A montain climber reaches the top of the Everest (8850m over Earth\'s equator) w

Question

A montain climber reaches the top of the Everest (8850m over Earth's equator) with a scale to measure his weight (the scale reads Newtons). What weight would the scale measure? For comparison, on the surface of the Earth, the climber weighs 980.7 Newtons. DATA: Equatorial radius of the Earth 6.378E6 meters; mass of the Earth 5.98E24 kg; Gravitational Constant 6.673E-11 Nm^2/kg^2 A montain climber reaches the top of the Everest (8850m over Earth's equator) with a scale to measure his weight (the scale reads Newtons). What weight would the scale measure? For comparison, on the surface of the Earth, the climber weighs 980.7 Newtons. DATA: Equatorial radius of the Earth 6.378E6 meters; mass of the Earth 5.98E24 kg; Gravitational Constant 6.673E-11 Nm^2/kg^2

Explanation / Answer

The acceleration due to gravity varies with height as follows:

g' = g (1 - 2h/R)

g' = 9.81 (1 - 2 x 8850/6.378 x 10^6) = 9.783 m/s^3

w = mg = 980.7 N => m = 980.7/g = 99.96 kg (g = 9.81 m/s^2)

w' = 99.96 x 9.783 = 978 N

Hence, W' = 978 N

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