Question

You check in at the airport and have your luggage weighed. It comes to 25kg. The airport is at sea level and you take off and climb to 30,000 ft. How much less does your luggage now weigh?

mass of earth = 5.98 × 10 ^24

radius of earth = 6.37 × 10^ 6​

Answer 1

0.705 kg less

Step-by-step explanation:

Altitude at sea level = 0 ft

Altitude after climbing = 30,000 ft = 30,000 x 0.3048 = 9,144 m

Weight = W = mg

Change in weight = ΔW = (M-luggage) × (g-sea level - g-altitude)

g at sea level:

g1 = (Gravitational constant × Mass of the Earth) / (Radius of the Earth)²

g at altitude of 30,000 ft:

g2 = (Gravitational constant × Mass of the Earth) / (Radius of the Earth + Altitude)²

Gravitational constant = 6.674 × 10^-11 m^3 kg^-1 s^-2

g1 = (6.674 × 10^-11 × 5.98 × 10^24) / (6.37 × 10^6)^2

g1 ≈ 9.8358 m/s^2

g2 = (6.674 × 10^-11 × 5.98 × 10^24) / (6.37 × 10^6 + 9,144)^2

g2 ≈ 9.8076 m/s^2

ΔW = (M-luggage) × (g1 - g2)

= 25 kg × (9.8358 - 9.8076)

≈ 0.705 kg

Therefore, your luggage would weigh approximately 0.705 kg less when you climb to 30,000 ft compared to its weight at the airport.

Can't guarantee this is right, but I checked the numbers a few times and this is the best I can do!