Free body diagram
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Drawing a free body diagram is a method often used by physicists working out kinetics or other mechanics problems to show all the mechanical vector forces acting on the given free body (or bodies) at any given time. Doing so can make it easier to understand the forces, and moments, in relation to one another and suggest to the physicist the proper trigonometry to apply in order to find the solution to the problem.
Making free body diagrams involves drawing vectors (which just look like arrows), representing the different forces acting on a given object. The vectors are meant to show the directions that the forces are acting towards. Additionally, much of the time the vectors are drawn to scale, so that if one force is larger in magnitude than another, its vector will be drawn so that it is longer than the other.
Vectors
A simple free body diagram is of an object sitting at rest on a surface. The free body diagram on the right (Image 1) illustrates this. It has the object’s weight pointing straight down and the object’s normal force pointing straight up. Below are more extensive explanations of weight and normal force.
- weight (W), always acts downwards on the centre of mass of an object. Weight has two vector components of force that get added together to make the final force of weight (see vector. The whole weight is the resultant force of the two components.
In order to conceptualize this better, consider the situation where an object is on an incline instead of a flat surface (as shown in Image 2). The two force components are expressed mathematically as ,<math> W cos\theta\ </math> and <math> W sin\theta\ </math>.
where:
- W = whole weight
- θ = the angle the incline creates with the horizontal
- To understand the following paragraph see also: glancing angle and angle of incidence
θ can also be the name for the angle that the incline makes with the vertical, at the top of the slope. This, however changes which direction <math> W cos\theta\ </math> and <math> W sin\theta\ </math> point in. In other words, if you measured θ this way, the direction that <math> W cos\theta\ </math> and <math> W sin\theta\ </math> point in would switch, so that <math> W cos\theta\ </math> ends up being where <math> W sin\theta\ </math> would normally be and vice-versa. This is shown in Image 3.)
If you measure θ as a glancing angle (as is normally done), <math> W cos\theta\ </math> points in downwards perpendicular to the slope of the incline, and <math> W sin\theta\ </math> points downwards parallel to the slope. In Image 1, the reason that <math> W cos\theta\ </math> is equal to the whole weight is simply because θ = 0 degrees <math> \sin0^\circ = 0 </math>.
- normal reaction (N) (also known as normal force) always acts perpendicular to the surface that the object is in contact with. Generally, if the object is sitting on a surface, normal force points in the opposite direction of <math> W cos\theta\ </math>, and is equal in magnitude to <math> W cos\theta\ </math> (as long as θ is measured from the horizontal, as explained above).
(See Newton's third law)
In Images 2 and 3, where an object is on an incline, there is one force that is not present in Image 1, where an object is resting on a flat surface. This force is friction (f). The reason that the force does not appear in Image 1 is that as long as an object is at rest on a flat surface, it does not feel friction. If, however the object was travelling at some velocity, the friction vector would have been noted in the opposite direction of its velocity vector.
See also
Concordia College physics course - The Normal Force and Free-body Diagramsnl:Vrijmaken