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