Current Attempt in Progress A hanging 'nickel wire with...

Current Attempt in Progress A hanging 'nickel wire with diameter 2.3 mm ($2.3 \times 10^{-3}$ m) is initially 0.95 m long. When a 108 kg mass is hung from it, the wire stretches an amount 1.21 mm. A mole of 'nickel has a mass of 59 grams, and its density is 8.90 g/cm$^3$. Find the approximate value of the effective spring stiffness of the interatomic force. $k_s = $ N/m

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00:01 So we're going to start out by finding the young's modulus.

00:04 Okay, so young's modulus y.

00:07 That is given by the 4 divided by the area, divided by the station, divided by the original length.

00:15 The force can also be mg divided by area over e over l.

00:24 Let's try the substitution.

00:26 The mass is 108.

00:29 E gravity is 9 .81, right? that divided by the area.

00:39 So the area is pi r squared, so pi the radius.

00:49 So the diameter is 2 .1.

00:51 So the radius is going to be 1 .05.

00:57 Let's be careful of the unit.

00:59 That one is in millimeters.

01:02 It has to be a meter.

01:03 So 10 to the negative 3 squared divided by the extension.

01:09 Let's look at the extension.

01:11 It's 0 .917 millimeters, but it has to be in meters, so it times 10 to the minus 3, that one to divide it by the original length, 0 .6.

01:25 So if you take out of the numerators and the denominator and you divide, you're gonna get the young models to be approximately 2 times 10 to the 11.

01:42 Okay, that's newton per meter squared.

01:47 Now all we need to do next is to find the distance between the atoms.

01:53 Let's get a distance between the atoms.

02:06 So that is deep.

02:09 It's going to be the mullah mass divided by a regardless number times a density, a cubic root of that...

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