do this (1 Viewer)

[abdo]

a particle P of mass m slides smoothly in a horizontal circle on the inner surface of a semi-spherical shell with centre O and radius r. the interval OP makes an angle of theta with the vertical through O.

ok, show that the magnitude of the force N exerted by the shell on the particle is given by:

N = m/2r( v² + root(v⁴ + 4r²g²) )

 

[ngai]

Ncos@ = mg
Nsin@ = mv^2/R, where R = radius of the circle it rotates in (ie. R = rsin@)
so Nsin^2 @ = mv^2/r
sin^2 @ = mv^2/rN
cos^2 @ = (mg/N)^2
(mg/N)^2 + mv^2/rN = 1
expand and simplify...
rN^2 - mv^2N -rm^2g^2 = 0
N = [mv^2 +- sqrt(m^2v^4+4r^2g^2)]/2r
= (m/2r)(v^2 +- sqrt(v^4 + 4r^2g^2)
but sqrt(v^4 + 4r^2g^2) > sqrt(v^4) = v^2, so can't take -sqrt(...) coz N > 0
therefore N = (m/2r)(v^2 + sqrt(v^4 + 4r^2g^2)

 

[abdo]

but sqrt(v^4 + 4r^2g^2) > sqrt(v^4) = v^2, so can't take -sqrt(...) coz N > 0

oh, i see...

thank you ngai

edit: hey how long did you take to do that? did you like see it straight away?

 

[ngai]

well, pretty much straight away
coz u have +-, and to get wot the question wants, u wanna remove the - by saying that it can't be -

 

[abdo]

cool, good luck with the trials

 

[jam3s]

fail abdo in ur 4 u hahaha