Physics Notes: Force and Motion II - Drag Force and Forces in Uniform Circular Motion

Learning Goals

• Understand and practice concepts of friction.

• Explore the concept of drag force.

• Analyze forces in uniform circular motion.

Recap of Clicker Questions

• Key Concepts of Forces on an Inclined Plane:

  • Consider a loaded sled on an inclined plane with a weight of $70.0 ext{ N}$ and incline angle $θ = 21.0°$.

  • Friction Coefficients:

  • Coefficient of static friction: $𝜇_s = 0.290$

  • Coefficient of kinetic friction: $𝜇_k = 0.200$

Clicker Question 12: Minimum Force to Prevent Sliding

• Forces on the Sled (x- and y-directions):

  • Normal force (N), weight (W), applied force (F), frictional force (f).

• Static Friction:

  • Relationship: $|f| = 𝜇_s |N|$

Clicker Question 13: Maximum Force to Prevent Sliding Upwards

• Forces on the Sled:

  • Normal force (N), weight (W), applied force (F), frictional force (f).

• Maximum Static Friction:

  • Relationship: $|f| = 𝜇_s |N|$

Clicker Question 14: Minimum Force to Start Moving Up

• Forces when the sled starts moving up:

• Same relationships as Question 12 and 13, but focused on overcoming static friction.

Clicker Question 15: Sled Sliding Up at Constant Velocity

• Forces on the Sled:

  • At constant velocity, net force is zero (acceleration = 0).

• Kinetic Friction:

  • Relationship: $|f| = 𝜇_k |N|$

Chapter 6.2: The Drag Force

• Definition of Drag Force:

  • Air resistance acting on an object due to velocity differences.

• Equation for Drag Force:

  • $F_{Drag} = C' v^2$

  • Where:

    • $C'$ = Drag coefficient

    • $v$ = relative velocity

Factors Affecting Drag Force for Skydivers

• Key Determinants:

  • Drag coefficient and air density

  • Area facing the air

  • Speed of descent

Air Resistance and Terminal Velocity

• Understanding Terminal Velocity:

  • Terminal velocity occurs when drag force equals the weight of the object: $F_{drag} - mg = 0$

  • Example reference: Typical terminal velocity for a skydiver is $200 ext{ km/h}$ or $120 ext{ mph}$.

Chapter 6.3: Forces in Uniform Circular Motion

• Concept of Uniform Circular Motion:

  • Motion at constant angular velocity; meaning the speed is constant but direction changes.

• Centripetal Acceleration and Force:

  • Acceleration: $a = rac{v^2}{R}$ where R is the radius.

  • Centripetal Force: $F = rac{mv^2}{R}$

  • Direction of centripetal force: Towards the center of the circular path.

Examples in Circular Motion**

• Tetherball Example:

  • In tetherball, the net force acts towards the top of the pole, along the tension in the rope.

• Ferris Wheel Example:

  • At the lowest point, net force is directed upwards; at the highest point, net force is directed downwards.

Example: Geosynchronous Orbits

• Definition:

  • A satellite orbiting the earth at a height where its orbital period matches the Earth's rotation period.

• Determining Altitude:

  • Use Newton's law of gravity and centripetal force equations to calculate heights based on given parameters such as the gravitational constant $G$ and Earth's mass $M_E$.

Summary of Chapter 6

• Main Objectives:

  • Study of friction forces, drag forces, and forces in uniform circular motion is crucial for understanding basic physics concepts.

Homework Assignment

• Complete the homework for Chapter 6 by this Friday.

Pre-Lecture for Next Class

• Complete Module 7.1 pre-lecture survey before the next lecture.

Key Equations and Concepts

1. Forces on an Inclined Plane

   • Weight of the sled: $W = 70.0 \, \text{N}$

   • Incline angle: $θ = 21.0°$

   • Coefficient of static friction: $𝜇_s = 0.290$

   • Coefficient of kinetic friction: $𝜇_k = 0.200$

2. Static Friction Relationship

   • $|f| = 𝜇_s |N|$

3. Kinetic Friction Relationship

   • $|f| = 𝜇_k |N|$

4. Drag Force

   • Definition: Air resistance acting on an object due to velocity differences

   • Equation:
     $F_{Drag} = C' v^2$

   • Where:

     • $C' = ext{Drag coefficient}$

     • $v = ext{relative velocity}$

5. Understanding Terminal Velocity

   • $F_{drag} - mg = 0$

   • Typical terminal velocity for a skydiver: $200 \, \text{km/h}$ or $120 \, \text{mph}$

6. Uniform Circular Motion

   • Centripetal Acceleration: $a = \frac{v^2}{R}$

   • Centripetal Force: $F = \frac{mv^2}{R}$

   • Direction of centripetal force: Towards the center of the circular path.

7. Geo-synchronous Orbits

   • Definition: A satellite orbiting the earth where its orbital period matches the Earth's rotation period.

   • Altitude Determination: Use:

     • Newton's law of gravity and centripetal force equations to calculate heights.

Summary

Studying these key equations and concepts is essential for understanding the principles of forces, drag forces, and motion in circular paths in physics.