To Move a Crate

The scenario shows a worker who shoves a heavy crate a distance, L, across a flat floor. Friction opposes the event; the coefficient of friction (static and dynamic) is μ. The masses of real crates are distributed masses and they can deform upon movement etc. As a needed simplification, we model the crate as an "extended Body."

A free-body-diagram of the crate (modeled as an extended body) is shown. The sketch shows its free-body-diagram and the orientation of the applied force.

Horizontal Force:  Suppose the applied force of the worker is horizontal. What is the work of the event for the crate as system?

Least Force:  Suppose the magnitude of applied force is the least possible. What force is that and at what angle would it be applied? What is the work of the event for the crate as system?

Least Work:  Suppose the applied force of the worker is such the the work of the event is the least possible. What is the force and work of the event for the crate as system?

worker applies the force hThe force is applied horizontally.

What force is required 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.