You are Here: Home >< Maths

# Edexcel Mechanics M4 Ch.5 Stability Question watch

1. as title says, this chapter concerns about the stability of a mechanical system.
Ex5A Q3.
A uniform heavy rod AB, of mass m and length 4a, can turn in a vertical plane about one end A which is fixed. To the other end B is attached a light elastic string of natural length 3a and modulus 1/2 mg. The other end of the string is attached to a light ring which can slide on a smooth horizontal bar which is fixed at a height of 8a above A and in the vertical plane through AB. Find the equilibrium position of the rod and determine their nature.

I tried to find the extension of the string, so that i can find the E.P.E. and hence the P.E. in that string. Afterwards, i can add the P.E. of the rod so that it forms a function V = f(theta), where V = P.E.. However, I can't seem to do the extension bit. Can someone help me?

For some further note, this chapter's main focus is:
In a system, possible position of equilibrium occur when the P.E. of the system has stationary values, which is d P.E. / d theta = 0.
Minimum values of the P.E. correspond to stable equilibrium positions.
Maximum values of the P.E. correspond to unstable equilibrium positions.
(d^2 P.E. / d theta^2)

2. the string must be vertical, right?
3. Doesn't have to, because it is linked to the smooth ring that is movable along the horizontal 8a above A rite?
4. if it's not vertical. how can it be equalibrium since no frictional force?
5. And I don't think there is a way to solve the problem without working this out first.
6. The answer given in the book says,
if theta = the angle between upward vertical and the rod, then
theta = 0 (unstable), pi/3 (stable), pi (unstable)
7. (Original post by kira18)
Doesn't have to, because it is linked to the smooth ring that is movable along the horizontal 8a above A rite?
Exactly. It's linked to a smooth ring mounted horizontally. So there can't be any horizontal force on the ring, because if there was, it would slide.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 8, 2008
Today on TSR

### The TSR A-level options discussion thread

Choosing A-levels is hard... we're here to help

### University open days

• Heriot-Watt University
School of Textiles and Design Undergraduate
Fri, 16 Nov '18
• University of Roehampton
Sat, 17 Nov '18
• Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 17 Nov '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams