Question
A plumb bob (a mass m hanging on a string) is deflected from the vertical by an angle θ due to a massive mountain.
A) Make an estimate of the mass of Mt. Everest, assuming it has the shape of a cone 3910 m high and base of diameter 3910 m. Assume its mass per unit volume is 3000 kg per m^3.
B)Estimate the angle of the plumb bob if it is 5.20 km from the center of Mt. Everest.
A) Make an estimate of the mass of Mt. Everest, assuming it has the shape of a cone 3910 m high and base of diameter 3910 m. Assume its mass per unit volume is 3000 kg per m^3.
B)Estimate the angle of the plumb bob if it is 5.20 km from the center of Mt. Everest.
Answers
bobpursley
mass estimate= volume*density=1/3 base area*height*density
= 1/3 (PI *(3910/2)^2)*3910*3000kg/m^3
=4.69483305 × 1013
So the angle must then be
sidways force: GMbob*4.69E13/5200^2
downward force: GMbob*Me/radiusearth^2
the angle sideways is
arctan*forcesideways/forcegravity
= (4.69E13/5200^2)/(Me/Re^2)
= arc tan(4.69E13/Me * (Re/5200)^2)
= 1/3 (PI *(3910/2)^2)*3910*3000kg/m^3
=4.69483305 × 1013
So the angle must then be
sidways force: GMbob*4.69E13/5200^2
downward force: GMbob*Me/radiusearth^2
the angle sideways is
arctan*forcesideways/forcegravity
= (4.69E13/5200^2)/(Me/Re^2)
= arc tan(4.69E13/Me * (Re/5200)^2)
Brett
Thanks a lot. For B the answer was 6.83x10^-4 deg.