Answer:
1) v = 7.70 10³ m/s
, 2) F = 115 N and 3) (F/W)% = 90.2%
Explanation:
1) To solve the problem let's use Newton's second law where force is gravitational force and acceleration is centripetal
F = ma.
F = G m M / r²
a = v² / r
G m M / r² = m v² / r
G M / r = v²
Let's look for the distance is the distance from the surface of the has to the station 345 103 m plus the radius of the Earth
r = Re + 345 103
r = 6.37 10⁶ + 3.45 10⁵
r = 6.715 10⁶ m
Let's calculate the speed
v = √ (6.67 10⁻¹¹ 5.98 10²⁴ / 6,715 10⁶) = √ (59,399 10⁶)
v = 7.70 10³ m/s
The speed module is constant, so we can use the uniform motion relationships
v = d / t
The distance is the length of the circle
d = 2π r
d = 2π 6.715 106
d = 42.2 10⁶ m
Let's calculate the time
t = d / v
t = 42.2 10⁶ / 7.70 10³
t = 5.48 10³ s
2) Let's use the universal gravitation equation
F = G m M / r²
F = 6.67 10⁻¹¹ 13.0 5.98 10²⁴ /(6.715 10⁶)²
F = 11.5 10¹ N
F = 115 N
3) in this for we are asked the relationship is out with the weight of the body on earth
F / W = F / mg
F / W = 115 / (13.0 9.8)
F / W = 0.902
F / W% = 90.2%
