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Work-Energy Theorem
When a net force acts on a particle through a
displacement, the net work done on the particle equals
the change in kinetic energy.
KE I + W = KE f
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Pre Example
A rocket of mass m is launched straight up. The force of
thrust is FT. What is the rocket’s speed at a height h?
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Example
A 150,000kg rocket is launched straight up. The force of
thrust is 4x106N. What is the rocket’s speed at a height of
500m?
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Example
A 1500kg car accelerates from rest. The figure shows the
net force on the car as it travels from x=0m to x=200m.
What is the car’s speed after traveling 200m?
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Dissipative Forces
If you slide a book across a table, it will slow down and
stop. Where does this energy go?
Friction is converting kinetic energy into thermal
energy (heating up both the book and the table).
Note: In almost all cases when friction converts kinetic
energy into thermal energy it is lost forever and can
not be converted back to the book as kinetic energy.
Dissipative forces are forces that convert kinetic
energy into thermal energy. Common examples are
Friction and Drag.
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Conservation of Energy Revisited
ΔKE = Wnet = Wc + Wnc
The net work is comprised of work done by conservative
forces and work done by nonconservative forces.
Work done by conservative forces is represented by a
potential energy PE:
ΔU = −Wc
Note: Potential energy is really just the precomputed work
of a conservative force.
Nonconservative forces are divided into dissipative forces
and external forces.
Wnc = Wdiss + Wext
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The work done by dissipative forces increases the system’s
thermal energy:
ΔEth = −Wdiss
The work-kinetic energy theorem can now be written as:
ΔKE = −ΔPE + − ΔEth + Wext
or as:
ΔKE + ΔPE + ΔEth = ΔEmech + Eth = ΔEsys = Wext
where Esys = Emech + Eth is the total energy of the system.
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ΔKE + ΔPE + ΔEth = ΔEmech + Eth = ΔEsys = Wext
Recall: an isolated system has no external forces and Wext
= 0.
The total energy Esys of an isolated system is conserved.
∆Esys = 0.
Conservation of Energy:
The kinetic, potential, and thermal energy within the
isolated system can be transformed into each other, but
their sum cannot change. The mechanical energy
Emech = KE + PE is conserved if the system is isolated and
nondissipative.
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Example
A 2kg book is sliding across a table with an initial velocity of
10m/s. When the book comes to a stop how much energy
was lost due to friction? What was the average force on the
book if it stopped after traveling 10m? μk = ?
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Example
ƒ A .40S&W pistol bullet of mass 165grains is initially
traveling at 1100ft/s. It enters a block of gel and
does not exit. If we assume the bullet is
unchanged (not deformed, not hotter, etc), how
much energy was deposited in the gel?
Note: 1gram = 15.4grains, 1m/s = 3.28ft/s
4 Videos: Bullets / Gel
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Power
Power is how much work is done per unit time.
Recall:
Work = F ⋅ Δx
When an object moves at constant velocity by a constant
force the power is:
F ⋅ Δx
P=
= Fv
Δt
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The land speed record is held by Thrust SSC which produced a
thrust of 223kN and reached a top speed of 1228km/h. How
much power did this car have?
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