There are two equations from which a change in the gravitational potential energy U of the system of mass m and the earth can be calculated. One is u = mgy the other is U = -(Gm_e * m)/r_e (where m_e and r_e are the mass & radius of the earth respectivly). As shown the first equation is correct only if the gravitational force is a constant over the change in height Δy. THe second is always correct. Consider the difference in U between a mass at the earth's surface and a distance h above it using both equations, and find the value of h for which u = mgy is in error by less than 1%. Express this value of h as a fraction of the earth's radius, and also obtain a numerical value for it.
i see what your saying :0, I will give it a shot and write back if I have a problem
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-(Gm_e * m)/(r_e) is the potential at r_e
-(Gm_e * m)/(r_e+h) is the potenial at r_e+h
(-(Gm_e * m)/(r_e+h) - -(Gm_e * m)/(r_e)) is the change in potential when you raise m from r_e to r_e+h
mgh assumes the force is constant
((-(Gm_e * m)/(r_e+h) - -(Gm_e * m)/(r_e)) - mgh)
is the absolute error
((-(Gm_e * m)/(r_e+h) - -(Gm_e * m)/(r_e)) - mgh)
/
(-(Gm_e * m)/(r_e+h) - -(Gm_e * m)/(r_e))
is the relative error
Let F be the first and S be the second equation. Then, the formula needed is..
Error/Actual
which is nothing but
(F-S)/S < 0.01
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Harish