Edexcel A Level Physics:复习笔记2.8 Forces as Vectors

Free-body Force Diagrams

  • Free body diagrams are useful for modeling the forces that are acting on an object
  • Each force is represented as a vector arrow, where each arrow:
    • Is scaled to the magnitude of the force it represents
    • Points in the direction that the force acts
    • Is labelled with the name of the force it represents or an appropriate symbol

     

  • Free body diagrams can be used:
    • To identify which forces act in which plane
    • To resolve the net force in a particular direction

Simple Free Body Diagrams

  • The rules for drawing a free-body diagram are the following:
    • Rule 1: Draw a point in the centre of mass of the body
    • Rule 2: Draw the body free from contact with any other object
    • Rule 3: Draw the forces acting on that body using vectors with correct direction and proportional length

     

free-body-diagram

Free body diagrams can be used to show the various forces acting on objects

 

Forces on a Particle or an Extended but Rigid Body

  • Free body diagrams simplify problems by reducing complex shapes into simple one
  • Any object can be thought of as a particle
    • Even something as large as the Earth can be modelled as a point mass for most calculations
  • Objects can also be thought of as being extended but rigid bodies
    • This simply means that all parts stay in the same position relative to each other when the object moves

2.2.1-Box-point-particle-example-1

Point particle representation of the forces acting on a moving object

 

  • The below example shows an object sitting on a slope in equilibrium

4.1.2.3-Vector-triangle-in-equilibrium

Three forces on an object in equilibrium form a closed vector triangle

Worked Example

Draw free-body diagrams for the following scenarios:

a) A picture frame hanging from a nail

b) A box sliding down a slope

Part (a)

A picture frame hanging from a nail:

 

3.3.3-Tension-Free-Body-Diagram

      • The size of the arrows should be such that the 3 forces would make a closed triangle as they are balanced

Part (b)

A box sliding down a slope:

 

3.3.4-Parallel-and-Perpendicular-to-the-slope

    • There are three forces acting on the box:
      • The normal contact force, R, acts perpendicular to the slope
      • Friction, F, acts parallel to the slope and in the opposite direction to the direction of motion
      • Weight, W, acts down towards the Earth

       

Exam Tip

When labeling force vectors, it is important to use conventional and appropriate naming or symbols such as:

  • w or Weight force or mg
  • N or R for normal reaction force (depending on your local context either of these could be acceptable)

Getting used to this notation will make labelling free-body diagrams automatic - leaving you time to focus on the Physics rather than the process. This is crucial as a good diagram will show you exactly what to include in your calculations.

 

 

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