Ch. 5 Work and Energy

5-1 Work W = F X d W net = F net d(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 mv 2

ΔKE = ½ mv f 2 – ½ mv i 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 W net = ½ mv f 2 – ½ mv i 2 W net = ΔKE W net = F net d(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

PE g = 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.

PE elastic = ½ kx 2 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 ME i = ME f Substituting Pe g and KE into the formula: ½ mv i 2 + mgh i = ½ mv f 2 + mgh f

Also, add PE elastic (1/2 kx 2 ) 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