## Strength of Solids

The weight of an object is proportional to its mass given (in Newtons) by *W* = *m, *where g is the force of gravity per unit mass.

Hooke’s Law: For a steel spring the tension is proportional to the extension, i.e. *T* = *ke*, where *e* = extension and *k* = spring constant

Material Properties: Strength and stiffness depend on the dimensions and on the material of an object. Strength is defined as how much force is required to break an object. Stiffness is a measure of the difficulty of stretching or bending an object. Elasticity, hardness and toughness are material properties and do not depend on dimensions. Elasticity allows an object to regain its shape after being distorted. The elastic limit of an object is the limit to which it can be distorted and still be able to regain its shape. Hardness is the resistance of the surface of a material to scratches and dents. Toughness is the ability of a material to withstand impact forces without cracks developing. A brittle material would snap suddenly when subjected to excessive forces.

Stress is defined as the force per unit area acting perpendicular to the area.

Strain is defined as the change of length per unit length

The Young modulus of elasticity (*E*) of a material is defined as the stress/strain.

The area under a force versus extension graph represents the work done.

The energy stored in a stretched spring = ½ *ke*^{2}, where *e* = extension, and *k* is the spring constant

The energy stored in a stretched wire = ½(*AE*)*e*^{2}/*L
*