Deformation Of Solid

Hooke's Law

Force is directly proportional to extension, provided the limit of proportionality (P) is not exceeded.

Beyond Limit of Elasticity

Plastid Extension occours, meaning after the force applied is removed, the string will not come back to its original form.

Elastic Potential Energy

1/2 × F × e

Strain Energy

1/2 × k × e² (k = spring constant)

Additional Strain Energy

1/2 × k × (e2² - e1²)

Springs in Series

Total extension increases: 2e for 2 springs, 3e for 3 springs; k is divided by the number of springs (k and e are inversely proportional: F = ke)

Springs in Parallel

Extension is divided by the number of springs; k is multiplied by the number of springs

Series

Extension × (no. of springs), k ÷ (no. of springs)

Parallel

Extension ÷ (no. of springs), k × (no. of springs)

Limit of Proportionality (P)

Point beyond which F is no longer proportional to e

Elastic Limit (E)

Point beyond P where permanent (plastic) deformation begins

Before E is crossed

spring returns to original shape when force is removed

After E is crossed

spring undergoes plastic deformation

Stress

Force / Area

Strain

ΔL / L (also written e/L) — no units, ratio of extension to original length

Young Modulus (E)

Stress / Strain = (F/A) / (e/L) = FL / Ae

Extension (x-axis) vs Force (y-axis)

Gradient = spring constant (k)

Force (x-axis) vs Extension (y-axis)

Gradient = 1/k