#AP Physics 1: Energy and Work - The Night Before 🚀

Hey! Let's get you prepped and confident for your AP Physics 1 exam. We're going to break down energy and work, making sure you're ready for anything the test throws your way. Let's dive in!

#Conservation of Energy: The Golden Rule 🌟

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• What is Conservation? Certain quantities remain constant within a system. Changes in these quantities are due to transfers between the system and its surroundings.
• Energy is King: Energy is always conserved. It can't be created or destroyed, only transformed. This is the Law of Conservation of Energy.
• Closed System: The total energy in a closed system stays the same, no matter what happens inside. What one part loses, another part gains.
• Forms of Energy: This law applies to all types of energy:
  • Kinetic Energy: Energy of motion.
  • Potential Energy: Energy of position or configuration.
  • Thermal Energy: Energy of heat.

#Total Energy Changes

• External Interactions: Interactions with external objects or systems can change the total energy of a system.

#Systems vs. Objects: Defining Your World 🌍

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• System Definition: A system is an object or a collection of objects we're focusing on. Objects are treated as having no internal structure.
• Thermodynamics View: In thermodynamics, a system is a region we're studying.
  • Open System: Exchanges both matter and energy with its surroundings. (Also called an exchange system).
  • Closed System: Exchanges only energy, not matter, with its surroundings.
  • Isolated System: Exchanges neither matter nor energy with its surroundings.

#Force Interactions: How Systems Interact 💪

• Interactions: These can be forces from outside the system or transfers of quantities with external objects.

#Defining the System

• Crucial Step: Always define your system before starting calculations.
• Internal vs. External Forces:
  • Internal Force: Caused by a member within the system.
  • External Force: Caused by something outside the system.

#Work: Energy in Motion ⚙️

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• Work as Energy Transfer: Work is the transfer of energy. It happens when an external force moves an object parallel to the force.

Image: Work is done when a force moves an object a distance.

• General Equation: $W = Fd\cos\theta$
  • F = Force applied.
  • d = Distance over which the force is applied.
  • $\theta$ = Angle between force and distance vectors.

Image: Diagram showing force, distance, and angle for work calculation.

• Graphical Approach: Work can be found from the area under a Force vs. displacement graph. Usually, this is simple geometric shapes like rectangles and triangles. (Calculus comes in handy in AP C: Mech for more complex shapes).

Image: A force vs. displacement graph; work is the area under the curve.

• Sign Conventions:
  • Positive Work: Work done on the system increases its total energy.
  • Negative Work: Work done by the system decreases its total energy.

#Power: The Rate of Doing Work ⚡

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• Definition: Power is the rate at which work is done or energy is transferred.
• Equation: $P = \frac{E}{t}$ (where E is the change in energy/Work, and t is the time taken).
• Units: Measured in watts (W) or joules per second (J/s).
• Scalar Quantity: Power has magnitude but no direction.
• Sign: Power can be positive or negative, depending on the direction of energy transfer.

#Final Exam Focus 🎯

#Key Areas

• Conservation of Energy: Understand how energy transforms and is conserved in different scenarios.
• Work-Energy Theorem: Relate work done to changes in kinetic energy.
• Power: Calculate the rate of energy transfer.
• System Definition: Clearly define your system before solving problems.

#Common Question Types

• Multiple Choice: Conceptual questions about energy conservation, work, and power.
• Free Response: Problems involving calculations of work, energy changes, and power in various situations (e.g., inclined planes, springs).

#Last-Minute Tips

• Time Management: Don't spend too long on one question. Move on and come back if you have time.
• Common Pitfalls:
  • Forgetting to consider the angle in work calculations.
  • Confusing work done on the system with work done by the system.
  • Not defining the system clearly.
• Strategies:
  • Draw free-body diagrams to visualize forces and motion.
  • Write down knowns and unknowns before starting calculations.
  • Use units to check your work.

#Practice Questions 📝

Practice Question

#Multiple Choice Questions

1. A block of mass m is pulled up a frictionless incline at a constant speed by a force F parallel to the incline. The block moves a distance d along the incline. What is the work done by the force F? (A) mgd (B) Fd (C) mgd sinθ (D) mgd cosθ

2. A 2 kg ball is dropped from a height of 10 m. Ignoring air resistance, what is the kinetic energy of the ball just before it hits the ground? (Assume g = 10 m/s²) (A) 20 J (B) 100 J (C) 200 J (D) 400 J

3. A 1000 kg car accelerates from rest to 20 m/s in 5 seconds. What is the average power delivered by the engine? (A) 20,000 W (B) 40,000 W (C) 80,000 W (D) 160,000 W

#Free Response Question

A 0.5 kg block is released from rest at the top of a frictionless ramp that is 2 meters high. At the bottom of the ramp, it slides across a rough horizontal surface with a coefficient of kinetic friction of 0.2 for a distance of 3 meters before coming to rest. (Assume g = 10 m/s²)

(a) Calculate the potential energy of the block at the top of the ramp.

(b) Calculate the kinetic energy of the block at the bottom of the ramp.

(c) Calculate the work done by friction as the block slides across the horizontal surface.

(d) Calculate the force of friction acting on the block as it slides across the horizontal surface.

(e) Calculate the acceleration of the block as it slides across the horizontal surface.

Scoring Breakdown:

(a) 2 points - 1 point for using the correct formula for potential energy (PE = mgh) - 1 point for correct calculation (PE = 0.5 kg * 10 m/s² * 2 m = 10 J)

(b) 2 points - 1 point for stating that kinetic energy at the bottom equals the potential energy at the top (conservation of energy) - 1 point for correct value (KE = 10 J)

(c) 3 points - 1 point for using the correct formula for work done by friction (W = -fd) - 1 point for finding the friction force (f = μmg = 0.2 * 0.5 kg * 10 m/s² = 1 N) - 1 point for correct calculation (W = -1 N * 3 m = -3 J)

(d) 2 points - 1 point for using the correct formula for friction force (f = μmg) - 1 point for correct calculation (f = 0.2 * 0.5 kg * 10 m/s² = 1 N)

(e) 2 points - 1 point for using Newton's second law to find the acceleration (F = ma) - 1 point for correct calculation (a = f/m = 1 N / 0.5 kg = 2 m/s²)

You've got this! You're now armed with the knowledge and strategies to tackle the AP Physics 1 exam. Go get 'em! 💪