To start the crate moving with the weakest possible applied force, the force should be applied in the opposite direction to the static friction force. In this case, the force should be applied in the direction that opposes the motion of the crate.
The coefficient of static friction (μ_s) represents the frictional resistance between two surfaces when they are not sliding relative to each other. The formula for static friction is given by:
Static friction force (f_s) = μ_s * Normal force
In this scenario, the crate is resting on a rough horizontal floor. To start the crate moving, the applied force must overcome the static friction force. The weakest possible applied force required to overcome static friction is known as the threshold force.
To determine the direction in which the force should be applied, we need to consider that the static friction force always acts in the direction that opposes motion. Therefore, to overcome the static friction force, the applied force should be in the opposite direction.
In summary, the force should be applied in the opposite direction to the intended motion of the crate.