AP Physics 1 Questions on Hooke's Law: Exam Prep

📚 Quick Study Guide

• 🍎 Hooke's Law: Describes the relationship between the force required to extend or compress a spring and the distance of that extension or compression.
• 📏 Formula: $F = -kx$, where:
  • 🔑 $F$ is the spring force (N)
  • 🌱 $k$ is the spring constant (N/m)
  • 🍁 $x$ is the displacement from the equilibrium position (m)
• 🧲 Spring Constant (k): A measure of the stiffness of the spring. A larger $k$ value indicates a stiffer spring.
• 💡 Elastic Potential Energy: The potential energy stored in a spring when it is stretched or compressed.
  • 🧪 Formula: $U = \frac{1}{2}kx^2$, where:
    • 🔑 $U$ is the elastic potential energy (J)
    • 🌱 $k$ is the spring constant (N/m)
    • 🍁 $x$ is the displacement from the equilibrium position (m)
• 📐 Important Considerations:
  • 🚨 Hooke's Law is a linear approximation and only valid within the elastic limit of the spring.
  • 🧭 The negative sign in $F = -kx$ indicates that the spring force is a restoring force, acting in the opposite direction to the displacement.

🧪 Practice Quiz

1. A spring with a spring constant of 50 N/m is stretched by 0.2 meters. What is the magnitude of the force exerted by the spring?
   1. A) 5 N
   2. B) 10 N
   3. C) 25 N
   4. D) 100 N
2. If a force of 20 N is applied to a spring, causing it to stretch by 0.5 meters, what is the spring constant?
   1. A) 10 N/m
   2. B) 20 N/m
   3. C) 40 N/m
   4. D) 80 N/m
3. A spring has a spring constant of 100 N/m. How much elastic potential energy is stored in the spring when it is compressed by 0.1 meters?
   1. A) 0.5 J
   2. B) 1 J
   3. C) 2 J
   4. D) 5 J
4. A mass of 2 kg is attached to a vertical spring with a spring constant of 80 N/m. What is the extension of the spring due to the weight of the mass? (Assume $g = 9.8 m/s^2$)
   1. A) 0.1225 m
   2. B) 0.245 m
   3. C) 0.49 m
   4. D) 0.98 m
5. Two identical springs are connected in series. If each spring has a spring constant of $k$, what is the effective spring constant of the combination?
   1. A) $2k$
   2. B) $k$
   3. C) $k/2$
   4. D) $k^2$
6. Two identical springs are connected in parallel. If each spring has a spring constant of $k$, what is the effective spring constant of the combination?
   1. A) $2k$
   2. B) $k$
   3. C) $k/2$
   4. D) $k^2$
7. A spring stretches by 5 cm when a force of 10 N is applied. How much will it stretch if a force of 30 N is applied, assuming it remains within its elastic limit?
   1. A) 10 cm
   2. B) 15 cm
   3. C) 20 cm
   4. D) 25 cm