AP Physics Questions on Elastic Potential Energy: Exam Prep

📚 Quick Study Guide

• 📏 Elastic Potential Energy Defined: Elastic potential energy ($U$) is the energy stored in a deformable object—such as a spring—when it is stretched or compressed.
• 🧮 Formula: The elastic potential energy stored in a spring is given by the formula: $U = \frac{1}{2}kx^2$, where $k$ is the spring constant (in N/m) and $x$ is the displacement from the equilibrium position (in meters).
• 💡 Spring Constant (k): Represents the stiffness of the spring. A higher value of $k$ indicates a stiffer spring.
• ↔️ Displacement (x): The amount the spring is stretched or compressed from its original, unstretched length.
• ⚠️ Units: Energy is always measured in Joules (J). Therefore, elastic potential energy is also measured in Joules.
• 🔑 Key Concepts: Understanding Hooke's Law ($F = -kx$) is crucial, as it relates the force required to stretch or compress a spring to the displacement.
• 📝 Important Note: The elastic potential energy is always positive because it is proportional to the square of the displacement ($x^2$).

🧪 Practice Quiz

1. A spring with a spring constant of 200 N/m is stretched by 0.2 m. What is the elastic potential energy stored in the spring?
   1. 0.8 J
   2. 4 J
   3. 8 J
   4. 40 J
2. If the elastic potential energy stored in a spring is 50 J when it is stretched by 0.5 m, what is the spring constant of the spring?
   1. 100 N/m
   2. 200 N/m
   3. 400 N/m
   4. 800 N/m
3. A spring is compressed by 0.1 m and has an elastic potential energy of 2 J. What is the spring constant?
   1. 200 N/m
   2. 400 N/m
   3. 20 N/m
   4. 100 N/m
4. A spring with a spring constant of 500 N/m is stretched. If the elastic potential energy stored is 25 J, by how much was the spring stretched?
   1. 0.1 m
   2. 0.2 m
   3. 0.316 m
   4. 0.5 m
5. Two identical springs are connected in series. If each spring has a spring constant $k$, what is the effective spring constant of the series combination?
   1. $2k$
   2. $k/2$
   3. $k$
   4. $4k$
6. Two identical springs are connected in parallel. If each spring has a spring constant $k$, what is the effective spring constant of the parallel combination?
   1. $2k$
   2. $k/2$
   3. $k$
   4. $4k$
7. A 0.5 kg mass is attached to a vertical spring with a spring constant of 100 N/m. How much does the spring stretch from its equilibrium position when the mass is at rest? (Assume g = 9.8 m/s²)
   1. 0.0245 m
   2. 0.049 m
   3. 0.245 m
   4. 0.49 m