#AP Physics 1: Energy Review - Get Ready to Ace It! 🚀

Hey! Let's dive into the world of energy. This guide is designed to help you feel confident and ready for your AP Physics 1 exam. We'll break down the key concepts, highlight important formulas, and give you some memory aids to help it all stick. Let's do this!

#Conservation of Energy: The Golden Rule 🌟

#What is it?

The Law of Conservation of Energy states that the total energy of an isolated system remains constant. Energy can change forms (kinetic, potential, thermal), but it's never created or destroyed. Think of it like a closed piggy bank—the total amount of money inside stays the same, even if you exchange coins for bills.
Key Idea: This only applies when no external forces are doing work on the system. A falling ball (system: ball + Earth) conserves energy, but a car (system: car only) doesn't due to friction.
Common Scenarios: Falling objects, sliding/rolling down ramps, masses & springs, and planetary orbits are classic examples where energy conservation is key.

#Visualizing Energy Conservation

Check out this roller coaster! Notice how potential and kinetic energy trade off, but the total energy remains constant.

Roller Coaster

Key Concept

Total Mechanical Energy (TME): This is usually what we mean by 'total energy' in most problems. It's the sum of potential (U) and kinetic (K) energies: $TME = U + K$ . Remember, TME is constant in a closed system with no non-conservative forces.

#Quick Facts

Energy is always conserved in a closed system.
Energy can transform between forms but is never lost.
Use energy conservation to analyze and predict system behavior.

Practice Question

Multiple Choice Questions

A block of mass m is released from rest at the top of a frictionless ramp of height h. What is the speed of the block at the bottom of the ramp? (A) $\sqrt{gh}$ (B) $\sqrt{2gh}$ (C) $2gh$ (D) $4gh$
A spring with spring constant k is compressed by a distance x. What is the potential energy stored in the spring? (A) $\frac{1}{2}kx$ (B) $kx^2$ (C) $\frac{1}{2}kx^2$ (D) $2kx^2$

Free Response Question

A 2.0 kg block is released from rest at the top of a 30° incline that is 5.0 m long. The coefficient of kinetic friction between the block and the incline is 0.20. (a) Calculate the potential energy of the block at the top of the incline. (b) Calculate the work done by friction as the block slides down the incline. (c) Calculate the kinetic energy of the block at the bottom of the incline. (d) Calculate the speed of the block at the bottom of the incline.

Scoring Guide (a) Potential Energy: (2 points)

1 point for using the correct formula: $U = mgh$
1 point for correct calculation: $U = (2.0 kg)(9.8 m/s^2)(5.0 m * sin(30)) = 49 J$ (b) Work done by friction: (3 points)
1 point for calculating the normal force: $N = mg cos(30) = 16.97 N$
1 point for calculating the frictional force: $f = \mu N = 0.2 * 16.97 = 3.394 N$
1 point for calculating work: $W = f d = 3.394 * 5 = 16.97 J$ (c) Kinetic Energy at the bottom: (2 points)
1 point for using the work-energy theorem: $K_f = U_i - W_f$
1 point for correct calculation: $K_f = 49 J - 16.97 J = 32.03 J$ (d) Speed at the bottom: (2 points)
1 point for using the kinetic energy formula: $K = \frac{1}{2}mv^2$
1 point for correct calculation: $v = \sqrt{2K/m} = \sqrt{2 * 32.03/2} = 5.66 m/s$

#The Work-Energy Principle: Linking Work and Kinetic Energy 🔗

#What is it?

The Work-Energy Principle states that the net work done on an object equals its change in kinetic energy. In other words, if you do work on an object, you change its motion, which is reflected in the change in its kinetic energy.
Formula: $W_{net} = \Delta K = K_f - K_i$ . Where $W_{net}$ is the net work, $K_f$ is the final kinetic energy, and $K_i$ is the initial kinetic energy.
Connection: This principle is a direct result of the law of conservation of energy. Work is the transfer of energy, and this principle quantifies that transfer into kinetic energy.

#Key Points

Work done on an object = change in its kinetic energy.
Applies to both linear and rotational motion.
Works for conservative and non-conservative forces.

Memory Aid

Think of it this way: Work is like giving a push (or a pull) to an object. The harder you push (more work), the more its motion (kinetic energy) changes.

Quick Fact

Work can be positive (speeding up), negative (slowing down), or zero (constant speed).

