#AP Physics 2: Electric Forces - The Ultimate Study Guide ⚡

Hey there, future AP Physics 2 master! Let's get you prepped and confident for the exam. This guide is designed to be your go-to resource, especially for that last-minute review. We'll break down the concepts, make connections, and get you ready to ace it!

#1. Forces and Newton's Laws: A Quick Review

Let's start with the basics. AP loves to test your understanding of forces, so let's nail down Newton's Laws. Remember, forces are interactions that can cause a change in an object's motion.

#1.1 Newton's First Law: The Law of Inertia

• What it says: An object at rest stays at rest, and an object in motion stays in motion with the same velocity unless acted upon by a net external force. ➡️
• Key Idea: Inertia is the tendency of an object to resist changes in its state of motion.
• Inertial Mass: Mass that is accelerated (mass in motion).
• Gravitational Mass: Mass based on an object’s weight (mass being pulled by the gravitational field).

#1.2 Newton's Second Law: F = ma

• What it says: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. 💡
• Formula: $F = ma$ where:
  • $F$ is the net force (in Newtons, N)
  • $m$ is the mass (in kilograms, kg)
  • $a$ is the acceleration (in meters per second squared, m/s²)

#1.3 Newton's Third Law: Action-Reaction

• What it says: For every action, there is an equal and opposite reaction. 🔄
• Key Idea: Forces always come in pairs. If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.
• Action-Reaction Pair: These forces act on different objects. (e.g., a book on a table: book pushes down, table pushes up).

Caption: Electric force at work! Paper sticking to comb!

#2. Introduction to Electric Forces

Now, let's dive into the world of electric forces. It's like gravity, but with charges! ⚛️

#2.1 Historical Context

• Ancient Observations: The Greeks noticed that amber, when rubbed, could attract small objects (triboelectricity).
• Key Players:
  • Benjamin Franklin: Explored electric charge, lightning, and grounding.
  • Charles-Augustin de Coulomb: Developed Coulomb's Law, quantifying the electric force.

#2.2 Coulomb's Law

• The Big Idea: The electric force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. 💡
• Formula: $F = k \frac{|q_1 q_2|}{r^2}$ where:
  • $F$ is the electric force (in Newtons, N)
  • $k$ is Coulomb's constant ($8.99 \times 10^9 N m^2/C^2$)
  • $q_1$ and $q_2$ are the magnitudes of the charges (in Coulombs, C)
  • $r$ is the distance between the charges (in meters, m)

#3. Connecting Concepts

AP loves to mix concepts, so let's see how these ideas relate:

• Forces & Motion: Newton's Laws still apply! Electric forces cause acceleration, just like any other force.
• Gravity vs. Electric Force: Both are inverse square laws, but gravity is always attractive, while electric force can be attractive or repulsive.
  • Gravity: $F = G \frac{m_1 m_2}{r^2}$
  • Electric Force: $F = k \frac{|q_1 q_2|}{r^2}$

#4. Example Problems

Let's put these concepts into action with some example problems.

#Example Problem #1 (Newton's Laws)

Problem: A car is driving down the road at a constant speed of 50 km/h. The driver suddenly slams on the brakes, causing the car to come to a stop in 5 seconds. What is the acceleration of the car during this time?

Solution:

1. Convert units: 50 km/h = 13.89 m/s
2. Use kinematic equation: $v_f = v_i + at$
3. Solve for a: $0 = 13.89 + a(5)$, so $a = -2.78 m/s^2$

#Example Problem #2 (Newton's Laws)

Problem: A ball is thrown straight up into the air with an initial velocity of 20 m/s. How high does the ball go before it reaches its maximum height and begins to fall back down?

Solution:

1. Use kinematic equation: $v_f^2 = v_i^2 + 2as$
2. Final velocity at max height: $v_f = 0$
3. Solve for s: $0 = 20^2 + 2(-9.8)s$, so $s = 20.4 m$

#5. Final Exam Focus

Okay, it's crunch time! Here's what to focus on for the exam:

**High-Value Topics:**

-   Newton's Laws of Motion (especially the 2nd law)
-   Coulomb's Law and its applications
-   Connections between forces, motion, and acceleration

• Common Question Types:
  • Calculating electric forces between point charges
  • Analyzing motion under the influence of electric forces
  • Conceptual questions about action-reaction pairs
• Last-Minute Tips:
  • Time Management: Don't spend too long on any one question. If you're stuck, move on and come back later.
  • Common Pitfalls: Pay attention to units, vector directions, and the difference between mass and charge.
  • Strategies: Draw free-body diagrams, write down knowns and unknowns, and use the formulas wisely. 💡

#6. Practice Questions

Let's test your knowledge with some practice questions!

Practice Question

Multiple Choice Questions

1. Two point charges, +Q and -Q, are separated by a distance r. If the distance between the charges is doubled, the electric force between them will be: (A) doubled (B) halved (C) quadrupled (D) quartered

2. A positively charged particle is placed in a uniform electric field. The direction of the electric force on the particle is: (A) in the direction of the electric field (B) opposite to the direction of the electric field (C) perpendicular to the direction of the electric field (D) zero

3. A 2 kg object is accelerated from rest to 10 m/s in 2 seconds. What is the net force on the object? (A) 5 N (B) 10 N (C) 20 N (D) 100 N

Free Response Question

Two small spheres, each with a mass of 0.002 kg, are suspended from the same point by threads of length 0.5 m. The spheres are given equal positive charges, and they come to equilibrium when each thread makes an angle of 10 degrees with the vertical.

(a) Draw a free-body diagram for one of the spheres, showing all the forces acting on it. (b) Calculate the magnitude of the electric force acting on each sphere. (c) Calculate the magnitude of the charge on each sphere.

Scoring Rubric:

(a) Free-body diagram (3 points) - 1 point for tension force - 1 point for gravitational force - 1 point for electric force

(b) Calculating electric force (4 points) - 1 point for resolving tension into components - 1 point for setting up the equilibrium condition in the horizontal direction - 1 point for calculating the tension force - 1 point for calculating the electric force

(c) Calculating charge (3 points) - 1 point for using Coulomb's Law - 1 point for calculating the distance between the charges - 1 point for calculating the charge

Good luck on your exam! You've got this! 💪