g John is walking along a trail when he comes to the bottom of a steep cliff. Before trying to climb up it, he wonders how high
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Answer:
Explanation:
The gravitational pull between two object is given by:
Where M and m are the masses of the object, r is the distance between the masses and G = 6.67× 10⁻¹¹ m³kg⁻¹ s⁻² is the gravitational constant.
We have to calculate the net force on Earth due to Venus, Jupiter and Saturn when they are in one line. It means when they are the closest distance.
Mass of Earth, Me = 5.98 × 10²⁴ kg
Mass of Venus, Mv = 0.815 Me
Mass of Jupiter, Mj = 318 Me
Mass of Saturn, Ms = 95.1 Me
closest distance between Earth and Venus, rv = 38 × 10⁶ km = 0.25 AU
closest distance between Jupiter and Earth, rj = 588 × 10⁶ km = 3.93 AU
closest distance between Earth and Saturn, rs = 1.2 × 10⁹ km = 8.0 AU
where 1 AU = 1.5 × 10¹¹ m
Inserting the values:
(a) 0.249 (24.9 %)
The maximum efficiency of a heat engine is given by
where
Tc is the low-temperature reservoir
Th is the high-temperature reservoir
For the engine in this problem,
Therefore the maximum efficiency is
(b-c) 0.221 (22.1 %)
The second steam engine operates using the exhaust of the first. So we have:
is the high-temperature reservoir
is the low-temperature reservoir
If we apply again the formula of the efficiency
The maximum efficiency of the second engine is