mechanics (1 Viewer)

[doiyoubi]

The force of attraction experienced by a particle of mass m at a distance x(>r) from the centre O of the earth towards O is mgr^2/x^2, where r is the radisu of the earth. A particle of mass m starts from the sufrace with speed u directly away from O.
(A)find the subsequent speed when the particle is distance x from O (done this one) *answer* v=sqrt{u^2-2gr(1-[r/x])
(B)Deduce that the particle will escape from the attraction of the earth if u^2>2gr

at ground level, where g=9.81ms^-2 a simple pendulum beats exact seconds (each half-oscillation takes one second.) If it is taken up to a mountain to a place where g=9.80ms^-2, find by how many seconds per day it will be wrong

thanks

 

[carrotsss]

If the particle can escape from the attraction of earth that means its velocity will never be equal to zero, therefore u^2-2gr(1-[r/x])>0 so u^2>2gr(1-[r/x]) for all values of x. The maximum value of 2gr(1-[r/x]) is when x->infinity and hence r/x->0, so therefore u^2>2gr

 

[scaryshark09]

bruh 2006