Relating tensions in a vertical circle help

In summary: So if I use the above equation (Tb - Tt) to calculate the energy in Pounds, I'd get: [(mVb^2)/2]+mg2r=(mVt^2)/2.right?Yes, that is correct.
  • #1
samjohnny
84
1

Homework Statement



Question: A mass m attached to a light string is spinning in a vertical circle, keeping its total energy constant. Find the difference in the magnitude of the tension between the top most and bottom most points.

The Attempt at a Solution



So for this one I've worked out that the tension at the top=(mVt^2/r)-mg and at the bottom=(mVb^2/r)+mg where r=radius of circle, Vb is the velocity at bottom and Vt is velocity at top. And I've also worked out that, since the total energy is conserved, Energy at top [KE+PE]=Energy at bottom [KE+PE] ==> [(mVt^2)/2]+mg2r=(mVb^2)/2.

But I don't where to go from there and work out the two tensions. Any suggestions?

Thanks
 
Physics news on Phys.org
  • #2
Hello.

You don't need to work out the tensions individually. You just need to find the difference in the tensions. Find an expression for the difference in tensions and then invoke your energy relation to simplify the expression for the difference.
 
  • #3
TSny said:
Hello.

You don't need to work out the tensions individually. You just need to find the difference in the tensions. Find an expression for the difference in tensions and then invoke your energy relation to simplify the expression for the difference.

Thanks for the reply. Ok, if I'm understanding you correctly, would I equate the forces with Newton's second and obtain two vector equations for the two tensions? In which case, how would I take into account the energy?
 
  • #4
In your first post, you gave expressions for the tension at the bottom, Tb, and the tension at the top,Tt. Use those to get an expression for the difference Tb - Tt.
 
  • #5
TSny said:
In your first post, you gave expressions for the tension at the bottom, Tb, and the tension at the top,Tt. Use those to get an expression for the difference Tb - Tt.

Ah yes, thanks a lot I've got it now. :)
 

FAQ: Relating tensions in a vertical circle help

1. How do you calculate the tension in a vertical circle?

The tension in a vertical circle can be calculated using the formula T = mv2/r + mg, where T is the tension, m is the mass of the object, v is the velocity, r is the radius of the circle, and g is the acceleration due to gravity.

2. What is the relationship between tension and velocity in a vertical circle?

The tension in a vertical circle is directly proportional to the square of the velocity. This means that as the velocity increases, the tension also increases. This is because the faster an object is moving, the more centripetal force is required to keep it in circular motion.

3. What happens to the tension in a vertical circle at the bottom and top of the circle?

At the bottom of the circle, the tension is at its maximum because the velocity is at its maximum and the object is experiencing the most centripetal force. At the top of the circle, the velocity is at its minimum and the tension is also at its minimum. In fact, if the velocity is too low, the tension at the top may become zero, causing the object to fall.

4. How does mass affect the tension in a vertical circle?

The mass of the object does not directly affect the tension in a vertical circle. However, a heavier object may require a higher velocity to maintain circular motion, which would in turn increase the tension. But if the velocity is constant, the tension will remain the same regardless of the mass.

5. What is the role of gravity in determining the tension in a vertical circle?

Gravity is an important factor in determining the tension in a vertical circle. It is responsible for providing the centripetal force needed to keep the object in circular motion. Without gravity, the tension would be zero and the object would not be able to complete the circle.

Similar threads

Back
Top