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Do you include static friction on a free body diagram for a static box on a flat surface? Or do you just include Force of gravity and Normal force?
We know when the box is moving there is Frictional force opposing the movement but I am confused with the static friction when it is standing still.
No. The magnitude of static friction (sf) is equal and opposite to the force applied. In your scenario the only force pair is the force of gravity and the normal force. Since there is no other force being applied to the object the sf is 0 and should not be part of the force diagram.
In your free body diagram, you need to show static friction since it is an external force. It will always be equal and opposite to the force which is applied horizontally to the box.
There can be two cases :-
If any external force is applied but still the box in at rest.
If no external force is applied on the box then also it would be at rest.
It depends on if any external force is applied on the box but still it is not moving then you need to include the static friction but if no external force is applied on the box then you dont need to include the static friction.
Just keep in mind that you will need to include the friction if any external force(except gravity and normal reaction) are applied on the object because friction always opposes the motion of any object. It can not act on a body until an external force is applied on that body which tries to move it.
Hope it helps!
The static friction force is always on the diagram if it exists.
Bottom line: Remember that static friction only is present if it is needed to prevent something from sliding. And if present, it must be drawn like any other (external) force.
