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DYNAMICS - THEORY


Direction of Force and Motion
 

Power is the rate at which work is expended,

     P = ΔU/Δt = dU/dt

Recall that work, dU, is simply the force through the distance. If the force is constant, the can be written as

     dU/dt = F · d(r)/dt

or simply,

 
P = v
 

Notice that the force and direction need to be parallel. The dot product forces the force vector and velocity vector to be parallel.

   
    Efficiency

Standard Units
SI: 1 Watt (W) = 1 N-m/s
US: 1 Horsepower = 550 ft-lb/s
 

Mechanical efficiency is the ratio of the "energy out" to the "energy in" of a system. This accounts for energy lost due to system in-efficiencies such as friction.

     

Efficiency can also be written in terms of power,

 
 
     
   
 
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