## Classical Mechanics: Lecture 26 Notes

Overview

Today is a 57 minute lecture on the traditional topics of mechanical engineering: stress, strain and young’s modulus. There is 6 minutes of nothing added to the end of this video.

**Details**

When you take a spring, with length l in its relaxed phase, pull with force C to dL. If you double the force, dL will double.

dL = kF

If the spring is made twice as long.

dL = kL

Two springs parallel are applied with a force, the new force will be half

dL = k/number of springs

A rod with length l and cross sectional area A. Pull down, it extends dL down.

Hooke’s Law:

F = -kx

dL = k/cross sectional area

dL = kFL/A

F/A = kdL/L

K is Y or Young’s modulus.

F/A is pressure and is stress

dL/L is dimensionless and is strain.

If you keep weighing down a material, it will stretch and eventually break. If the force is removed, it may return to its original length. If a certain point is exceeded, it will not return and will deform. This is the ultimate tensile strength.

The strain is no longer proportional to the stress. It flows. Hooke’s law is violated.

Graph of stress versus strain. Linear graph reaches the elastic limit then a small increase in stress will lead to a huge increase in strain. The rod gets hot. It will keep increasing non-linearly, a horizontal portion, then it will decrease then break.

Plastic flow occurs when no increase in stress leads to a change in strain. It pinches with a decreased area. F/A’ > F/A. Machines do this experiment which shows how the material tries to decrease stress.

Measure small changes in F. Before you increase the force, you decrease it.

A copper wire holds a solid rod with holds a mirror and weights. The mirror can tilt but not do down. This leads to a change in angle, which we measure.

He performs the experiment from 23 minutes on.

F=-YAdL/L

k = -YA/L

The speed of sound depends upon Young’s modulus. The higher young’s modulus, the higher the speed of sound. The higher young’s modulus, the stiffer the material.

V sound = sqrt Y/density

The sound a bar will make when struck will be

2 length/ v sound

Get time, then 1/t = f.

**Review**

F = 1/T

c = w f

F = ma

p = mv

F/A = YdL/L