Question

the mass of a given airplane at sea level (g=32.1 fps^2) is 10 tons.find its mass in lb, slugs, and kg and its (gravitational) weight in lb when it is travelling at a 50000-ft elevation. the acceleration of gravity G decreases by 3.33 x 10^-6 fps^2 for each foot of elevation.

Answer 1

Answer:

Its mass is 20,000 lbs, 621.619 slugs and 10,000 kg.

Gravitational weight is 19896.26 lb .

Explanation:

Given data:  

Mass, m = 10 tons

g = 32.1 fps²

Height, h = 50,000 ft

Acceleration of gravity decreases by 3.33*10⁻⁶ fps² for each foot of elevation

To find: mass in lb, slugs and kg and its gravitational weight in lb.  

• 1 ton = 2000 lbs

         ∴ 10 tons = 10 * 2000 = 20,000 lbs

•   1 ton = 62.1619 slugs

           ∴ 10 tons = 10 * 62.1619 = 621.619 slugs

•   1 ton = 1000 kg

         ∴ 10 tons = 10 * 1000 = 10,000 kg

•    h =  ∆a / (acceleration of gravity)

              or, 50000 = (a – 32.1) / (-3.33 * 10⁻⁶)

                 or, a = 32.1 – 0.1665 = 31.9335 ft/s²

              Gravitational weight, Fg = (mass * acceleration) / g

                ∴ Fg = (20000 * 31.9335) / 32.1

                             = 19896.26 lb