Energy

ENERGY

WORK•Work is a transfer of energy

•In order to do work on an object, you must increase the energy within it

•Any type of energy can do work

•Let’s look at a few…

WORK

KINETIC ENERGY•Energy is the ability to do work

•Kinetic Energy (KE) is the energy of motion

•More speed means more KE

KINETIC ENERGY

POTENTIAL ENERGY (GPE)•Potential Energy is stored energy

•Gravitational Potential Energy (GPE) is when the energy is stored in its position (height)

•The higher an object goes, the more GPE

•(the faster the speed it will have when it hits the ground)

POTENTIAL ENERGY (EPE)•The other type of Potential Energy we will look at is Elastic Potential Energy (EPE)

•Instead of height, the energy is stored by stretching an object.

•More stretching means more EPE

•ex. rubber band, spring

POTENTIAL ENERGY

HEAT•Heat energy is the energy created by friction

•This could be from scraping, rubbing or deformation

WORK EXAMPLES•Let’s look at the following scenarios:

•Work or not?

•Lifting a box above your head

•Holding that box there for 2 hours

•Sliding a box across a frictionless surface at constant speed

work

not work

not work

ENERGY EQUATIONS: WORK•Work is the product of the force applied in the direction of motion and the distance it is applied

•When the force and the movement are parallel, work is simply

€

W = F cosθ × d

€

W = Fdθ

Force (F)

ENERGY UNITS•Notice: from the work formula, energy units are a combo of Force (Newtons) and distance (m) or Newton•meters (N•m)

•The SI units for energy are Joules (J).

•So, one Joule is equal to 1 Newton•meter.

€

1 J =1N⋅m

ENERGY EQUATIONS: GPE•For GPE, we still have force x distance, but this time the force is the objects weight, mg

•This gives us the equation:

€

GPE = mgh

•We use h instead of d since it will always be height for GPE

F=mg

m

ENERGY EQUATIONS: KE•Now let’s throw a block

•The work is done while the block is being accelerated by the hand a distance of d

ENERGY EQUATIONS: KE•This time the force is simply ma

•So, the work done is:

•Quick time warp back to acceleration equation:

€

KE =Work = Fd

€

=mad

€

v f2 = v i

2 + 2ad

€

⇒ ad =v f

2 − v i2

2

ENERGY EQUATIONS: KE•Let’s substitute:

•The normal equation assumes starting from rest (vi = 0):€

KE = m⋅ad = m⋅v f

2 − v i2

2

€

⇒ KE = 12m(v f

2 − v i2)

€

KE = 12mv

2

ENERGY EQUATIONS: HEAT•When pushing a block at constant speed across a surface, the friction force is turned into heat

•Since added force is only working against friction (no a), all of the work done on the block is then turned into heat

f

ENERGY EQUATIONS: HEAT

•Remember that d is only during the friction

€

heat = work done

€

heat = f ⋅ d

ENERGY EQUATIONS: EPE•EPE is trickier than GPE

•force changes depending on how much you stretch the object

•This force depends on both the distance stretched (x) and a spring constant (k)

•This equation is known as Hooke’s Law

€

Fs = kx

ENERGY EQUATIONS: EPE•This k comes from how much force is needed to stretch a spring per a certain distance

•What is the k for this spring?

€

20 Nm

ENERGY EQUATIONS: EPE•Since the force at the beginning of the stretch is different than the end, we use an average to calculate the EPE:

•Since we usually start the stretch from rest:

€

EPE = Favgx =Fsf + Fsi

2

⎛

⎝ ⎜

⎞

⎠ ⎟x

€

EPE =Fsf + 0

2

⎛

⎝ ⎜

⎞

⎠ ⎟x =

kx

2

⎛

⎝ ⎜

⎞

⎠ ⎟x

€

EPE = 12 kx

2

POWER•In physics, power just means the rate of doing work

•So, faster work means more power

•The units come out to Joules per second. •We call this a Watt (W) for short

€

P =W

t

€

1W =1J

s

Check Yourself

Go to pg. 445

CONSERVATION OF ENERGY

•Energy cannot be created nor destroyed, but only changed from one form to another

•What does this mean?

CONSERVATION OF ENERGY•All of the energy that you start with…

•you end with!

•initial energy = final energy

•Total energy at top equals•Total energy at bottom•Total energy anywhere

CONSERVATION OF ENERGY•All of the energy that you start with…

•you end with!

•initial energy = final energy

•Total energy at top equals•Total energy at bottom•Total energy anywhere

CONSERVATION OF ENERGYAll GPE

All KE

GPE and KE

CONSERVATION OF ENERGY PROBLEMS•Identify type of energy at beginning and end

•Full law in equation form:

•For most problems, many are zero€

KE i +GPE i + EPE i +work added =KE f +GPE f + EPE f + heat

CONSERVATION OF ENERGY: EXAMPLE•Rolling down a hill from rest

•Top (initial): all GPE

•Bottom (final): all KE

•Left with:

•or:

€


€

GPE i =KE f

€

mgh = 12mv

2

€

gh = 12 v

2

CONSERVATION OF ENERGY: EXAMPLE•A bow is used to shoot a .050 kg arrow into the air. If the average force used to draw the bow is 110 N and the bow is drawn .50 m, how fast is the arrow moving when it has risen 35 meters above the bow? (Assume air resistance is negligible)

Define:

initial :and final :

when bow is drawn

when arrow is at 35 m

(work)

(KE & GPE)

What type of energy is it?

CONSERVATION OF ENERGY: EXAMPLE

Write out CoE eqn and cross out missing E’s

€


at rest

start at h = 0

finding through work

(no k)

moving

goes higher

nothing stretched/press

ed no air

resistance


rewrite and expand

€

work added =KE f +GPE f

€

Fd = 12mv

2 +mgh

€

Fd −mgh = 12mv

2

solve for v

€

2(Fd −mgh)

m= v 2

€

⇒ v =2(Fd −mgh)

m


plug and chug

€

v =2(Fd −mgh)

m

€

v =2 110N( ) 0.50m( ) − .050kg( ) 9.8 m

s2( ) 35m( )[ ]

.050kg( )

€

v = 39 ms

TIME TO PRACTICETurn to pg. 456

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Energy