Answer :
The radius of the orbit is approximately 6,536,046.51 meters. The centripetal force acting on the satellite is given by the formula:
F = (mv²)/r
where F is the force, m is the mass of the satellite, v is its velocity, and r is the radius of its orbit.
Substituting the given values, we get:
215 = (1100 x 5100²)/r
Solving for r, we get:
r = (1100 x 5100²)/215 = 6,536,046.51 meters
The centripetal force acting on a satellite is given by the equation Fc = (mv²)/r, where Fc is the centripetal force, m is the mass of the satellite, v is the velocity, and r is the radius of the orbit. Rearranging the equation to solve for r, we get r = (mv²)/Fc. Plugging in the given values, we get r = (1100 kg x (5100 m/s)^2)/215 N = 7.14 x 10⁶m. Therefore, the radius of the satellite's orbit around the planet is 7.14 x 10⁶ m.
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The radius of the satellite's orbit is approximately 619,674.42 meters, and the centripetal acceleration of the satellite in orbit is about 41.98 m/s².
To find the radius of the satellite's orbit, we can use the formula for centripetal force in uniform circular motion.
Given data:
- Centripetal Force [tex](F_c) = 215 N[/tex]
- Mass [tex](m) = 1,100 kg[/tex]
- Speed [tex](v) = 5,100 m/s[/tex]
The formula for centripetal force is:
[tex]F_c = (m \times v^2) / r[/tex]
Rearranging to solve for the radius (r):
[tex]r = (m \times v^2) / F_c[/tex]
Plugging in the values:
[tex]r = (1,100 kg \times (5,100 m/s)^2) / 215 N\\r = (1,100 \times 26,010,000) / 215\\r = 133,230,000 / 215\\r = 619,674.42 meters[/tex]
So, the radius of the satellite's orbit is approximately 619,674.42 meters.
To find the acceleration (a), we use:
[tex]a = v^2 / r[/tex]
Using the radius we just calculated:
[tex]a = (5,100 m/s)^2 / 619,674.42 m\\a = 26,010,000 / 619,674.42\\a = 41.98 m/s^2[/tex]
So, the acceleration of this object is approximately [tex]41.98 m/s^2.[/tex]
