#AP Physics 2: Contact Forces Study Guide

Hey there, future AP Physics 2 master! Let's dive into contact forces – the ones that happen when things touch. This guide is your secret weapon for acing the exam. We'll make sure you're not just memorizing, but truly understanding, so you can tackle any problem with confidence. Let's get started!

#1. Introduction to Contact Forces

Contact forces are all about interactions at the atomic level. They arise from the electromagnetic forces between atoms when objects touch. Think of it like tiny springs pushing and pulling at the contact points. These forces are fundamental to understanding how objects interact in our world. Let's break down the key players:

#1.1 Types of Contact Forces

• Tension: 🔗 The force exerted by a rope, string, or cable when it's pulled taut. It always acts along the direction of the rope.
• Friction: 🧱 The force that opposes motion between two surfaces in contact. It can be static (preventing motion) or kinetic (opposing sliding motion).
• Normal: ⬆️ The force exerted by a surface on an object, acting perpendicular to the surface. It's what keeps objects from falling through surfaces.
• Spring: ➿ The force exerted by a spring when it's stretched or compressed. It always acts to restore the spring to its equilibrium length. (Review from Physics 1!)
• Buoyant: 🌊 The upward force exerted by a fluid on an object that's submerged or floating. (Physics 2 focus!)

#1.2 Visualizing Contact Forces

When drawing Free Body Diagrams (FBDs), remember:

• Tension: Draw the arrow in the direction of the rope or string.
• Friction: Draw the arrow opposite to the direction of motion (or intended motion).
• Normal: Draw the arrow perpendicular to the surface.
• Spring: Draw the arrow opposing the direction of the stretch or compression.

#2. Key Concepts from Physics 1

Let's quickly revisit some essential concepts from Physics 1 that are super relevant here:

#2.1 Hooke's Law

Hooke's Law describes the behavior of springs:

$$F = -kx$$

Where:

• $F$ is the spring force
• $k$ is the spring constant (in N/m)
• $x$ is the displacement from the equilibrium position

#2.2 Friction

Friction opposes motion and is given by:

$$F_f = \mu N$$

Where:

• $F_f$ is the force of friction
• $\mu$ is the coefficient of friction (static or kinetic)
• $N$ is the normal force

#3. Buoyancy: A Physics 2 Essential

Buoyancy is a big deal in Physics 2. It's the upward force exerted by a fluid on an object. Here's the breakdown:

#3.1 Archimedes' Principle

The buoyant force is equal to the weight of the fluid displaced by the object:

$$F_B = \rho_{fluid} V_{displaced} g$$

Where:

• $F_B$ is the buoyant force
• $\rho_{fluid}$ is the density of the fluid
• $V_{displaced}$ is the volume of the fluid displaced
• $g$ is the acceleration due to gravity

#3.2 Floating vs. Sinking

• If an object's density is less than the fluid's density, it floats.
• If an object's density is greater than the fluid's density, it sinks.

#4. Conservative vs. Non-Conservative Forces

Contact forces can be categorized as either conservative or non-conservative:

• Conservative Forces: These forces (like tension and normal force) do not convert mechanical energy into other forms. They store energy as potential energy that can be recovered.
• Non-Conservative Forces: These forces (like friction and air resistance) convert mechanical energy into other forms like heat. Energy is not conserved in systems with non-conservative forces.

Understanding the difference between conservative and non-conservative forces is crucial for energy conservation problems. Remember, friction always dissipates energy!

#5. Practice Problems

Let's solidify your understanding with some examples:

#5.1 Example Problem #1: Friction

Problem: A 20 kg box sits on a horizontal surface. A 60 N horizontal force is applied. Calculate the friction force.

Solution:

1. The normal force equals the weight of the box: $N = mg = 20 \text{ kg} \times 9.8 \text{ m/s}^2 = 196 \text{ N}$.
2. Since the applied force (60 N) is not enough to overcome static friction, the box doesn't move.
3. The static friction force is equal to the applied force: $F_f = 60 \text{ N}$.

