Answer:
a) r = 4.22 10⁷ m, b) v = 3.07 10³ m / s and c) a = 0.224 m / s²
Explanation:
a) For this exercise we will use Newton's second law where acceleration is centripetal and force is gravitational force
F = m a
a = v² / r
F = G m M / r²
G m M / r² = m v² / r
G M / r = v²
The squared velocity is a scalar and this value is constant, so let's use the uniform motion relationships
v = d / t
As the orbit is circular the distance is the length of the circle in 24 h time
d = 2π r
t = 24 h (3600 s / 1 h) = 86400 s
Let's replace
G M / r = (2π r / t)²
G M = 4 π² r³ / t²
r = ∛(G M t² / (4π²)
r = ∛( 6.67 10⁻¹¹ 5.98 10²⁴ 86400² / (4π²)) = ∛( 75.4 10²¹)
r = 4.22 10⁷ m
b) the speed module is
v = √G M / r
v = √(6.67 10⁻¹¹ 5.98 10²⁴/ 4.22 10⁷
v = 3.07 10³ m / s
c) the acceleration is
a = G M / r²
a = 6.67 10⁻¹¹ 5.98 10²⁴ / (4.22 10⁷)²
a = 0.224 m / s²
ANSWER:
300 J
STEP-BY-STEP EXPLANATION:
To know the work required, we must calculate the work in both cases, the difference would be the amount of work necessary for the speed to increase. The work done is the same as the amount of energy increase. The formula for kinetic energy is:
We calculate in each case:
We calculate the difference between the two to find out the work required:
The work required is 300 J
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Entropy
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#SPJ 4
Assuming the same deformation and elastic modulus, we can use the relationship:
(P/D)1 = (P/D)2
Where P is the load, Dis the diameter of the wire, 1 is the first wire, and 2 is the second wire. Using the given values and solving for the diameter of the second wire:
D = (24 / 0.24) (1)
D = 100 mm
