Solving Stress in a Ring of Radius 1/10 m, Mass 1 kg/m

[altamashghazi]

Homework Statement

a thin wire of crosssection area 10^-2 m^2 is used to make a ring of radius 1/10 m. it is given ω=2 rad/s on a smooth table about its centre. find stress in ring?( mass/length of wire is 1 kg/m.)

Homework Equations

s=f/a
f=mv^2/r

The Attempt at a Solution

my only difficulty is the area on which i should take the force to be acting.

 

[emailanmol]

On a small mass dm at an angle d(theta) tension force acts which is tangential to circle.

The component of this force towards the centre is 2Tsin(d(θ)). For small angles sin(dθ) is equal to dθ so centripetal force is 2Tdθ.

What should this centripetal force be equal to in terms of mass dm radius and ω. (Hint : you have written an equation in velocity.substitute velocity with rω.[Why?])

2Tdθ=(dm*r*ω^2)

Now all that is left is to calculate value of small mass dm in terms of mass M of ring and dθ (assuming uniform density) What will the equation be?

If you can write it you can cancel dθ on both sides and obtain value of tension force.

Using stress equation you wrote i.e Force/Area its acting upon

The force is tension.
What will be the area.?

What is the final answer