Weight is equal to the mass of the object multiplied by the force of gravity attracting the object. giving the equation W=mg with mass in kg
(i)W=2000x9.8
= 19,600N
(ii) for this one we need to work out what the force of gravity will be at an altitude of 1000km above the Earth's surface
the equation to find g = GM/r^2
where G is universal gravitational constant 6.67x10^-11
M is the mass of the central body (earth)
and r is the distance between the center of masses of the 2 objects in meters(earth and satellite) we will assume that it is 1000km to the center of the satellite.
so g = (6.67x10^-11 x 5.98x10^24)/(6.98x10^6 + 1x10^6)^2
g = 6.26 m/s^2
if working with an object at an altitude do not forget to factor in the radius of the central body to your "r" value. in this case it is the radius of the earth (6.98x10^6 m)
now we put the value calculated above back into the equation W=mg
so the weight of the satellite at an altitude of 1000km = approximately 12,527N
hope this helps :) feel free to ask for clarification, i know its not the clearest
The MASS OF A SATELLITE IS 2000Kg .DETERMINE THE WEIGHT OF OF THE THE SATELLITE WHEN IT IS
(i)resting on the earth
(ii) 1000km above earth surface
2 answers
The previous answer posted by Jordan uses a correct approach but the wrong radius for the Earth. The mean radius is 6.378*10^6 km, not 6.98x10^6 m.
This makes the answer to part (ii)
g'(1000 km) = g(sea level)*(6378/7378)^2
g' = 7.33 m/s^2
The satellite weight at 1000 km altitude is therefore 14,700 N, rounded to three significant figures.
This makes the answer to part (ii)
g'(1000 km) = g(sea level)*(6378/7378)^2
g' = 7.33 m/s^2
The satellite weight at 1000 km altitude is therefore 14,700 N, rounded to three significant figures.