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Ch. 5 Work and Energy
5-1 Work
• W = F X d
• Wnet = Fnetd(cos θ)
• Work (J) Force (N) distance (m)
• Work is NOT done on an object unless it moves
• Work is only done when the force is parallel to the movement of the object
• W = F X d (cos θ)
• Cos θ = 1
• Work is a scalar quantity with a (-) or (+)
• Sign depends on the force and direction
• If force is in the direction of motion, then (+) work
• If the force opposes motion, then (-) work
• If the force is 90° to the motion, then no work
• If the object is not in motion, then no work
• If the object speeds up, then (+) work
• If the object slows down, then (-) work
Sample Problem 5A
5-2 Energy
Kinetic Energy- energy associated with motion
KE dependes on speed and mass
KE = ½ mv2
• ΔKE = ½ mvf2 – ½ mvi
2
• KE is a scalar quantity-The SI unit is Joules (J)
• Two objects traveling at the same speed, The object with the most mass will have more KE
• Ex: 18 wheeler vs bicycle
• In order to use a formula for net work, we need to use all forces that do work on the object
• Net work (+) = speed increases• Net work (-) = speed decreases• Kinetic energy is the work an object can
do
Work-Kinetic Energy Theorem
• Wnet = ½ mvf2 – ½ mvi
2
• Wnet = ΔKE
• Wnet = Fnetd(cos θ)
Potential Energy
• Potential Energy is stored energy because of its position relative to some other location.
• Gravitational Potential Energy-energy due to an object’s position relative to a gravitational source
• PEg = mgh• Gravitational potential energy turns into
kinetic energy • SI unit for GPE is Joule (J)• GPE depends on the height and free fall
acceleration of an object• GPE is a result of an object’s position so it
must be measured relative to some zero level.
Elastic Potential Energy
• Elastic Potential Energy-stored energy in a stretch or compressed spring
• Relaxed length-the length of a spring with no external forces acting on it
• The amount of energy depends on the distance the spring is compressed or stretched from the relaxed length.
• PEelastic = ½ kx2
• K is the spring constant or force constant
• X is the distance the spring is stretched or compressed
• Flexible spring, k is usually small• Stiff spring, k is large• Unit for spring constant is N/m
5-3 Conservaton of Energy
• Conservation means we have a constant amount but it can change forms
• Ex: mass
• Motion of objects involves a combination of kinetic and potential energy
• We will ignore other forms of energy because they have very little influence on the motion of objects
• Mechanical energy-the sum of kinetic energy and all forms of potential energy
• ME = KE + ΣPE
• Nonmechanical energy = all energy not mechanical such as nuclear, chemical, internal, and electrical
• Mechanical energy is often conserved in the absence of friction but it can change forms
• Potential energy is continuously converted into kinetic energy and back into potential energy
• Conservation of Mechanical Energy
• MEi = MEf
• Substituting Peg and KE into the formula:
• ½ mvi2 + mghi = ½ mvf
2 + mghf
• Also, add PEelastic (1/2 kx2) into both sides if the situation also has a spring
• Conservation of mechanical energy will not hold true with friction because not all kinetic energy is converted back to potential energy.
• Energy conservation occurs even when acceleration varies as long as friction can be ignored.
• Friction: Kinetic energy is converted to nonmechanical energy (heat) so mechanical energy (KE and PE) is no longer conserved.
• Total energy is always conserved
5-4 Power
• Power-the rate at which work is done or the rate energy is transferred
• Power= Work/Time Interval
• P = W/Δt
Alternative Formulas
• P = Fd/Δt because W = Fd
or P = mgd/Δt
• P = Fv because d/Δt = v
• SI unit of Power is Watt (W)
• 1 W = 1 J/s
• Another unit of power is horsepower (hp)
• 1 hp = 746 Watts
• Different power ratings do the same work in different time intervals
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