AP Physics 1 Questions on Law of Conservation of Energy

📚 Quick Study Guide

• 💡 The Law of Conservation of Energy states that the total energy of an isolated system remains constant. Energy can neither be created nor destroyed, but it can change from one form to another.
• 🔥 Common forms of energy include kinetic energy ($KE = \frac{1}{2}mv^2$), potential energy (gravitational $PE_g = mgh$, spring $PE_s = \frac{1}{2}kx^2$), thermal energy, and others.
• ⚙️ In a closed system, the total energy (E) is conserved: $E_{initial} = E_{final}$. This means the sum of all forms of energy at the beginning is equal to the sum of all forms of energy at the end.
• 🚧 When dealing with non-conservative forces like friction, some energy is converted into thermal energy (heat). The work done by friction is $W_f = f_k d$, where $f_k$ is the kinetic friction force and $d$ is the distance. In this case, $E_{initial} = E_{final} + |W_f|$.
• 🍎 Remember to choose a reference point (usually the ground) for gravitational potential energy.

🧪 Practice Quiz

1. A roller coaster car starts at rest at the top of a 50-meter hill. Assuming no friction, what is the car's speed at the bottom of the hill?
   1. A) 22.1 m/s
   2. B) 31.3 m/s
   3. C) 44.2 m/s
   4. D) 9.8 m/s
2. A 2 kg block is released from rest on a frictionless inclined plane at a height of 3 meters. What is the kinetic energy of the block when it reaches the bottom of the incline?
   1. A) 6 J
   2. B) 30 J
   3. C) 58.8 J
   4. D) 100 J
3. A spring with a spring constant of 200 N/m is compressed by 0.3 meters. What is the potential energy stored in the spring?
   1. A) 6 J
   2. B) 9 J
   3. C) 18 J
   4. D) 30 J
4. A 0.5 kg ball is thrown upwards with an initial velocity of 20 m/s. What is the maximum height reached by the ball, assuming no air resistance?
   1. A) 10.2 m
   2. B) 20.4 m
   3. C) 30.6 m
   4. D) 40.8 m
5. A 1 kg block slides down a rough inclined plane. At the bottom, its kinetic energy is 8 J less than its initial potential energy. How much work was done by friction?
   1. A) 4 J
   2. B) 8 J
   3. C) 12 J
   4. D) 16 J
6. A pendulum is released from rest at an angle of 30 degrees with the vertical. At the lowest point of its swing, which of the following is true about its energy?
   1. A) All potential energy has been converted to kinetic energy.
   2. B) All kinetic energy has been converted to potential energy.
   3. C) Half of the potential energy has been converted to kinetic energy.
   4. D) The total energy is zero.
7. A 50 g marble is dropped from a height of 2 meters. If its speed just before hitting the ground is 5 m/s, how much energy was lost due to air resistance?
   1. A) 0.125 J
   2. B) 0.23 J
   3. C) 0.35 J
   4. D) 0.42 J