Light inextensible string problem

In summary: This was a really easy problem for me. Thanks for clarifying everything for me.In summary, the revolving mass has a centripetal force that is inversely proportional to its distance from the static mass.

Homework Statement

Two particles of masses m and 2m are connected by a light inextensible string, which is
threaded through a fixed smooth ring. If the lighter particle moves uniformly round a
horizontal circle of radius a, while the other particle remains stationary, find the lighter
particle's speed.

accel = aw^2

The Attempt at a Solution

Here is my diagram of the problem, I would appreciate it if someone could tell me if this is correct. p is the angle between the 2 ends of string.

http://img166.imageshack.us/img166/7560/question3diagram122lo7.jpg

Particle is moving uniformly with constant angular speed, w.

T2 - 2mg = 0 by resolving.

So T2 = 2mg.

T1 cos p = mg by resolving.

Using F = m(accel), F = T1 sin p, accel = aw^2

T1 sin p = maw^2

Question 1. Are the tensions equal because if they werent, the string would break?
Question 2. Have I now got to go on and find w? How?

Last edited by a moderator:
Question 1. Are the tensions equal because if they werent, the string would break?
Yes, the tensions are equal. There's no friction from the ring.

Question 2. Have I now got to go on and find w? How?
Using the vertical force equation you can solve for the angle. Then use it in the horizontal force equation to solve for $\omega$ or v.

$$a_c = r\omega^2 = v^2/r$$

Particle is moving uniformly with constant angular speed, w.

T2 - 2mg = 0 by resolving.

So T2 = 2mg.

The tension is the same throughout the string, since there is no friction involved anywhere and the string is massless.

For the static mass, T=2mg.

For the revolving mass, Tcosp=mg and Tsinp=centripetal force, as you have written.

Now you can find v.

(EDIT: Overlooked 2mg in the diagram. Mistake pointed out by Doc Al.)

Last edited:
T2 - 2mg = 0 by resolving.

So T2 = 2mg.
This is perfectly correct.

Doc Al said:
This is perfectly correct.

So it is. I thought the static mass was also m; overlooked the 2mg in the diagram...Thanks Doc!

Last edited:

I end up with v = root(a*g*root(3)).

Looks good!

So that's all there is to it? For some reason I thought it would be much more complex than this. My knowledge of physics/mechanics is very very limited. I'm actually not sure I even understand the concept of angular speed.

1. What is the light inextensible string problem?

The light inextensible string problem is a physics problem that involves a string or rope that is assumed to have no mass and does not stretch or deform under tension. It is often used in mechanics problems to simplify calculations and focus on other factors, such as forces and motion.

2. How is the light inextensible string problem used in physics?

The light inextensible string problem is used to simplify calculations in mechanics problems by assuming that the string has no mass and does not stretch or deform. This allows physicists to focus on other factors, such as forces and motion, without having to account for the weight or elasticity of the string.

3. What are the assumptions made in the light inextensible string problem?

The light inextensible string problem relies on two main assumptions: that the string has no mass and does not stretch or deform under tension. These assumptions allow for simpler calculations and analysis of forces and motion in mechanics problems.

4. Can a real string or rope be light inextensible?

No, a real string or rope will always have some mass and will stretch or deform under tension to some degree. The light inextensible string is a theoretical concept used in physics problems to simplify calculations and focus on other factors.

5. What are some common applications of the light inextensible string problem?

The light inextensible string problem is commonly used in physics problems involving mechanics, such as pulley systems, inclined planes, and simple machines. It is also used in engineering and design, particularly in structures that involve cables or ropes, such as suspension bridges and cranes.

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