Mechanics Tension in String

I am struggling to understand tensions in strings. If two strings are connected, would tension be constant throughout? And can someone explain to me how tensions acts when one string is has both ends attached fixed points when there is a mass in between, please?

Need to see the question really. These problems often requie the vertical components of the tension in the strings to be added together to give the total upwards force which = the weight downwards when in equilibrium

There are two questions
first question is an elastic spring has natural length 2a and modulus of elasticity 2mg. a particle of mass m is attached to the midpoint of the spring. One end of the spring, A, is attached to the floor of a room of height 5a and the other end is attached to the ceiling of the room at a point B vertically above A. The spring is modeled as light.
Find the distance of the particle below the ceiling when it is in equilibrium.
Second question is a light elastic string AB has natural length l Andy modulus of elasticity 2mg. Another light elastic string CD has natural length l and modulus of elasticity 4mg. The strings are joined at their ends B and C and the end A is attached to a fixed point. A particle of mass m is hung from the end D Andy is at rest in equilibrium. Find length AD

First question. Have you modelled the scenario with an appropriate diagram?

I was able to draw out the right diagram but in the answers it showed that there’s two tensions in the opposite direction and I didn't know why there is tension downwards on the string.

Because tension acts throughout the string.

The particle doesn't disconnect the string into to parts.

But why is there two in opposite direction and different in magnitude? I thought there was only upward tension?

Hang on, do you mean to stay 'spring' in your first question, and not 'string' like you enquire in OP?

I meant elastic strings in the OP. Sorry for the confusion.

OK but question 1 talks about springs instead.

The springs and strings are similar but not the same. Do you still need help with it?

Yes. I am still struggling to understand the tensions in springs. Could you tell me there is two tensions in the spring on questions 1, please?

Ok so, ignore what I said previously.

The question states that a particle is attached to the middle of the spring. Think of this particle now decomposing the spring into two springs of equal length $a$.

Now in our situation, we have the following diagram:




Obviously, $5a$ is the height of the room, and let us denote our wanted distance by $x$.

Naturally, the particle (shown as the box) is below the half-way point of AB.

Note that with springs, they can be either compressed or extended. In either case, they have tension in them that make them want to return to their natural state.

Let us suppose that both strings are extended. Therefore both strings do their best to return to their natural length. The top string tries to pull the particle up with its own tension of $T_1$, and the bottom string tries to pull the particle down with its own force of $T_2$.

The extension in the top string is $e_1 = x-a$.

The extension in the bottom string is $e_2 = (5a-x) - a = 4a-x$

Then you can work out the tensions in both springs by applying the formula $T = \dfrac{\lambda e}{l}$ where $\lambda$ is the same in both springs.

Then proceed to solve for $x$ by equating the appropriate forces.

Thank you so much for your help. I think I understand now.

Then the second question should be more straight forward. It's literally two strings joined together, with a particle at the end, hung vertically. Clearly, the two strings have different moduli of elasticity hence they will have different tensions when keeping the system in equilibrium.