Posted by Brett on .
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.
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
= arc tan(4.69E13/Me * (Re/5200)^2)
Thanks a lot. For B the answer was 6.83x10^-4 deg.