#5.2 Example Problem #2: Tension

Problem: A 10 kg mass hangs from a rope with 200 N tension. Calculate the weight of the pulley (assuming the rope is massless and the pulley is frictionless).

Solution:

1. The tension in the rope is equal to the weight it supports. Since the tension is 200N, the weight of the mass attached to the rope is 200 N.
2. The weight of the mass is $W = mg$, so the mass is $m = W/g = 200 \text{ N} / 9.8 \text{ m/s}^2 = 20.4 \text{ kg}$.

#5.3 Example Problem #3: Buoyancy

Problem: A 0.02 m³ wooden block (density 600 kg/m³) is placed in water (density 1000 kg/m³). Calculate the buoyant force.

Solution:

1. The buoyant force is equal to the weight of the water displaced.
2. The volume of displaced water is equal to the volume of the block: $V_{displaced} = 0.02 \text{ m}^3$.
3. $F_B = \rho_{water} V_{displaced} g = 1000 \text{ kg/m}^3 \times 0.02 \text{ m}^3 \times 9.8 \text{ m/s}^2 = 196 \text{ N}$.

#6. Final Exam Focus

Alright, let's get down to brass tacks. Here's what you absolutely need to nail on the exam:

• High-Priority Topics:
  • Buoyancy and Archimedes' Principle: Expect at least one problem related to floating/sinking or buoyant force calculations.
  • Friction: Know the difference between static and kinetic friction and how to apply them in various scenarios.
  • Free Body Diagrams: Be proficient in drawing and interpreting FBDs. They are the basis for solving force problems.
• Common Question Types:
  • Force analysis problems that combine multiple forces (tension, friction, normal, etc.).
  • Problems involving buoyant force and fluid dynamics.
  • Conceptual questions about conservative vs. non-conservative forces.
• Time Management Tips:
  • Quickly scan the problem for keywords (friction, buoyancy, tension) to identify the relevant concepts.
  • Draw a clear FBD before attempting any calculations.
  • If you get stuck, move on and come back later. Don't waste too much time on one question.
• Common Pitfalls:
  • Forgetting to consider all the forces acting on an object.
  • Using the wrong coefficient of friction (static vs. kinetic).
  • Confusing the density of an object with the density of the fluid in buoyancy problems.
  • Not drawing a FBD before attempting to solve a problem.

#7. Practice Questions

Let's wrap up with some practice questions to get you exam-ready!

- 1 point for correctly drawing the weight force (mg) pointing downwards.
- 1 point for correctly drawing the normal force (N) perpendicular to the incline.
- 1 point for correctly drawing the tension force (T) along the incline, pointing upwards.
- 1 point for correctly drawing the static frictional force (fs) along the incline, pointing downwards.

- 1 point for using <math-inline>W = mg = 5 \text{ kg} \times 9.8 \text{ m/s}^2 = 49 \text{ N}</math-inline>.

- 1 point for using <math-inline>W\_{parallel} = mg \sin(30) = 49 \text{ N} \times \sin(30)</math-inline>.
- 1 point for calculating <math-inline>W\_{parallel} = 24.5 \text{ N}</math-inline>.

- 1 point for using <math-inline>N = mg \cos(30) = 49 \text{ N} \times \cos(30)</math-inline>.
- 1 point for calculating <math-inline>N = 42.4 \text{ N}</math-inline>.

- 1 point for using <math-inline>f\_s = \mu\_s N = 0.4 \times 42.4 \text{ N}</math-inline>.
- 1 point for calculating <math-inline>f\_s = 16.96 \text{ N}</math-inline>.

- 1 point for using <math-inline>W = mg = 2 \text{ kg} \times 9.8 \text{ m/s}^2 = 19.6 \text{ N}</math-inline>.

- 1 point for comparing the forces acting up the incline with forces acting down the incline.
- 1 point for recognizing that the force pulling the block up the incline (19.6 N) is less than the sum of the forces pulling it down the incline (24.5 N + 16.96 N = 41.46 N).
- 1 point for concluding that the system will remain at rest due to static friction.

You've got this! Remember to stay calm, trust your preparation, and tackle each problem step-by-step. You're ready to rock the AP Physics 2 exam!