Elastic Potential Energy Formula: Explained with Examples

📚 Quick Study Guide

• 📏 Elastic potential energy is the energy stored in deformable objects, like springs, when they are stretched or compressed.
• 🧮 The formula for elastic potential energy ($U$) is: $U = \frac{1}{2}kx^2$, where:
  • $k$ is the spring constant (a measure of the stiffness of the spring).
  • $x$ is the displacement (the amount the spring is stretched or compressed from its equilibrium position).
• 💡 The spring constant ($k$) is measured in Newtons per meter (N/m).
• 📝 Displacement ($x$) is measured in meters (m).
• 🔑 Elastic potential energy ($U$) is measured in Joules (J).
• 🧪 The formula assumes the spring obeys Hooke's Law, which states that the force needed to extend or compress a spring by some distance is proportional to that distance.

Practice Quiz

1. Question 1: A spring with a spring constant of 50 N/m is stretched by 0.2 meters. What is the elastic potential energy stored in the spring?
   1. 0.5 J
   2. 1 J
   3. 2 J
   4. 2.5 J
2. Question 2: If a spring stores 4 J of elastic potential energy when compressed by 0.4 meters, what is the spring constant?
   1. 20 N/m
   2. 25 N/m
   3. 50 N/m
   4. 100 N/m
3. Question 3: A spring has a spring constant of 80 N/m. How much must it be stretched to store 10 J of elastic potential energy?
   1. 0.25 m
   2. 0.5 m
   3. 0.75 m
   4. 1 m
4. Question 4: What happens to the elastic potential energy stored in a spring if the displacement is doubled?
   1. It doubles
   2. It quadruples
   3. It halves
   4. It remains the same
5. Question 5: A spring with a spring constant of 120 N/m is compressed by 0.3 meters. What is the elastic potential energy stored in the spring?
   1. 2.7 J
   2. 5.4 J
   3. 10.8 J
   4. 16.2 J
6. Question 6: If the elastic potential energy stored in a spring is 18 J when it is stretched by 0.6 meters, what is the spring constant?
   1. 50 N/m
   2. 75 N/m
   3. 100 N/m
   4. 150 N/m
7. Question 7: A spring has a spring constant of 60 N/m. How much must it be compressed to store 7.5 J of elastic potential energy?
   1. 0.25 m
   2. 0.5 m
   3. 0.75 m
   4. 1 m