Practice Question

Multiple Choice Questions

A 2 kg object is moving at a speed of 5 m/s. If a net force does 100 J of work on the object, what is the new speed of the object? (A) 5 m/s (B) 10 m/s (C) 11.2 m/s (D) 15 m/s
A box is pushed across a rough floor with a force of 50 N for a distance of 10 m. If the work done by friction is -200 J, what is the net work done on the box? (A) 200 J (B) 300 J (C) 500 J (D) 700 J

Free Response Question

A 0.5 kg ball is thrown vertically upward with an initial speed of 20 m/s. Assume air resistance is negligible.

(a) Calculate the initial kinetic energy of the ball. (b) Calculate the maximum height the ball reaches. (c) If air resistance does -10 J of work on the ball as it goes up, what is the maximum height the ball reaches now?

Scoring Guide (a) Initial Kinetic Energy: (2 points)

1 point for using the correct formula: $K = \frac{1}{2}mv^2$
1 point for correct calculation: $K = 0.5 * 0.5 * 20^2 = 100 J$ (b) Maximum height without air resistance: (3 points)
1 point for recognizing that at max height, kinetic energy is zero, and all initial kinetic energy is converted to potential energy: $U = mgh$
1 point for equating initial kinetic energy to final potential energy: $100 J = mgh$
1 point for correct calculation: $h = 100 / (0.5 * 9.8) = 20.4 m$ (c) Maximum height with air resistance: (4 points) * 1 point for using the work-energy theorem $W = \Delta K$ , where $W = W_{gravity} + W_{air}$ * 1 point for recognizing that $W_{gravity} = -mgh$ and $W_{air} = -10J$ * 1 point for setting up the equation: $-100J = -mgh - 10J$ * 1 point for correct calculation: $h = (100 - 10) / (0.5 * 9.8) = 18.37 m$

#Power: The Rate of Energy Transfer ⚡

#What is it?

Power is the rate at which work is done or energy is transferred. It tells you how quickly energy is being used or converted.
Formula: $P = \frac{W}{t}$ or $P = \frac{\Delta E}{t}$ where P is power, W is work, $\Delta E$ is change in energy, and t is time.
Units: Power is measured in watts (W), which is equivalent to joules per second (J/s).

#Key Points

Power is a scalar quantity (magnitude only).
Power can be positive or negative, depending on whether energy is being added or removed from the system.
Higher power means more work is done or more energy is transferred in a given time.

Common Mistake

Don't confuse power with energy or work. Power is the rate at which energy is used or work is done.

Exam Tip

Remember, power is about speed. If you need to do something quickly, you need more power.

Practice Question

Multiple Choice Questions

A machine does 500 J of work in 10 seconds. What is the power output of the machine? (A) 5 W (B) 50 W (C) 500 W (D) 5000 W
A 100 W light bulb is left on for 1 hour. How much energy does it use? (A) 100 J (B) 3600 J (C) 360000 J (D) 100000 J

Free Response Question

A 1000 kg car accelerates from rest to 20 m/s in 5 seconds. Assume the acceleration is constant.

(a) Calculate the kinetic energy of the car when it reaches 20 m/s. (b) Calculate the work done by the engine to accelerate the car. (c) Calculate the average power output of the engine during this acceleration.

Scoring Guide (a) Kinetic Energy: (2 points)

1 point for using the correct formula: $K = \frac{1}{2}mv^2$
1 point for correct calculation: $K = 0.5 * 1000 * 20^2 = 200000 J$ (b) Work done: (2 points)
1 point for using the work-energy theorem: $W = \Delta K$
1 point for correct calculation: $W = 200000 J$ (c) Average power output: (2 points)
1 point for using the power formula: $P = W/t$
1 point for correct calculation: $P = 200000 / 5 = 40000 W$

#Final Exam Focus 🎯

Okay, you've made it! Here's what to focus on for the exam:

Conservation of Energy: This is HUGE. Practice problems involving falling objects, springs, and ramps. Understand when energy is conserved and when it's not.
Work-Energy Principle: Master the relationship between work and kinetic energy. Be ready to use it in various scenarios.
Power: Know how to calculate power and what it represents. Understand the difference between energy, work, and power.

#Last-Minute Tips

Time Management: Don't spend too long on one question. If you're stuck, move on and come back later.
Units: Always include units in your answers. It's an easy way to gain or lose points.
Free Response: Show all your work. Even if you don't get the final answer, you can still get partial credit for the correct process.
Diagrams: Draw diagrams! They help visualize the problem and can earn you points.

#You've Got This! 💪

Remember, you've prepared for this. Stay calm, read each question carefully, and apply what you've learned. Good luck, and go crush that AP Physics 1 exam! 🎉