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A force is applied to move a heavy crate across a horizontal surface. The coefficient of friction of the crate and surface is 0.3 (**μ = 0.3**). The crate is modeled as an extended body. The sketch shows its free-body-diagram and the orientation of the applied force.
The event is that the crate is pushed a distance, **L**, to the right.

**a) Obtain** a general expression for the least magnitude of the applied force required, as a function of the angle of application of that force, **θ**.

**b) Calculate** the required force and work of the event for the angle of application, **θ = 0**

**c) Calculate** the least force required to accomplish the event and the least work.

Below is incomplete. When someone asks, I'll complete it.