Forces and elasticity

This section explores how forces affect elastic objects, the relationship between force and extension, and energy stored in stretched or compressed springs.

Forces and deformation

1. Forces Involved in Stretching, Bending, or Compressing Objects:

   • Forces can cause objects to stretch (e.g., springs), bend (e.g., beams), or compress (e.g., foam).

   • Examples:

     • Stretching: A bungee cord during a jump.

     • Bending: A diving board under a diver’s weight.

     • Compressing: A car suspension spring under load.

2. Why Multiple Forces are Needed:

   • To change the shape of a stationary object (by stretching, bending, or compressing), more than one force must be applied.

   • A single force would cause the object to move rather than change shape.

   • Example: Stretching a spring requires pulling forces at both ends.

Elastic and inelastic deformation

• Elastic Deformation:

  • The object returns to its original shape once the forces are removed.

  • Example: A rubber band being stretched within its limit.

• Inelastic Deformation:

  • The object does not return to its original shape after the forces are removed.

  • Example: Stretching a plastic bag until it tears.

Hooke's law

The extension of an elastic object (e.g., a spring) is directly proportional to the force applied, provided the limit of proportionality is not exceeded.

Equation for Force and Extension:

F = k × e

Where:

• F = Force applied (N)

• k = Spring constant (N/m)

• e = Extension (m)

Key Points:

• The spring constant (k) represents the stiffness of the spring.

  • A higher kkk value means the spring is stiffer.

• Beyond the limit of proportionality, the relationship becomes non-linear, and Hooke's Law no longer applies.

Example:

If a spring with k = 50 N/m is stretched by e = 0.2 m:

F = 50 N/m × 0.2 m = 10 N

Extension of a spring

Elastic potential energy

When a spring is stretched or compressed, elastic potential energy is stored.

Formula for Elastic Potential Energy:

Where:

• Ee​ = Elastic potential energy (J)

• k = Spring constant (N/m)

• e = Extension (m)

Example:

For a spring with k = 50 N/m stretched by e = 0.2 m:

Ee = 1/2 × 50 N/m × (0.2 m)2 = 1 J

Investigating force and extension

1. Linear Relationships:

   • For forces below the limit of proportionality, the force-extension graph is a straight line.

2. Non-Linear Relationships:

   • Beyond the limit of proportionality, the graph curves, indicating permanent deformation or inelastic behavior.

3. Practical Example:

   • Measure the extension of a spring for different weights added.

   • Plot a graph of force (F) vs extension (e) to determine k.

Force-extension graph

Key skills and application