circular motion (1 Viewer)

[Newbie]

a basic question i think but im just too bloody newbie

a mass is undergoing circular motion on the inside surface of teh cone at w (w = omega) rad/s length of string is 1 unit and the normal force makes with teh vertical the same angle as taht of the apex of the come.
i) show that the tension in the string is 2mg/[(root3) + 1)] when w = (root2g)

ii) show that the mass will leave the cone surface when w = [root2/(root3)]

and a diagram too

 

[Constip8edSkunk]

where did u get this q from johnny?

1/ w=[sqrt2g] -> w²=2g @=pi/6 -> 2@=pi/3
resolving vert.
mg=Ncos@+Tcos@=N/2 + T[sqrt3]/2
resolving hor.
mw²r=Vsin2@+Tsin@ -> mg=N[sqrt3]/2+T/2

[mg-T/2]/[mg-T[sqrt3]/2] = [N[sqrt3]/2]/[N/2]
[2mg-T]/[2mg-T[sqrt3]] = [sqrt3]
2mg - T = 2[sqrt3]mg - 3T
T=mg[[sqrt3]-1]
=2mg/[[sqrt3]+1]

2/
mg=N/2 + T[sqrt3]/2 --1
mw²/2=N[sqrt3]/2+T/2 --2
2*[sqrt3]-1: [sqrt3]mw²/2-mg = 3N/2 - N/2 =N
N=m[[sqrt3]w²/2-g]
when N=0
[sqrt3]w²/2=g
w²=2g/[sqrt3]
w=[sqrt 2g/[sqrt3] ]

??? shouldnt there b a g there or did i screw up somewhere in the 2nd part ???

 

[Newbie]

hey
what book do you recoomend learning circular off?
i still havent learnt it

 

[freaking_out]

Originally posted by Newbie
hey
what book do you recoomend learning circular off?
i still havent learnt it

do the arnold examples and if ur confident, then just do past papers....also use this old book written by "komaromi".

 

[freaking_out]

Originally posted by Constip8edSkunk
where did u get this q from johnny?

1/ w=[sqrt2g] -> w²=2g @=pi/6 -> 2@=pi/3...

can someone explain to me how u get @=pi/6?

 

[ND]

Originally posted by freaking_out
can someone explain to me how u get @=pi/6?

Look at the diagram: One triangle has angles 2@, @, and pi/2 (cos the normal is perpendicular to the surface).

 

[freaking_out]

Originally posted by ND
Look at the diagram: One triangle has angles 2@, @, and pi/2 (cos the normal is perpendicular to the surface).

shit!!!....yeah, didn't really note that down in my diagram.

yeah, that makes the question much simpler.

 

[Constip8edSkunk]

ive only done arnold qs, which is surprisingly easy compared wif other topics in the book, no time to do others.... (seriously, y do our school start 4U 1 term late, spend another 6 weeks on complex.... and rush conics, circular motion, harder 3 unit in the final 2 weeks -_-)

 

[Newbie]

ok
arnold it is

 

[freaking_out]

Originally posted by Newbie
ok
arnold it is

as its always been.

 

[Newbie]

yeah i saw your post
just needed a double confirm

 

[freaking_out]

Originally posted by Newbie
yeah i saw your post
just needed a double confirm