AP Physics C: Mechanics - Newton's Third Law & Tension Review 🚀

Hey there! Let's get you prepped for the AP Physics C: Mechanics exam. This guide is designed to be your go-to resource for a quick, effective review, especially the night before the test. We'll break down Newton's Third Law and its applications, focusing on what matters most for the exam. Let's dive in!

Newton's Third Law: Action-Reaction Pairs

• What it is: For every action, there's an equal and opposite reaction. This means forces always come in pairs. 👯‍♀️
• Formula: $$\vec{F}_{A \text{ on } B} = -\vec{F}_{B \text{ on } A}$$
  • The negative sign indicates the forces act in opposite directions.
  • These forces act on different objects. This is super important!
• Example: When you push on a wall, the wall pushes back on you with the same amount of force, but in the opposite direction.

- Explains how forces work in pairs during interactions between objects. - Essential for understanding how things move, from rocket propulsion to everyday pushes and pulls. - Helps us understand why internal forces don't affect a system's center of mass motion, while external forces do.

Internal vs. External Forces

Internal Forces

• Definition: Forces between objects within a system. Think of the forces between molecules in a solid.
• Key Point: Internal forces do not affect the motion of the system's center of mass. They cancel each other out within the system.

External Forces

• Definition: Forces between an object in the system and something outside the system. Gravity pulling down on an object is a great example.
• Key Point: External forces do change the motion of the center of mass. The net external force determines the acceleration of the center of mass.

Tension in Strings and Cables

What is Tension?

• Definition: The pulling force transmitted through a string, cable, or similar object when it's pulled tight. 🪢
• Microscopic View: Tension is the result of microscopic forces between atoms within the string.
• Ideal String: An ideal string has negligible mass and doesn't stretch.

- **Negligible Mass:** Mass is so small compared to connected objects that we can ignore it. - **Inelastic:** Doesn't stretch when a force is applied. - **Flexible:** Can bend around objects like pulleys with negligible friction. - **Constant Tension:** Tension is the same at all points along an ideal string.

Tension Variations

• Real Strings: In real strings with mass, tension can vary along the length.
• Weight Effect: The string's weight is an external force that can cause tension to change.
• Tension Gradient: Tension is usually maximum at the top of a suspended string and decreases toward the bottom.

Ideal Pulleys

What are Ideal Pulleys?

• Definition: A simple machine that changes the direction of a tension force. 🧵
• Properties:
  • Negligible mass (no rotational inertia to worry about).
  • Rotates about an axle through its center of mass.
  • Negligible friction between the pulley and the axle.
• Key Function: Ideal pulleys do not change the magnitude of the tension force, only its direction.

How Pulleys Help

• Tension is Constant: The tension is the same on both sides of an ideal pulley.
• Applications: Used for lifting loads, applying forces, and transmitting power.
• Block and Tackle: Multiple pulleys can be used to multiply the applied force.

Final Exam Focus

High-Priority Topics

• Newton's Third Law: Understand action-reaction pairs and how they apply in different scenarios.
• Internal vs. External Forces: Know how these affect the motion of a system's center of mass.
• Tension: Be comfortable analyzing tension in ideal strings and pulleys, and know when to consider mass in non-ideal situations.

Common Question Types

• Multiple Choice: Conceptual questions about action-reaction pairs, identifying forces, and understanding ideal string/pulley assumptions.
• Free Response: Problems involving systems of objects connected by strings and pulleys, requiring you to draw free-body diagrams and apply Newton's laws.

Last-Minute Tips

• Time Management: Quickly identify the key concepts in each question. Don't get bogged down on one problem. If you're stuck, move on and come back to it later.
• Free-Body Diagrams: Always draw free-body diagrams to visualize forces acting on objects. This is crucial for setting up equations correctly.
• Units: Pay close attention to units and make sure they are consistent throughout your calculations.
• Assumptions: Clearly state any assumptions you make, such as using an ideal string or pulley. This shows the graders you understand the concepts.
• Practice: Do a few practice problems to get comfortable with the types of questions you'll see on the exam.

Practice Questions

Practice Question

Multiple Choice Questions

1. Two blocks are connected by a string over an ideal pulley. Block A has a mass of 2 kg and block B has a mass of 4 kg. If the system is released from rest, what is the magnitude of the tension in the string? (Assume g = 10 m/s²) (A) 13.3 N (B) 20 N (C) 26.7 N (D) 40 N

2. A person pushes a box across a horizontal floor at a constant speed. Which of the following statements is true regarding the forces acting on the box? (A) The force applied by the person is greater than the frictional force. (B) The force applied by the person is equal to the frictional force. (C) The force applied by the person is less than the frictional force. (D) The normal force is greater than the weight of the box.

3. A ball is thrown vertically upward. At the highest point of its trajectory, which of the following is true? (A) The velocity and acceleration are both zero. (B) The velocity is zero, but the acceleration is not zero. (C) The velocity is not zero, but the acceleration is zero. (D) Neither the velocity nor the acceleration is zero.

Free Response Question

Two blocks, of mass m1 = 2.0 kg and m2 = 4.0 kg, are connected by a light string that passes over a frictionless pulley, as shown in the figure below. The table is frictionless. The system is released from rest.

(a) Draw free-body diagrams for each block, showing all the forces acting on each.

(b) Derive an expression for the acceleration of the blocks in terms of m1, m2, and g.

(c) Calculate the acceleration of the blocks, assuming g = 9.8 m/s².

(d) Calculate the tension in the string.

Scoring Rubric

(a) Free-Body Diagrams (4 points) - 2 points for correctly drawing and labeling all the forces on m1 (T and N, and w1) - 2 points for correctly drawing and labeling all the forces on m2 (T and w2)

(b) Derivation of Acceleration (4 points) - 1 point for applying Newton's second law to m1: T = m1a - 1 point for applying Newton's second law to m2: m2g - T = m2a - 1 point for solving for acceleration: a = (m2g)/(m1+m2) - 1 point for correct final expression

(c) Calculation of Acceleration (1 point) - 1 point for correct numerical answer: a = 6.53 m/s²

(d) Calculation of Tension (2 points) - 1 point for using the correct formula T = m1a - 1 point for correct numerical answer: T = 13.06 N

Good luck, you've got this! 💪