What is energy?
Energy is a conserved, substance-like quantity with the capability to produce change. It can be transferred or can remain stored in an object. A helpful way to visualize energy is to think of it like money. The system is the place where the $$ is kept, like a checking or savings account. As you transfer the mula from one account to another, the amount of cash stays the same, but the way you access the $$ is different. Some transfers may cost money, similar to Ediss when energy is dissipated.
In order to visualize energy, we started off the unit by learning about pie charts, bar graphs, and energy flow diagrams.
Above is an LOL chart, given the name because of the obvious L-O-L the bar graphs and system circle create.
Here is an example of the energy pie charts we used to represent the transfer of energy during an action. The size of the circle reflects the total energy of the system, and the size of each piece of the pie shows how the energy is distributed.
Lastly, we have the mathematical expression at the bottom of the picture above. The sum of the initial stored energy, Eg in this case, is equal to the energy(s) in the final bar graph. Therefore, the expression would read:
Eg + W= Ek + Eg + Ediss
W represents work. Work is the force that Buffy applies to the water balloon, as she applies additional energy to the system.
The first worksheet we dealt with required us to use pie charts to analyze the energy changes in different situations.
1) Where does the energy come from?
2) What does the energy do?
3) Where does the energy go?
So for the toy bunny in #2, it is moving, which requires Ekinetic. Then, it starts to slow down so it still has some Ekinetic but also some Ediss since energy is dissipating. Lastly, the toy comes to a stop, with all the energy gone.
Here are the energy pie charts to represent this:
Note that the size of the circles do not change.
Next, we started our journey with LOL charts.
Since there is no friction, there will not be any Ediss, as friction slows a system down and dissipates energy. At point A in the picture, the cart is pressed against a spring, with all Eelastic. Next, at point B, the cart is cruising through the loop with 4 units of Egravity and 1 unit of Ekinetic. The system is comprised of the cart, earth, track, and spring. The mathematical equation would look like this:
Eel= Eg + Ek
After we got the fundamentals down, we incorporated equations & numbers and solved for speed, ∆x, and power. The first equations we learned were:
F=Kx
K is the spring constant or how stiff the spring is & x is the distance.
Eel=1/2Kx^2 (formula for the elastic potential energy in a spring)
K=7n/m & x= .1m
Always remember to convert your distance to meters.
Therefore, the equation would read: Eel=1/2(7)(.1)^2
Eel=(3.5)(.01)
Eel= .035 J
META Sheet
- As Ek decreases, the energy has to go somewhere if it isn't falling
- energy of movement= kinetic
- pie chart tells a story about where the energy goes
- stiffness of the spring is represented by the steepness of the slope
- when a spring is stretched, energy is stored
- µs= static (object not moving)
- µk=kinetic (object moving)
- work=anytime you're adding energy to the system
- remember Ediss whens something slows down
- rise/run = N/kg
- k=slope of the line
- x=x-axis
- slope=spring constant
- need same amount of Eg if your system goes to same height
- slower you go, less Ek you have
- Friction slows system down
- use Echem if theres energy being burned in your body, food, etc
- in order to find spring constant: must find slope
- work also in J (an energy)
- Eek=1/2mv^2
- any time there is work, put the bar outside of the system on an LOL chart
- energy total b4=energy total after
- whenever Ediss is included, system slows down & include it in mathematical equation
- work has to come from outside the system
- an object with more Ek is going faster than an object with a lower bar of Ek
- Eg=mgh
- ∆x=stretch or compression
- g=strength of gravitational field
- power=∆energy/time (in watts)
- watts= J/s = Nm/s = N*m/s
- ∆Ek= Efinal-Einitial
- Power is a rate
- ∆energy=power*time
- W=F∆x
- How fast is something moving? solve for Ek
- What speed is something going? solve for velocity
- whenever we're asked how many calories, solving for chemical
- Ediss=F∆x
- Eg=Ek in certain instances
- power=∆energy/time (energy can be replaced by mgh b/c Eg=mgh
- Echem=chemical work from a car or rollercoaster
70m/1 hr x 1600m/1 mile x hr/3600s = m/s 31.1s
Eek=1/2mv^2
Eek=1/2 (2000) (31.1)^2
Eek= 967,210 J
Eel=1/2kx^2
Eel=1/2 (140) (25)^2
Eel=43,750 J
First convert grams to kilograms. 50g=.05kg
Ek=1/2mv^2
40=1/2(.05)v^2
40=.025v^2
1600=v^2
v=40m/s
