# Elasticity Problem

1. Jan 17, 2014

### Dumbledore211

1. The problem statement, all variables and given/known data
In the fig AB is a wire of diameter 0.6mm and Young modulus of the material 2x10^11Nm^-2. C is the mid point of the wire. How much will the point B go down?

2. Relevant equations

Y=FL/Al where L= original length of the wire and l=extension in the wire

3. The attempt at a solution
Here the entire system is in equilibrium which means that there is no net force and there is no extra acceleration caused by the system. ∑Fy=0. The distance by which the point B goes down depends on the overall extension of the wire caused by the two masses. What I tried to do is find out l1 at point C where I use L=1.5 l1= FL/AY=1.0398x10^-5m
l2= 1.0398x10^-5
Total distance= l1 +l2= 2x1.0398x10^-5m= 2.0796x10^-5m. But the answer is 3.12x10^-3m. Where did I go wrong?????

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2. Jan 17, 2014

### nasu

What is the meaning of this?
" L=1.5 l1= FL/AY=1.0398x10^-5m"

3. Jan 17, 2014

### Dumbledore211

Sorry what I meant is L=1.5 and small L sub 1= FL/AY since the first mass is attached at the mid point of L which is actually 3cm

4. Jan 17, 2014

### nasu

And what did you take as F? And what did you get for area?
You should show all steps. Otherwise how can someone figure out where the error is?

5. Jan 17, 2014

### lightgrav

How can the bottom half stretch the same amount as the top half?
Isn't the top half the same diameter wire, but holding up twice as much mass?

6. Jan 17, 2014

### Dumbledore211

The top half is holding up the same amount of mass as the bottom half according to the figure. I took F to be equal 39.2N as it is 4kg-wt. The area in each case is π(0.3x10^-3)^2. This begs the question does the cross- sectional area change for each half as there is extension in each case..

7. Jan 18, 2014

### nasu

The tensions in the strings are not the same.
Write the balance of the forces for the body attached in the middle of the string and you will see it.

8. Jan 19, 2014

### Dumbledore211

@Nasu, okay I get what you are saying. The body attached in the middle is apparently in equilibrium which means that it's weight and the tension acting downward nullify the tension acting upward. So the tension in the upper part is more. But, we are not allowed to use the equation of tension which is T=λl/L because there is no modulus of elasticity. So, what equation should we use to find the different tensions in each halve of the string

9. Jan 19, 2014

### Tanya Sharma

Do F=ma on the two masses to find the tensions in the two wires .Let T1 be the tension in the upper wire and T2 be the tension in the lower wire .

For the upper wire T1 = T2 +mg
For the lower wire T2 = mg

10. Jan 19, 2014

### Dumbledore211

@Tanya Sharma, I do get the answer which is 3.119419727X10^-5 which is 3.12x10^-5m≈ but the actual answer is 3.12x10^-3m

11. Jan 19, 2014

### Tanya Sharma

3.12x10-5 looks alright to me .

12. Jan 19, 2014

### nasu

Are you sure the length is 3 cm and not 3 m?

13. Jan 21, 2014

### Dumbledore211

I think it should be 3.12X10^5m because there are often minor printing mistakes in our books. Thank you.Your help is appreciated

Last edited: Jan 21, 2014
14. Jan 21, 2014

### Tanya Sharma

Yes...Either the answer is 3.12x10-5m or as nasu has pointed the length is 3m in which case the book answer is correct.