Free body diagram
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.
The most simple and easy to understand 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 (spatial) and then click on "vector addition" for more information). The whole weight is called the resultant force of the two components of weight. 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 components are expressed mathematically as Wcosθ and Wsinθ, meaning the whole weight multiplied by either the sine or cosine of the angle the incline creates with the horizontal. (θ can also be measured by the angle that the incline makes with the vertical, at the top of the slope. This, however changes which direction Wcosθ and Wsinθ point in. In other words, if you measure θ this way, the direction that Wcosθ and Wsinθ point in would switch, so that Wcosθ ends up being where Wsinθ would normally be and vice-versa. This is shown in Image 3.) If you measure θ the first way (as is normally done), Wcosθ points in downwards perpendicular to the slope of the incline, and Wsinθ points downwards parallel to the slope. In Image 1, the reason that Wcosθ is equal to the whole weight is simply because Wsinθ=0. Wsinθ=0 because in this case the angle made with the horizontal is 0 degrees, and sin(0)=0.
- 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 Wcosθ, and is equal in magnitude to Wcosθ (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 an friction. If, however the object were travelling at some velocity, let's say to the right, friction would have been noted pointing to the left.
See also
Concordia College physics course - The Normal Force and Free-body Diagrams
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