Question

You are in Denver, which is 5,280 ft above sea level. Compare the acceleration due to gravity in Denver to that at sea level (h = 0). What are your Weight and your mass at each of these locations? Rearth = 6.371 x 10^6 m. Mearth = 5.9763 x 10^24 kg

a) list the given

b) List what you are trying to find

c) what equations will you use? List below

d) calculate the accelerations due to gravity for each location ( report your answer to 3 decimal places)

e) compare these accelerations (make a ration of the two to see the relationship)

f) calculate your mass (in kg) and your weight (in newtons) for both locations

Answer 1

a) Given data

h = 5280 ft = 1609.344 m

R = 6.371e6 m

m = 5.9763e24 Kg

-----------------------------------

b) we are trying to find the 'g' value at given altitude

-------------------------------

c) we will use the following equations

g = GM / (R + h )² ( To find the acceleration due to gravity)

W = mg ( To find weight)

---------------------------

d) For h = 0

g_o = 6.67e-11 * 5.9763e24 / 6.371e6²

g_o = 9.821 m/s²

For h = 5280 ft = 1609.344 m

g = 6.67e-11 * 5.9763e24 / (6.371e6 + 1609.344) ²

g = 9.8157 m/s²

----------------------------------------

e) Let's compare

g_o / g = 9.821 / 9.8157

g_o / g = 1

as we can see at this alitude, the acceleration due to gravity is almost same as gravity on the surface

--------------------------------

f)

The question is asking for YOUR mass and weight.

I will take my own mass

My mass is 70 Kg

so,

mass = 70 kg (mass does not change with location)

weight = mg = 70 * 9.821 = 687.47 N ( at h = 0 )

weight = 687.099 N ( at h = 5280 ft)