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Unformatted text preview: Chapter 5 Additional Notes!
From the notes we can write work as W K = ΔKE
as well as € W P = −ΔPE Summing then the change in kinetic energy with the change in potential energy then gives us € ΔE = ΔKE + ΔPE = W K − W P Here we define the total mechanical energy as the sum of the change in kinetic energy and the change in potential energy. The right hand side of the last expression is the difference in the work done by the kinetic energy and the potential energy. For a conservative force, these two works will be exactly the same. So we can write ΔE = ΔKE + ΔPE = 0
This tells us that the total energy of the system is a constant, so the initial energy of the system is equal to the final energy of the system. € What about when the two works are not equal? In this case, the change in the work will be exactly equal to the work done by the force dissipating the energy (for the purposes of this class friction). We can then write ΔE = ΔKE + ΔPE = W NC
Here the subscript NC stands for non-conservative force (friction). Here we will have to use free-body diagrams to find the work done € by the non-conservative force since W = F cosθΔx
Remember that here the angle is the angle between the force and the displacement, so we have to represent them as vectors to determine € the angle. Power: Or more importantly average power, is the rate of energy transfer. So we can write W FΔx P= = = Fv t t
Here we simplified things by assuming that the force is parallel to the displacement (hence the no cosine term). We also used that velocity is the change in position divided by the change in time. € Notes Example 1: a) Since the car moves on the same horizontal surface, the change in gravitational potential must be zero. Since there is no spring, the spring potential energy is also zero. Thus the only change in energy comes from the kinetic energy, so we can write ΔE = ΔKE
Due to the presence of the frictional force, we can then write the above expression as € ΔE = ΔKE = W NC € Drawing a free-body diagram of the car gives FN fk € mg Δx
Since the displacement vector points to the right and the frictional force points to t...
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- Fall '08