Help~~~plz~~~2 Machanics Qs (2 Viewers)

[Hikari Clover]

Two particles A and B of masses m and M respectively are attached to the ends of a light inextensible string which passes over a smooth hook at O which is free to rotate. The particle A hangs at rest vertically below O while the particle B moves in a horizontal circle with constant speed v. Find expressions for:
a)the length OB and the angle AOB
b)the radius of the circle in which B moves


a particle A of mass 2m is attached by a light inextensible string of length L to a fixed point O and is also attached by another light inextensible string of the same length to a small ring B of mass 3m which can slide on a fixed smooth vertical wire passing through O. The particle A describes a horizontal circle with OA inclined at an angle π/3 with the downward vertical. Find
a)the tension in the strings
b)the angular velocity of A





for the first one , what speed v is? how does it relate to angular velocity ?
the second one, i couldn't even draw diagram................

plz help me , thx~~~~

 

[alcalder]

Actually, the diagram for both is the same. In the first, mass A hangs vertically, in the second, mass B hangs vertically.

Anyway, in question 1.

On mass A there are two forces:

F_Gravity = -mg (ie down)
F_{String Tension}=T (ie up)

Add the forces and the mass is stationary so resultant F=0

0 = T-mg

On mass B there are two forces:
F_{String Tension}=T (at an angle equal to angle AOB from the vertical)
F_Gravity = -Mg (ie down)

We can take the tension and break it into the vertical and horizontal components:

F_{T vertical} = TcosAOB (ie up)
F_{T horizontal} = TsinAOB (towards centre of motion)

The mass is going in a circle and is not moving up or down so forces are equal up and down. Resultant F =0

0 = TcosAOB - Mg

In horizontal direction the resultant force is
F_Centripetal = Mv²/r (horizontally towards the centre)

SO

Mv²/r = TsinAOB

put these all together and you get an expression for r and angle AOB.

Hope that helps

Now, do the same for question 2.

 

[Hikari Clover]

thx ~~~~

Centripetal force = Mv2/r ?

i thought it is mr times omega square.........

so they r actually the same , just depends on what is given ,and then choose one for centripetal force?

 

[STx]

thx ~~~~

Centripetal force = Mv2/r ?

i thought it is mr times omega square.........

so they r actually the same , just depends on what is given ,and then choose one for centripetal force?

^ yeah mv^2/r and mrw^2 are linked by v=rw, and just go with with what the question already has.