How would the weight of a 100 kg person change as he increases in altitude? Find his weight at (a) sea level, (b) 5000 meters, (c) 10,000 meters, and (d) 20,000 meters.

Answer 1

Weight = mg

At sea level g = 9.81 so weight = 100 x 9.81 = 981 N

g = G m1 m2 / r² , so g decreases as we move away from the center of the earth.

radius of Earth is 6371 km = 6371 000 m

So when r = 6371 000 m, g = 9.81

So G m1 m2 = r² g = (6371 000)² x 9.81 = 3.98 x 10¹⁴ approx.

So when r = 6371 000 + 5000, g = 9.7946

when r = 6371000 + 10000, g = 9.7793

when r = 6371000 + 20000. g = 9.7442

So

height weight (N)

sea level 9.81 x 100 = 981

5000 m 9.6946 x 100 = 969

10000 m 9.7793 x 100 = 978

20000 m 9.7742 x 100 = 977