Gravitational Potential Energy near the Earth

# Gravitational Potential Energy near the Earth -...

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Gravitational Potential Energy near the Earth We can see what happens to our expression for gravitational potential energy near the earth. In this case M = M e . Consider a mass m at a distance r from the center of the earth. Its gravitational potential energy is: U ( r ) = - Similarly, the gravitational potential energy at the surface is: U ( r e ) = - The difference in potential between these two points is: ΔU = U ( r U ( r e ) - + = ( GM e m ) However, r ± r e is simply the height h above the earth's surface and since we are near the earth ( r r e ), we can make the approximation that rr e = r e 2 . Then we have: ΔU = h = mgh since we found in Gravity Near the Earth that g = . This is the familiar result for gravitational potential energy near the earth. Likewise gravitational potential near the earth is Φ g = gh . Inertial and Gravitational Masses The mass used in Newton's Second Law , = m i is usually called the inertial mass. This mass is found with respect to a standard by measuring the respective acceleration of the mass and the standard when they are made to exert a force on one another. However, when two masses are

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