Mechanical Testing

Here’s what we’re going to learn about!

•Forces•Newton’s 2nd

•Stress•Strain•Young’s Modulus

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Force

• A force is a push or a pull

•A Force is represented in diagrams by an arrow

•SI unit of force is Newton (N)

N = kg m

s2

5 N 10 N

20 N

Newton’s 2nd Law of Motion

F = ma

Force = (mass)(acceleration)

Units

F: N = kg m/s2

m: kg

a: acceleration (due to gravity)Symbol: a or g

Value: 9.81 m/s2

Newton’s 2nd Law of Motion

F = ma

Force = (mass)(acceleration)

Weight = (mass)(acceleration)

W = mga = g = 9.81 m/s2

Only on Earth!

Newton 2 can describe weight:

Example: Use Newton 2 to calculate your mass

F = maW= mg 1 lb = 4.45 N

150 lb1 lb

4.45 N = 668 N

m= W/g

m= 668 N / 9.81 m/s2

m= 68 kg

Formulas

Convert your weight in lb to SI unit of Newtons

Rearrange the equation to solve for mass

Plug and chug

This is a conversion factor

Example: Use Newton 2 to calculate your weight on Mars!

a = g = 3.71 m/s2

On Mars

F = maW= mg

Formulasm = 68 kg

W= mg

W= (68 kg)(3.71 m/s2)W= 252 N

1 lb = 4.45 N

252N 1 lb4.45 N

= 57 lb

Hey

Hi

Question:

We just saw that my mass on Earth is 68 kg.

What is my mass on Mars?

Answer: 68 kg-my mass will not change.

My weight changes because acceleration changes on mars

Stress

Stress =ForceArea

s =FA

Stress

Stress =ForceArea

s =FA

12 N

1 m

3 m

Example

Stress

Stress =ForceArea

s =FA

12 N

1 m

3 mF = 12 N

Example

Stress

Stress =ForceArea

s =FA

12 N

1 m

3 mF = 12 N

Example

A= (1m)(3m) = 3m2

We want the area that isperpendicular to the force

Stress

Stress =ForceArea

s =FA

12 N

1 m

3 mF = 12 N

Example

A= (1m)(3m) = 3m2

s =FA

=12 N

3m2= 4 N/m2

= 4 Pascals= 4 Pa

You try one!

s =FA

F =

A=

s =FA

=

3.14 N

Diameter = 2 m

Strain

Strain =Lf - Li

Li

e =Lf - Li

Li

Li

initial

Strain

Li

Lf

Force

Strain =Lf - Li

Li

e =Lf - Li

Li

initial

final

Strain

Li

Lf

Force

Lf - LiStrain =Lf - Li

Li

e =Lf - Li

Li

initial

final

Example

10 N

10 NLf =

e =Lf - Li

Li

Li =

e =

initial

final

1 mm

5 mm

Now put it together

What if we make a plot of stress vs. strain?

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Young’s Modulus

Stress vs. StrainThe slope of the stress-strain curve is a material property of stiffness

We call this parameter Young’s Modulus

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Young’s Modulus

Stress vs. StrainThe higher the slope, the stiffer the material

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Material 1

Material 2

Material 3

Material 3 is the stiffest

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