AP Physics 1: Systems and Their Properties - The Night Before 🚀

Hey! Let's get you prepped for tomorrow. This guide is designed to be your quick, high-impact review. We'll focus on what matters most, keep it visual, and make sure you're feeling confident. Let's do this!

1. Defining a System

What Exactly is a System? 🤔

In physics, a system is simply a collection of objects we're choosing to analyze together. Think of it as your 'focus group' for a problem. It could be anything from a single block to a whole pulley setup. The key thing is that we treat the objects within the system as having no internal structure for the purpose of our analysis.

Boundaries: Systems have boundaries (physical or conceptual) that separate the 'inside' from the 'outside'.
Exchange: Systems can exchange energy, matter, or both with their surroundings.
Types:
- Closed System: No exchange of matter or energy with surroundings. 🔒
- Open System: Exchanges matter and/or energy with surroundings. 🔄
Equilibrium:
- Equilibrium: No change over time.
- Dynamic Equilibrium: Changes occur, but the system returns to equilibrium. ⚖️

Fundamental Particles ⚛️

Subatomic Particles: Found within atoms (protons, neutrons, electrons).
Quarks: The smallest units of matter that make up protons and neutrons. Held together by the strong force.
- Up Quarks: Positive charge.
- Down Quarks: Negative charge.
- Protons: Two up quarks and one down quark (positive charge).
- Neutrons: Combination of up and down quarks (neutral charge).

Key Concept

Remember: When analyzing a system, we focus on external forces and how they affect the system's overall motion. Internal forces (like tension within the system) are often ignored when analyzing the system as a whole.

System Approach to Newton's Second Law

When using Newton's Second Law (ΣF = ma), we consider the total mass of the system and the net external force acting on it. This helps us find the overall acceleration of the system. 💡

$\Sigma F = ma$

Memory Aid

Remember F = ma: Force equals mass times acceleration. This is the key to understanding how systems move! 🚀

Example Problem #1: Box on an Incline

Let's break this down:

System: Box, pulley, rope, and incline.
External Forces: Gravity on the box and the normal force from the incline.
Acceleration: Use ΣF = ma, where F is the net force (gravity minus normal force) on the box.
Normal Force: If the incline angle is 30 degrees, N = mg*cos(30). For a 10kg box, N = 49 Newtons.

Example Problem #2: Closed System

A closed system is isolated, with no exchange of matter or energy. A sealed container of gas is a perfect example. Gas molecules interact internally, but nothing enters or leaves the container.

Practice Question

{
"mcqs": [
    {
        "question": "A system consists of two blocks connected by a string over a pulley. Block A has a mass of 2 kg and Block B has a mass of 3 kg. If the system is released from rest, what is the magnitude of the acceleration of the system? (Assume no friction and a massless pulley)",
        "options": ["1 m/s²", "2 m/s²", "3 m/s²", "4 m/s²"],
        "answer": "2 m/s²"
    },
    {
        "question": "Which of the following best describes a closed system?",
        "options": ["A system that exchanges energy with its surroundings but not matter", "A system that exchanges matter with its surroundings but not energy", "A system that exchanges both matter and energy with its surroundings", "A system that does not exchange matter or energy with its surroundings"],
        "answer": "A system that does not exchange matter or energy with its surroundings"
    },
  {
        "question": "A box of mass m is placed on a frictionless incline at an angle θ. What is the magnitude of the normal force acting on the box?",
        "options": ["mg", "mg sin θ", "mg cos θ", "mg tan θ"],
        "answer": "mg cos θ"
    }
],
"frq": {
        "question": "Two blocks, A and B, with masses m_A = 2.0 kg and m_B = 3.0 kg, respectively, are connected by a light string that passes over a frictionless pulley. Block A is on a horizontal surface with a coefficient of kinetic friction μ_k = 0.20, while Block B hangs vertically. The system is released from rest.\n(a) Draw free-body diagrams for each block, showing all forces acting on them.\n(b) Calculate the magnitude of the acceleration of the system.\n(c) Calculate the tension in the string.\n(d) If the system starts from rest, how far will Block B have descended after 1.5 seconds?",
        "scoring_breakdown": {
          "a": "2 points: 1 point for each correct free-body diagram (showing forces like tension, weight, friction, and normal force)",
          "b": "3 points: 1 point for setting up Newton's second law equations for each block, 1 point for correctly solving for acceleration, 1 point for correct numerical value (approx. 4.9 m/s^2)",
          "c": "2 points: 1 point for using Newton's second law to find tension, 1 point for correct numerical value (approx. 14.7 N)",
          "d": "2 points: 1 point for using kinematic equation to find distance, 1 point for correct numerical value (approx. 5.5 m)"
        }
    }
}

2. Properties of a System

System Properties and External Forces

Remember, a system's properties are determined by its internal structure. However, when modeling a system, we often treat it as a single object, especially when the internal details aren't crucial. 🧐

External forces are what cause a system to accelerate, as stated by Newton’s First Law. An object at rest stays at rest, and an object in motion stays in motion unless acted upon by an external force. ➡️
Defining Boundaries is essential to understand which forces are affecting the system.

