Lecture 21: Practice on Free Body Diagrams and Friction Forces

Practicing Free Body Diagrams (FBDs)

• Understanding tension forces in systems involving pulleys and blocks is critical for solving real-world mechanical problems.

Learning Goals

• Master the concept of tension forces

Key Concepts

• Atwood's Machine Example:

  • Two different masses, (m1) and (m2) connected via a string around a pulley.

  • Given: (m1 = 1.00 \text{ kg}), (m2 = 2.00 \text{ kg})

  • Objective: Find acceleration.

Free Body Diagram (FBD)

• In cases where the mass of the pulley is negligible and (m2 > m1):

  • For (m_1):

    • Forces acting: (-m_1 g \mathbf{j})

    • Tension (T)

  • For (m_2):

    • Forces acting: (-m_2 g \mathbf{j})

    • Tension (T)

Example Problems

• Analyzing an Elevator:

  • A box inside a descending elevator slowing at (2.8 \text{ m/s}^2).

    1. Free body diagram (FBD) for the elevator contains both the box and tension from the cable.

    2. Free body diagram for the box considering:

    • Weight (W = m_{box}g \mathbf{j})

    • Normal force (N)

• Clicker Questions Analysis:

  • Understanding the net forces acting in different scenarios involving elevators, including FBDs for both boxes and elevators.

  • Examples cover tension dynamics in elevators slowing down or accelerating.

Group Activity Example

• When a box's normal force is (51 \text{ N}) in a descending elevator, determine:

  • Mass of the box using Newton’s 2nd law:

  • FBD analysis helps derive (N = m_{box}(g - a)).

  • When the elevator ascends with an upward acceleration of (2.8 \text{ m/s}^2), analyze how normal force changes.

Summary of Chapter 5

• Forces concepts:

  • Understand forces, Newton’s three laws, application, and specific forces like gravitational force:

    • Gravitational force formula:
      $|F<em>{grav}| = \frac{G m</em>1 m_2}{r^2}$

  • Importance of free-body diagrams, Atwood’s machine, and dynamics on frictionless surfaces.

Chapter 6.1: Friction Forces

• Definition: Friction is a resistance force that opposes sliding motion, acting parallel to the surface and arising from molecular roughness.

  • Static Friction: No movement occurs; it counters initial motion.

  • Kinetic Friction: Resistance during sliding motion.

Equations for Friction

• Static friction magnitude:
  $|f<em>s| \leq \mu</em>s |N|$

• Kinetic friction equation:
  $|f<em>k| = \mu</em>k |N|$

Real-World Implications of Friction

• Friction can be beneficial (e.g., walking) or detrimental (e.g., in machines).

• Balance is key: Too little friction leads to slipping; too much can lead to overheating and inefficiency.

Homework and Assignments

• Chapter 5 problems assigned, focus on applying these concepts, due date: March 22.

• Students to complete preparatory work for Chapter 6.1.2 (friction) before the next lecture.

Key Concepts

• Free Body Diagrams (FBDs): A graphical illustration used to visualize the forces acting on an object.

• Tension Forces: Forces transmitted through a string, rope, or cable when pulled tight.

• Newton's Laws of Motion: Fundamental principles describing the relationship between the motion of an object and the forces acting upon it.

Important Equations

Gravitational Force

• The formula for gravitational force is:
  $|F<em>{grav}| = \frac{G m</em>1 m_2}{r^2}$

Static Friction

• The magnitude of static friction is defined by:
  $|f<em>s| \leq \mu</em>s |N|$

Kinetic Friction

• The equation for kinetic friction is:
  $|f<em>k| = \mu</em>k |N|$

Example Problems

1. Atwood's Machine: Analyze two different masses connected via a string around a pulley.

   • Given: (m1 = 1.00 kg), (m2 = 2.00 kg)

   • Objective: Find acceleration.

2. Elevator Dynamics: Tension and weight acting on a box in an elevator.

   • Analyze forces in scenarios of descending or ascending movement.