I need help with part \'A\' of this exercise. Please show all the work so i can

Question

I need help with part 'A' of this exercise. Please show all the work so i can get study and understand this! Thanks!

H Gravity Traint en.wikipedia.org/wiki Lobachevsky %28song%29, and Lehrer s performance can be viewed at https:// As we go to press the song is archived at https: www.youtube.com/watch?v=UQHaGhC7C2E. Legend has it that Robert Hooke proposed to Isaac Newton that a straight tunnel be drilled from Moscow to St. Petersburg to accommodate a "gravity train" serving the two cities. Upon departure gravity would accelerate the train toward the center of the tunnel, then decelerate it as it continued toward the terminal. It is amusing to investigate the mechanics of such a conveyance, under idealized conditions. As depicted in Figure 4.38 , x denotes the distance of the train from the center of the tunnel, R denotes its distance from the center of the earth, and mg denotes the pull of gravity. MOCKBa

Explanation / Answer

a)From the diagram we know that the accleartion in the direction of the movement of the train is given as x||

from newtons law we know that force is equal to mass* x||

the force in the direction of the movement of train :

mg*x/R{since force is mg sin where is angle between mg line and y line }{sin =x/R}

so m* x|| = mg*x/R

b)

mg/R = k

àm* x|| = k*x

given g=9.8 m/s2 and R= 6400 *1000 m

distance from Moscow to st.pitsburg is 650*1000 m.

equation:

m* x||= k*x

g/R= 9.8/6400*1000=1.53125*10-6

equation:

x||=1.53125*10-6 * x

c)

displacement ,s= u*t +(g*t2/2)

d)the timings at which the trains reach on statio to another changes even the distances like 17000 km and 16000 km etc. are more than the radius and sin is greater than 1 which is not possible so these timetables are unusual.

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