Interactions Within a System

Objects within a system accelerate together with the same magnitude. 🤝
Internal interactions (like tension) have minimal or no change and can often be ignored when analyzing the entire system. 🧵

markdown-image

Image courtesy of physics.stackexchange.com

Quick Fact

In a system, objects move together with the same acceleration. Internal forces, like tension, don't affect the system's overall motion.

Example Problem: Block on a Table

If you apply a force to a block of wood resting on a table:

Force Magnitude: A larger force means greater acceleration. 💪
Mass: A heavier block needs more force to accelerate the same amount. 🏋️
Force Direction: Force in the direction of motion increases velocity; force opposite to motion decreases velocity. ⬆️⬇️

Common Mistake

Don't confuse internal and external forces! Only external forces affect the overall motion of a system.

Exam Tip

When solving problems, always start by clearly defining your system and identifying the external forces acting on it. This will make applying Newton's laws much easier.

Practice Question

{
  "mcqs": [
    {
      "question": "A block is pushed across a horizontal surface with a constant force. The block is part of a system. Which of the following forces is considered an external force acting on the system?",
      "options": ["The normal force from the surface", "The gravitational force on the block", "The frictional force between the block and the surface", "The internal forces within the block"],
      "answer": "The gravitational force on the block"
    },
    {
       "question": "Two blocks are connected by a string and pulled across a frictionless surface. If the tension in the string is an internal force, what does this imply about the system?",
       "options": ["The blocks are accelerating at different rates", "The blocks are not moving", "The blocks are moving with the same acceleration", "The blocks are moving at constant velocities"],
       "answer": "The blocks are moving with the same acceleration"
    },
   {
      "question": "What is the primary factor that determines the acceleration of a system?",
      "options": ["The internal forces within the system", "The total mass of the system", "The net external force acting on the system", "The individual masses of the objects within the system"],
      "answer": "The net external force acting on the system"
    }
  ],
  "frq": {
    "question": "A 5.0 kg block is placed on a frictionless horizontal surface and connected to a 2.0 kg block by a string that passes over a frictionless pulley. The 2.0 kg block hangs vertically. The system is released from rest.\n(a) Draw free-body diagrams for each block, showing all forces acting on them.\n(b) Calculate the magnitude of the acceleration of the system.\n(c) Calculate the tension in the string.\n(d) If the system starts from rest, how fast will the 2.0 kg block be moving after it has descended 1.0 meter?",
    "scoring_breakdown": {
      "a": "2 points: 1 point for each correct free-body diagram",
      "b": "3 points: 1 point for setting up Newton's second law equations, 1 point for correct solving for acceleration, 1 point for correct numerical value (approx. 2.8 m/s^2)",
      "c": "2 points: 1 point for using Newton's second law to find tension, 1 point for correct numerical value (approx. 14 N)",
      "d": "2 points: 1 point for using kinematic equation to find final velocity, 1 point for correct numerical value (approx. 2.4 m/s)"
    }
  }
}

Final Exam Focus 🎯

High-Priority Topics

Newton's Laws: Especially the Second Law (ΣF = ma) and how it applies to systems.
Defining Systems: Understanding what a system is and how to identify its boundaries.
External vs. Internal Forces: Knowing which forces affect the system's motion.
Closed vs. Open Systems: Understanding the difference and their implications.

Common Question Types

Multiple Choice: Conceptual questions about system definitions, forces, and types of systems.
Free Response: Problems involving multiple objects, pulleys, inclines, and applying Newton's laws to find acceleration and tension.

Last-Minute Tips

Time Management: Quickly identify the system and external forces before diving into calculations.
Common Pitfalls: Be careful not to include internal forces in your net force calculations. ⚠️
Strategies: Draw free-body diagrams for each object in the system. This will help you visualize the forces and apply Newton's laws correctly. ✍️

You've got this! Take a deep breath, trust your prep, and go ace that exam! 💪

Systems

Grace Lewis