit, the voltage between the plates is related to time t. Initially the voltage is equal to that of battery V₀ = emf = 100V. But After time t the resistance and capacitor changes it and the final voltage is V that is given by
Taking natural log on both sides,
(1)
Now we can calculate the capacitance by using the area of the plates.
C = ε₀A/d
=
= 18×10⁻¹²F
Now we can get the time when the voltage drop from 100 to 55 V by putting the values of C, V₀, V and R in the equation (1)
= -(1025Ω)(18×10⁻¹² F) ln( 1 - 55/100)
= 15×10⁻⁹s
= 15 ns
Answers:
1) 2951.39 m
2) 0.000952 m
3)
Explanation:
1) We know the Schwarzschild radius is given by the following equation:
(1)
Where:
is the Universal Gravitational Constant
the mass of the black hole
is the speed of light
Now, if we have a black hole with the mass of the Sun (), its radius will be:
(2)
(3)
(4) This is the radius of the black hole with the mass of the Sun
2) On the other hand, if the black hole has the mass of Mars (), its radius will be:
(5)
(6)
(7) This is the radius of the black hole with the mass of Mars
3) In this case, we have to isolate from (1):
(8)
Where
Solving (8) with the known values:
(9)
(10) This is the mass of the black hole