contestada

What is the difference in the weight of a 117 kg person as measured at sea level and at the top of the Vinson Massif, the highest peak in Antarctica? The product GMEarth = 3.99 x 10^14 N x m2 x kg-1, the radius of the Earth is 6.38 × 10^6 m, and the height above sea level of the Vinson Massif is 5.14 × 10^3 m. Neglect the flattening of the Earth at the poles.

Respuesta :

oladayoademosu

The difference in weight  of a 117 kg person as measured at sea level and at the top of the Vinson Massif, the highest peak in Antarctica is -1.847 N

How to find the difference in weight?

To find the difference in weight, we find the change in acceleration due to gravity.

What is acceleration due to gravity?

The acceleration due to gravity is the acceleration exerted by the force of gravity on an object. It is given by

g = GM/r² where

  • GM = 3.99 × 10¹⁴ Nm²/kg and
  • r = radius of earth = 6.38 × 10⁶ m

The change in acceleration due to gravity

Now, to find the change in g, we differentiate g with respect to r,

So, dg/dr = d(GM/r²)

= -2GM/r³

So, the change in acceleration due to gravity, Δg is

Δg = dg/dr × Δr

= -2GM/r³ × Δr

Now, Δr = height above sea level of Vinson Massif = 5.14 × 10³ m

Substituting the values of the variables into the equation, we have

Δg = -2GM/r³ × Δr

Δg = [(-2 × 3.99 × 10¹⁴ Nm²/kg)/(6.38 × 10⁶ m)³] × 5.14 × 10³ m

Δg =[ (-7.98 × 10¹⁴ Nm²/kg)/259.69 × 10¹⁸ m³] × 5.14 × 10³ m

Δg = -0.03073 × 10⁻⁴ N/mkg × 5.14 × 10³ m

Δg = -0.1579 × 10⁻¹ N/kg

Δg = -0.01579 N/kg

The difference in weight of the 117 kg person

Since weight W = mg where

  • m = mass of person and
  • g = acceleration due to gravity

The difference in weight is dW = mdg

Since

  • m = 117 kg and
  • dg = -0.01579 N/kg

dW = mdg

= 117 kg × -0.01579 N/kg

= -1.847 N

So, the difference in weight  of a 117 kg person as measured at sea level and at the top of the Vinson Massif, the highest peak in Antarctica is -1.847 N

Learn more about weight here:

https://brainly.com/question/17490356

#SPJ1