AP Physics 1: Linear Motion & Forces Study Guide 🚀

Hey there, future physics pro! Let's get you prepped for the AP Physics 1 exam with this supercharged study guide. We'll break down linear motion, forces, and those tricky tension/apparent weight problems. Let's do this!

1. Kinematics: Describing Motion 🏃

1.1 Center of Mass Motion

• Remember those kinematic equations? They're your best friends for solving motion problems. Here they are, ready for action:

• Δx: Displacement (m)

• Vf: Final velocity (m/s)

• Vo: Initial velocity (m/s)

• t: Time (s)

• a: Acceleration (m/s²)

1.2 Acceleration: The Rate of Change ⏱️

• Acceleration is the rate of change of velocity, and velocity is the rate of change of position. Here are the key formulas:

$$a = \frac{\Delta v}{\Delta t}$$

$$v = \frac{\Delta x}{\Delta t}$$

$$a = \frac{v_f - v_i}{t}$$

2. Forces: Newton's Laws in Action 💪

2.1 Newton's Second Law: F = ma

• This is the heart of dynamics! Newton's Second Law (F = ma) relates force, mass, and acceleration.

• Steps for Solving F=ma Problems:

  1. Draw a Free-Body Diagram (FBD): Isolate the object and draw all forces acting on it.
  2. Identify Forces: Include all forces, even the small ones.
  3. Direction: Determine if forces are positive or negative based on your chosen coordinate system.
  4. Calculate Magnitudes: Use physics laws to find the size of each force.
  5. Apply F = ma: Solve for unknowns like acceleration or force.
  6. Check Units: Make sure your answer makes sense dimensionally.
  7. Break It Down: If stuck, divide the problem into smaller parts.

2.2 Angular Tension: Forces at an Angle 📐

• Steps for Angular Tension:

  1. FBD: Draw a clear free-body diagram.
  2. Identify Forces: Include all tension forces.
  3. Direction of Tension: Tension acts along the string, but might have x and y components.
  4. Calculate Magnitudes: Use trigonometry and Newton's laws.
  5. Solve for Unknowns: Find angles, tensions, or acceleration.
  6. Check Solution: Make sure your answer is reasonable.

• Here's a visual to help:

• And another one:

• 🎥 Video: Angular Tension by Organic Chemistry Tutor

2.3 Apparent Weight: Feeling Heavier or Lighter? ⚖️

• Apparent weight changes when the normal force (Fn) doesn't equal the gravitational force (mg).

• Here's a visual:

• Elevator Scenarios:

  • Upward Acceleration: Fn > mg (feel heavier)
  • Downward Acceleration: Fn < mg (feel lighter)
  • No Acceleration: Fn = mg (feel normal)
  • Free Fall: Fn = 0 (feel weightless)

• Steps for Apparent Weight Problems:

  1. FBD: Draw a free-body diagram.
  2. Identify Forces: Gravity (weight) and normal force.
  3. Direction: Weight is always down, normal force is perpendicular to the surface.
  4. Calculate Magnitudes: Use Newton's laws.
  5. Solve for Unknowns: Find acceleration, mass, or normal force.

3. Final Exam Focus 🎯

• High-Priority Topics: Kinematics, Newton's Second Law, Angular Tension, and Apparent Weight are all very important. Make sure you understand the concepts and know how to apply the formulas.

• Common Question Types:

  • Multiple Choice: Conceptual questions, calculations, and graph analysis.
  • Free Response: Multi-step problems requiring detailed solutions and explanations.

• Last-Minute Tips:
  • Review your FBD skills.
  • Practice a few problems from each topic.
  • Take a deep breath – you've got this!

4. Practice Questions 💪

Practice Question

Multiple Choice Questions

1. A block of mass m is pulled across a horizontal surface at a constant velocity by a force F that is applied at an angle θ above the horizontal. The coefficient of kinetic friction between the block and the surface is μ. What is the magnitude of the frictional force acting on the block? (A) F cos θ (B) F sin θ (C) μ(mg - F sin θ) (D) μ(mg + F sin θ)

2. A 2 kg object is subjected to three forces, F1, F2, and F3. F1 = 10 N at 0 degrees, F2 = 10 N at 120 degrees, and F3 = 10 N at 240 degrees. What is the magnitude of the net force acting on the object? (A) 0 N (B) 10 N (C) 20 N (D) 30 N

3. An elevator is moving upwards and slowing down. Which of the following statements is correct about the apparent weight of a person inside the elevator? (A) The apparent weight is greater than the true weight. (B) The apparent weight is less than the true weight. (C) The apparent weight is equal to the true weight. (D) The apparent weight is zero.

Free Response Question

A 5 kg block is placed on a 30-degree incline. The coefficient of kinetic friction between the block and the incline is 0.2. The block is released from rest.

(a) Draw a free-body diagram of the block on the incline. (2 points)

(b) Calculate the component of the gravitational force parallel to the incline. (2 points)

(c) Calculate the normal force acting on the block. (2 points)

(d) Calculate the frictional force acting on the block. (2 points)

(e) Calculate the acceleration of the block down the incline. (2 points)

Scoring Breakdown:

(a) Free-Body Diagram (2 points)

• 1 point for correctly drawing the weight (mg) vector pointing downwards.
• 1 point for correctly drawing the normal force (N) vector perpendicular to the incline and the friction force (f) vector parallel to the incline, pointing up the incline.

(b) Gravitational Force Parallel to the Incline (2 points)

• 1 point for using the correct formula: $mg\sin(\theta)$
• 1 point for the correct answer: 5 \times 9.8 \times \sin(30) = 24.5 N

(c) Normal Force (2 points)

• 1 point for using the correct formula: $mg\cos(\theta)$
• 1 point for the correct answer: 5 \times 9.8 \times \cos(30) = 42.4 N

(d) Frictional Force (2 points)

• 1 point for using the correct formula: $f = \mu N$
• 1 point for the correct answer: 0.2 \times 42.4 = 8.48 N

(e) Acceleration (2 points)

• 1 point for using Newton's second law: $F_{net} = ma$
• 1 point for the correct answer: 24.5 - 8.48 = 5a, so $a = 3.2 m/s^2$