# Force problem for elastic stretch

1. Jan 31, 2005

### hackerdiety03

The force required to elastically stretch a wire is given by:

F= ( l - lo / lo ) EA

where A is the cross-sectional area of the wire, lo is the length of the unstretched wire and l the length of the wire after it is stretched. E is the elastic modulus, sometimes called Young's modulus. Using this equation, compute the force as a function of distance stretched for the gold nanowire as it is stretched from E-I to E-II. The elastic modulus for bulk pure gold is 7.448 x 10^10 Pa. Is the behavior of the nanowire qualitatively/quantitatively different from that of the bulk?

my work:

l value = 10 Angstroms (from my graph of E-II)
lo value = 8 Angstromgs (from my graph of E-I)

F = (10-8)/8 * (7.448x10^10 Pa) A

my problem is how would i find the value for the cross-sectional area of the wire (A)??? is there a formula i can use to calculate the cross-secitonal area?

2. Jan 31, 2005

### Andrew Mason

Does the problem give you the mass of the wire? If it did, you can compute the mass/length and find A from: $\rho A = m/l$. Otherwise, you don't have sufficient information here to solve the problem.

AM

3. Jan 31, 2005

### hackerdiety03

im not really given any values for EI-EII which is the configuration of the Au3-SCH3 molecule. instead, the length of the wire from the distance in which it was stretched. this is all in a graph dealing with nanwires.

4. Jan 31, 2005

### Andrew Mason

Why not just give us, word for word, the actual problem and post a copy of the graph. There is something missing from the information provided.

AM