Question

Mountain pull. A large mountain can slightly affect the direction of “down” as determined by a plumb line. Assume that we can model a mountain as a sphere of radius R = 3.00 km and density (mass per unit volume) 2.6 × 103 kg/m3. Assume also that we hang a 0.250 m plumb line at a distance of 3R from the sphere's center and such that the sphere pulls horizontally on the lower end. How far would the lower end move toward the sphere?

Answer 1

figure the force of attraction to the sphere, and the force of attration to the Earth.

TanTheta= forcetoSphere/ForceGravity

figure out theta

Answer 2

use acceleration of gravitation=gravitational constant*mass/(r^2)

use the radius and density to find the mass of the large mountain.

Find the distance from the center of the sphere (mountain) to the plumb.

Find the acceleration due to gravity in the x horizontal direction on the plumb using the equation.

Draw a right triangle with the vertical leg as 9.8 m/ss and the horizontal leg as the acceleration you found.

Use inverse tan to find the angle in the top corner of the triangle. Use the angle and the sin function to find the length of the horizontal leg. (the hypotenuse is 0.250m)

Remember to use proper units and convert km to m!!! check through your work for small mistakes.

Answer 3

There has been so much said, and on the whole so well said, that I shall not occupy the time.

Answer 4

In other words, refer to the answers above and perhaps to others on the internet.

You're welcome!