Elastic Potential Energy

Jamie Z 2024-06-18

Learning Goals

• Describe elastic potential energy as energy stored in springs and elastic bands
• Solve problems involving Hooke’s law

Hooke’s Law

\[ F_s = kx \]

• F = Force (N)
• x = Displacement (m)
• k = Spring Constant (N/m)

Example

A spring of unextended length 20cm and spring constant 22N/m supports a mass of 250g. What is the new length of the spring

\[ F=ma \ = 0.25*9.8 \=2.45 \]

\[ F_s = kx \ 2.45 = 22x \ x=\frac{2.45}{22} \ x=0.11 \]

• Therefore, the new length of the spring is 31cm long

Elastic Potential Energy

• The energy stored as a result of applying a force to deform an elastic object
• The graph of F vs x for a spring that is IDEAL in nature will always produce a line with a positive linear slope. Thus the area under the line will always be represented as a triangle

\[ U_s = \frac{1}{2}kx^2 \]