# Forces: Forces and Elasticity

## Forces and Elasticity

### Characteristics of Elastic Objects

• An elastic object is one that can return to its original shape after the force is removed.

• Certain materials like rubber, springs or certain types of metal are typically elastic, but all materials have some degree of elasticity.

• If you apply a force to an elastic object, it extends or compresses, and does work by storing elastic potential energy. When the force is removed, this energy is released as the object returns to its original shape.

### Hooke’s Law

• The extension of an elastic object is directly proportional to the force applied, up to its limit of proportionality. This relationship is known as Hooke’s Law.

• Mathematically, Hooke’s Law can be expressed as: Force (F) = spring constant (k) x extension (e)

• The spring constant is a measure of the stiffness of the object. A larger spring constant indicates a stiffer, harder to extend spring.

• The limit of proportionality is reached when the force applied is so great that the elastic object no longer obeys Hooke’s Law. Beyond this point, the object will permanently deform or even snap.

### Energy Stored in a Spring

• The energy stored in an extended or compressed elastic object can be calculated using the equation: Elastic potential energy = 0.5 x spring constant (k) x extension^2 (e^2).

• Any object that can stretch or compress in an elastic way can store elastic potential energy, such as a drawn bow, an inflated balloon or a compressed spring.

• The energy stored is equal to the work done on the object to stretch or compress it.

### Stretching Materials

• When an object begins to stretch, deform or bend, it is said to be under tensile stress.

• Tensile stress is directly linked to tensile strain, which measures the extension per unit length of a material as a result of tensile stress.

• By pulling a wire with a known cross-sectional area under controlled conditions and measuring its extension, students can determine its Young Modulus - a measure of its stiffness.