A wheel of radius 30 cm is rotating at a rate of 2.0 revolutions every 0.080 s. (A) through what angle, in radians, does the whe
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Answer:
Eccentricity = 0.0557
Semi-major axis = 9,095 km
Angular momentum/mass = 60,116
Kinetic energies/mass = 24,500 KJ
Potential energies/mass = 21,673 KJ
Explanation:
Eccentricity
To find the eccentricity use the following formula
Eccentricity = [ Altitude from the earth x ( / Gravitational parameter for the Earth ) ] - 1
Where
Altitude from the earth radius = Radius of the earth + Altitude of the earth from radius = 6,378 km + 2,210 km = 8,588 km
Velocity = 7,000 m/s
Gravitational parameter for the Earth = 3.986004418 ×
Eccentricity = ?
Placing values in the formula
Eccentricity = [ ( 8,588 km x 1000 ) x ( / 3.986004418 ×
) ] - 1
Eccentricity = 0.0557
Semi-major axis
Total Distance = Semi-major axis x ( 1 - Eccentricity )
Where
Total Distance = 8,588 km
Eccentricity = 0.0557
8,588 x 1,000 m = Semi-major axis x ( 1 - 0.0557 )
8,588,000 m = Semi-major axis x 0.9443
Semi-major axis = 8,588,000 m / 0.9443
Semi-major axis = 9,094,567.40 m
Semi-major axis = 9,094.56740 km
Semi-major axis = 9,095 km
Angular momentum/mass
L = MVR
L/M = VR
Where
V = Velocity = = 7 km/s
R = Total Radius = Radius of Earth + Altitude = 6,378 km + 2,210 km = 8,588 km
Placing values in the formula
L/M = 7 km/s x 8,588 km = 60,116
Kinetic energies/mass
Ke = I
Ke =
( Where I =
)
=
=
(
=
)
=
=
= 24,500,000 J
= 24,500 KJ
Potential energies/mass
PE = mgh
= gh
Where
g = 9.807
h = 2,210 km x 1,000 = 2,210,000 m
Placing values in the formula
= 9.807
x 2,210,000 m
= 21,673,470 J
= 21,673.470 KJ
= 21,673 KJ