AP Physics questions on Conservation of Mechanical Energy

📚 Quick Study Guide

• 🔍 Conservation of Mechanical Energy: In a closed system, the total mechanical energy (potential + kinetic) remains constant if only conservative forces (like gravity) do work.
• 📏 Potential Energy (Gravitational): $U = mgh$, where $m$ is mass, $g$ is the acceleration due to gravity, and $h$ is height.
• 🏃 Kinetic Energy: $K = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity.
• 💡 Total Mechanical Energy: $E = U + K$. If mechanical energy is conserved, then $E_i = E_f$, which means $U_i + K_i = U_f + K_f$.
• 📝 Non-Conservative Forces: If non-conservative forces (like friction) are present, mechanical energy is not conserved. The work done by these forces changes the total mechanical energy.

Practice Quiz

1. A roller coaster car starts at rest at the top of a 30-meter hill. Assuming no friction, what is the car's speed at the bottom of the hill?
   1. 14.0 m/s
   2. 24.2 m/s
   3. 34.3 m/s
   4. 40.1 m/s
2. A pendulum is released from rest at an angle of 45 degrees. What is the speed of the pendulum bob at the lowest point of its swing if the length of the pendulum is 2 meters?
   1. 2.4 m/s
   2. 3.4 m/s
   3. 4.4 m/s
   4. 5.4 m/s
3. A 2 kg block is released from rest on a frictionless inclined plane at a height of 5 meters. What is the kinetic energy of the block when it reaches the bottom of the incline?
   1. 49 J
   2. 98 J
   3. 147 J
   4. 196 J
4. A spring with a spring constant of 200 N/m is compressed by 0.3 meters. A 0.1 kg ball is placed against the compressed spring. When the spring is released, what is the speed of the ball just as it leaves the spring?
   1. 3 m/s
   2. 6 m/s
   3. 9 m/s
   4. 12 m/s
5. A 0.5 kg ball is thrown vertically upwards with an initial velocity of 20 m/s. What is the potential energy of the ball at its maximum height?
   1. 25 J
   2. 50 J
   3. 75 J
   4. 100 J
6. A skier starts from rest at the top of a slope. After skiing down, they reach a speed of 15 m/s at the bottom. If the height of the slope is 20 meters, how much energy was lost due to friction (assuming the skier's mass is 60 kg)?
   1. 2820 J
   2. 3900 J
   3. 4200 J
   4. 5760 J
7. A simple pendulum of length 1 meter has a bob of mass 0.2 kg. If the pendulum is released from an angle of 60° from the vertical, what is the kinetic energy of the bob at the lowest point of its swing?
   1. 0.48 J
   2. 0.98 J
   3. 1.48 J
   4. 1.96 J