AP Physics 1: Electricity & Forces - Night Before Cram

Hey! Let's get you prepped for the AP Physics 1 exam. This guide is designed to be your quick, high-impact review, focusing on key concepts and strategies. Remember, you've got this! 💪

⚡️ Electric Charge Fundamentals

What is Charge?

• Charge is a fundamental property of matter, like mass. It comes in two types: positive (carried by protons) and negative (carried by electrons).
• Atoms are neutral when they have an equal number of protons and electrons.

How Objects Become Charged

• Negative Charge: An atom gains extra electrons.
• Positive Charge: An atom loses electrons, resulting in more protons than electrons.

- **Dipoles:** Separation of charge within an object, creating partial positive and negative ends, even if the overall charge is neutral.

Measuring Charge

• Charge is measured in coulombs (C).
• The charge of an object is always a multiple of the elementary charge (charge of one electron).
• Elementary charge (e) = 1.602 x 10^-19 C.

- "Point charge" refers to a charged particle where charge is concentrated at a single point.

🧲 Electric Force: Coulomb's Law

Coulomb's Law

• Describes the force between two charged particles. The force is attractive for unlike charges and repulsive for like charges.

• The magnitude of the electric force is given by:

  $$F = k \frac{|q_1 q_2|}{r^2}$$

  Where:

  • F is the electric force.
  • k is Coulomb's constant (8.99 x 10^9 Nm²/C²).
  • q1 and q2 are the magnitudes of the two charges.
  • r is the distance between the charges.

Coulomb’s Law Example

• Problem: Atom 1 has +1e charge, Atom 2 has -1e charge, separated by 0.5m.

• Solution:

  $$F = (8.99 \times 10^9) \frac{|(1.602 \times 10^{-19})(-1.602 \times 10^{-19})|}{(0.5)^2} = 9.23 \times 10^{-28} N$$

• The force is attractive. Atom 1 experiences a force towards Atom 2, and vice versa.

Superposition Principle

• The net force on a charge due to multiple other charges is the vector sum of the individual forces.
• Treat forces as vectors and add them accordingly.

Net Forces at an Angle

• If forces act at an angle, resolve them into x and y components.

• Find the net force in the x-direction (Fx_net) and y-direction (Fy_net).

• Use the Pythagorean theorem to find the magnitude of the net force:

  $$F_{net} = \sqrt{F_{x_{net}}^2 + F_{y_{net}}^2}$$

• Use trigonometry to find the direction of the net force.

📝 Practice Problems

Here are some practice problems to solidify your understanding. Remember to use the given constants:

• e = 1.602 x 10^-19 C
• k = 8.99 x 10^9 Nm²/C²

1. Charge Calculation: 4.16 x 10^19 electrons are moved through a wire. How many Coulombs of charge were moved?
2. Coulomb's Law: What is the attractive force between a sock (-2.00 C) and a carpet (3.00 C) 0.500 m apart?
3. Net Force: Find the net force on q3. q1=-2.00 x 10^-3 C at (0,-3), q2=-1.00 x 10^-3 C at (3,0), and q3=+3.00 x 10^-3 C at (0,2).

🎯 What to Know About Electric Force

• Electric force is a force exerted by charged objects on each other.
• It's a vector, meaning it has magnitude and direction.
• Use Coulomb's Law to calculate the magnitude of the force: $$F = k \frac{|q_1 q_2|}{r^2}$$
• The net electric force is the vector sum of all electric forces acting on a charge.

🚀 Final Exam Focus

• High-Value Topics: Coulomb's Law, Superposition Principle, Net Force Calculations (especially with angles).
• Common Question Types:
  • Calculating electric force between two charges.
  • Finding the net force on a charge due to multiple charges.
  • Problems involving forces at angles and vector addition.

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⏱️ Last-Minute Tips

• Time Management: Quickly identify the core concept in each question. Don't get bogged down on one problem.
• Common Pitfalls:
  • Forgetting to square the distance in Coulomb's Law.
  • Not treating forces as vectors (especially when adding multiple forces).
  • Incorrectly resolving forces into components.
• Strategies:
  • Start with a free-body diagram.
  • Write down the relevant formulas.
  • Double-check your calculations and units.

❓ 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 magnitude of the electric force between them will be: (A) Four times as large (B) Twice as large (C) One-half as large (D) One-fourth as large

2. A small, positively charged sphere is placed near a larger, negatively charged sphere. Which of the following statements is true about the forces the spheres exert on each other? (A) The positive sphere exerts a larger force on the negative sphere than the negative sphere exerts on the positive sphere. (B) The negative sphere exerts a larger force on the positive sphere than the positive sphere exerts on the negative sphere. (C) The spheres exert equal forces on each other. (D) The forces are zero since they are not touching.

3. A charge of +2q is placed at the origin, and a charge of -q is placed at x = a. At what point on the x-axis is the net electric force on a third charge equal to zero? (A) x = a/3 (B) x = 2a/3 (C) x = 2a (D) There is no such point

Free Response Question

Two small spheres, each with a mass of 0.002 kg, are suspended from the same point by insulating threads of length 0.5 m, as shown in the diagram. Each sphere carries a positive charge, q. The spheres repel each other and come to equilibrium when the angle θ between each thread and the vertical is 30°. Assume that the charges are point charges. (k = 8.99 x 10^9 Nm²/C²)

(a) Draw a free-body diagram for one of the spheres, showing all the forces acting on it.

(b) Determine the magnitude of the electric force acting on one of the spheres.

(c) Determine the charge q on each sphere.

(d) If the length of the threads is doubled, what will be the new angle between the thread and the vertical at equilibrium? (Justify your answer)

Scoring Guidelines for FRQ

(a) Free-body diagram (3 points)

• 1 point for showing the tension force (T) acting along the string
• 1 point for showing the gravitational force (mg) acting downwards
• 1 point for showing the electric force (Fe) acting horizontally away from the other charge

(b) Electric force calculation (3 points)

• 1 point for recognizing that the system is in equilibrium
• 1 point for setting up the correct trigonometric relationship: tan(30) = Fe / mg
• 1 point for correct calculation: Fe = mg * tan(30) = 0.002 * 9.8 * tan(30) = 0.0113 N

(c) Charge calculation (3 points)

• 1 point for recognizing the distance between charges: r = 2 * 0.5 * sin(30) = 0.5 m
• 1 point for using Coulomb's Law: Fe = k * q^2 / r^2
• 1 point for correct calculation: q = sqrt(Fe * r^2 / k) = sqrt(0.0113 * 0.5^2 / 8.99e9) = 1.77e-7 C

(d) New angle (3 points)

• 1 point for recognizing that the electric force will decrease due to increased distance
• 1 point for stating that the angle will decrease
• 1 point for justification: The electric force decreases, the tension force will have a smaller horizontal component, and the angle will be smaller

You've got this! Go ace that exam! 🚀