Question

In Kansas City, Missouri (elevation 1,026 feet) you step on a scale and weigh 128 pounds, using the same scale in Portland (elevation 27 feet) you would weigh

Answer 1

Answer: Same

Acceleration due to gravity varies with height like the following:

$g_h=g[1-\frac{2h}{R}]$

This is insignificant when$h<<R$

In the given question,

$h=1026 ft << R (2.09\times10^9 ft)$ and in the second case it is even smaller. Hence, acceleration due to gravity would remain same in the two cities.

The weight depends on acceleration due to gravity. The mass is constant.

$w=mg$

Hence, our weight would remain same in the two cities as the change in the value of acceleration due to gravity is negligible.

Answer 2

Answer:

More in Portland

Explanation:

Hello,

In this case, since we are talking about weight, it is measured as a force instead of a mass, that is why to know the weight one must multiply the mass by the gravity. Now, we do not need any calculation, this is solved by reasoning that the mass in Kansas and in Portland is the same, but the gravity does not, because the higher the height the lower the gravity (inversely proportional relationship - Thermodynamics, Cengel), thus, the lower gravity in Kansas turn out into a lower weight as a force meanwhile the weight is higher in Portland as the gravity is higher.

Best regards.