Further Mechanics 1 question (Elastic String and Springs)

Two elastic strings, AB of modulus 15N and natural length 1m and CD of modulus 18N and natural length 0.5m are joined B to C, to form one long string. End A is fixed to a ceiling. A particle of mass 0.5kg is attached to D and hangs in equilibrium. Calculate the length of the combined string.
I called the extensions of the two strings X1 and X2 and I got to 15X1+36X2=0.5g but I'm not sure what to do from here.

Reply 1

ghostwalker

17

Original post by Penelope276

Two elastic strings, AB of modulus 15N and natural length 1m and CD of modulus 18N and natural length 0.5m are joined B to C, to form one long string. End A is fixed to a ceiling. A particle of mass 0.5kg is attached to D and hangs in equilibrium. Calculate the length of the combined string.
I called the extensions of the two strings X1 and X2 and I got to 15X1+36X2=0.5g but I'm not sure what to do from here.

Draw a diagram if you haven't done so already.

Not sure how you would arrive at that particular equation. It's saying that the tension in AB plus the tension in CD equals the weight. Does this seem reasonable? Are they both directly attached to the weight?

Reply 2

Penelope276

OP

2

I see why what I've done is wrong but I'm not sure what I'm supposed to do as I don't understand if the tension is acting up or down in each string.

Reply 3

ghostwalker

17

Original post by Penelope276

I see why what I've done is wrong but I'm not sure what I'm supposed to do as I don't understand if the tension is acting up or down in each string.

Within the string tension acts towards the body of the string, i.e. inwards from either end. Standard for anything under tension.

If you think about a single string and pull the ends, the string resists. You're pulling outwards, and the string resists by pulling inwards.

Assuming you have the diagram correct, there is a very simple relationship between the tension in AB and the tension in CD (the fact that they are elastic is irrelevant when considering this).

Reply 4

Penelope276

OP

2

Original post by ghostwalker

Within the string tension acts towards the body of the string, i.e. inwards from either end. Standard for anything under tension.
If you think about a single string and pull the ends, the string resists. You're pulling outwards, and the string resists by pulling inwards.
Assuming you have the diagram correct, there is a very simple relationship between the tension in AB and the tension in CD (the fact that they are elastic is irrelevant when considering this).

Oh so T1=T2 and then T2=0.5g?