time. is the answer.
Answer:
The horizontal component of this force is about 36 N.
Explanation:
Given that,
Bruce is is pulling on his lead with a force of 40 N
Angle below horizontal,
We need to find the horizontal component of this force. The horizontal component of any vector is given by :
or
So, the horizontal component of this force is about 36 N. Hence, this is the required solution.
(b) What is the value of g at the location of this satellite?
(a) above Earth's surface
The orbital speed of a satellite orbiting the Earth can be found using the equation
where
G is the gravitational constant
is the Earth's mass
r is the radius of the satellite's orbit
The orbital speed can also be rewritten as the ratio between the circumference of the orbit and the orbital period, T:
where
T = 129 min = 7740 s is the period
Combining the two equations,
And solving for r,
This is, however, the orbital radius: this means we have to subtract the Earth's radius to find the altitude of the satellite, which is
therefore, the altitude of the satellite is
b)
The value of g at the location of the satellite is given by
where:
G is the gravitational constant
is the Earth's mass
is the radius of the satellite's orbit
Substituting into the equation, we find
The satellite orbits at an altitude of approximately 800 km. The gravitational constant, 'g', at this location is approximately 8.66 m/s^2.
The orbital period of an artificial satellite can be used to calculate the altitude at which it orbits. For a satellite that completes each orbit in 129 min (or approximately 2.15 hr), we can apply Kepler's third law which states that the square of the period of a satellite is proportional to the cube of its semi-major axis (distance from the center of the Earth to the satellite).
The formula for the altitude is given by: h = [(GMT^2)/(4π^2)]^(1/3) - R, where G is the gravitational constant, M the mass of Earth, T the orbital period, and R the Earth's radius. With the values G=6.67 x 10^-11 N(m/kg)^2, M=5.98 x 10^24 kg, T=2.15 hr = 7740s, and R=6.371 x 10^6 m, we get h approximately equals 800 km.
The value of 'g' at the satellite's location is given by g = GM/(R+h)^2. Substituting the aforementioned values, we get g to be approximately 8.66 m/s^2. This is less than the 9.81 m/s^2 at Earth's surface due to the increased distance from the Earth's center.
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