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

In summary, the problem involves a thin wire with a cross-section area of 10^-2 m^2 that is used to make a ring with a radius of 1/10 m. The ring is given an angular velocity of 2 rad/s on a smooth table around its center. The task is to find the stress in the ring, given that the mass per unit length of the wire is 1 kg/m. The solution involves finding the centripetal force acting on a small mass element, which is equal to 2Tsin(dθ), and then equating it to the equation for centripetal force, which is 2Tdθ=(dm*r*ω^2). The value of the small mass
  • #1
altamashghazi
43
0

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.
 
Physics news on Phys.org
  • #2
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
 

Attachments

  • tension.jpg
    tension.jpg
    5.6 KB · Views: 505

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

What is the formula for calculating stress in a ring?

The formula for calculating stress in a ring is stress = force / area. In this case, the force is equal to the weight of the ring, which is equal to mass x gravity. The area is equal to the circumference of the ring multiplied by its thickness.

What is the unit of stress in this scenario?

The unit of stress in this scenario is pascals (Pa), which is equivalent to 1 Newton per square meter (N/m^2).

How do you determine the weight of the ring?

To determine the weight of the ring, you can use the formula weight = mass x gravity. In this case, the mass is given as 1 kg/m and the gravity is a constant value of 9.8 m/s^2. Therefore, the weight of the ring is 9.8 N.

What is the significance of the radius and mass in this scenario?

The radius and mass are both important factors in determining the stress in the ring. The radius affects the area of the ring, which is used in the stress formula. The mass affects the weight of the ring, which is also used in the stress formula. Therefore, changing either the radius or mass will result in a change in the stress of the ring.

How can the stress in the ring be reduced?

The stress in the ring can be reduced by either decreasing the weight of the ring or increasing the area. This can be achieved by either using a lighter material for the ring or increasing its thickness. Additionally, distributing the weight evenly throughout the ring can also help reduce stress.

Similar threads

Replies
14
Views
2K
Replies
10
Views
2K
Replies
7
Views
534
Replies
3
Views
2K
Replies
12
Views
4K
Replies
2
Views
2K
Replies
16
Views
452
Back
Top