Lecture Notes on Normal Forces & Free Body Diagrams in Mechanics

Lecture Overview

  • Course: PHYS 225 - Fundamentals of Physics: Mechanics

  • Instructor: Prof. Meng (Stephanie) Shen

  • Topic: Normal Force & Free Body Diagrams

Learning Goals

  • Understand how to draw Free Body Diagrams (FBD).

Steps to Draw a Free Body Diagram (FBD)

  • Step 1: Draw the coordinate system.

  • Step 2: Illustrate all the forces acting on the object or system.

  • Step 3: Decompose any forces that are not aligned with the coordinate axes.

Free Body Diagram Example

  • Scenario: A block sliding down a frictionless inclined plane.

    • Determine the proper FBD representing all forces acting on the block.

Detailed Analysis of Forces on an Incline

  • Given:

    • Mass of block: m1m_1

    • Angle of incline: θ\theta

Force Components

  • Weight of the block (W):

    • Weight acting vertically downwards: W=m1gW = m_1 g

  • Components of Weight:

    • Parallel to incline: W<em>x=m</em>1gsin⁡(θ)W<em>x = m</em>1 g \sin(\theta)

    • Perpendicular to incline: W<em>y=m</em>1gcos⁡(θ)W<em>y = m</em>1 g \cos(\theta)

Normal Force Considerations

  • Normal Force (N):

    • On flat surface: N=mgN = m g

    • On incline: 0 < N < mg

Example Problems

  • Example 2: FBD for a block on an incline without friction:

    • Incline angle: θ=30∘\theta = 30^{\circ}

    • Mass of block: m1=1extkgm_1 = 1 ext{ kg}

  • Question: What is the acceleration of the box and the normal force?

Additional Example

  • Scenario: A block of mass m1=104extkgm_1 = 104 ext{ kg} is pushed at constant speed up a ramp at θ=33∘\theta = 33^{\circ} by horizontal force, FF.

    • Forces to analyze: Net force, acceleration, and free body diagram.

    • Key questions:

    • Is acceleration up the ramp, down the ramp, or zero?

    • What is the complete FBD representing all interactions?

Clicker Questions Overview

  • Question 1: Proper sketch for block sliding down incline?

  • Question 2: Direction of acceleration for the block released on incline?

  • Question 3: Component of weight acting parallel to incline (WxW_x)?

  • Question 4: Component of weight acting perpendicular to incline (WyW_y)?

  • Question 5: Compare normal forces on flat surface vs incline.

Conclusion

  • Understanding normal forces, free body diagrams, and forces acting on inclined planes is crucial for analyzing motion in mechanics.

  • Apply this knowledge to solve related problems effectively in physics exams.

Key Equations and Concepts
Free Body Diagrams (FBD)

  • Steps to Draw FBD:

    1. Draw the coordinate system.

    2. Illustrate all the forces acting on the object or system.

    3. Decompose any forces that are not aligned with the coordinate axes.

Forces on an Inclined Plane

  • Weight of the block (W):

    • Weight acting vertically downwards: W=m1gW = m_1 g

  • Force Components:

    • Parallel to incline: W<em>x=m</em>1gan(heta)W<em>x = m</em>1 g an( heta)

    • Perpendicular to incline: Wy = m1 g rac{1}{ ext{cos}( heta)}

Normal Force Considerations

  • Normal Force (N):

    • On flat surface: N=mgN = m g

    • On incline: 0 < N < mg

Example Problem Formulas

  • For a block sliding down a frictionless incline:

    • Acceleration down the incline can be calculated using:
      a=gan(heta)a = g an( heta)

  • For a block pushed at constant speed on an incline:

    • Net force must be zero (acceleration = 0), analyze the forces accordingly.

Conclusion

Understanding normal forces and free body diagrams is essential for analyzing motion in mechanics, especially on inclined planes.