Question

1. An object of mass m moves trough a straight tunnel between two point over the Earth (figure 1). between the mass and the tunnel there is no friction. Assume that the density of the Earth is uniform.

Figura 1:

a) Find the force wield by the Earth over the object. (Consider that the Earth is an homogeneous solid sphere).

b) Show that the object moves with a Simple Harmonic Movement.

c) Find the period of the movement of the object.

Answer 1

Gie. 1. we are trying to drand in a Simple way. Al a time it, Let the Particle be ab in the tunnel where cpap and op-a. & Force per unit was on the Parliches = – 4 where p = uniform density of the sphere. and et is directed along soi & Porce per niet mors aling po = - 4 HP GPX (2) = n I (a. Parce con m is = – 4 Gpmx. :. Ignation of motion of the Parlicle is. Mä = - 4 Gpmx. x = - + GPx. (ud-) 6) 27 ä+ wa a=0 where cu 4 IGP. som we can say the object executes the S. 14. M. So, the time period 2210 та плато T = 21 AT 17 for ensthi g = n RGP | R = 6400km J29.8 m/s² - T=21 J 6400 x103 - T = 1 hour 24 min.