Energy
Different Types of Energy (Always measured in J)
Eel - Elastic Energy (usually used with a spring/rope)
- Eel = 1/2Kx^2
Echem - Chemical Energy (usually used when a person is in the system)
- Echem =
Ek - Kinetic Energy (when a cart is moving at a speed and no other forces are adding energy into it)
- Ek = 1/2mv^2
Eg - Gravitational Energy (has to do with how high the object is off of the ground)
- Eg = mgh
Etherm - Thermal Energy/Dissipate (always caused by the presence of friction, makes the object slow down)
W - Work (when energy is being put into an object from an outside force)
- W = F x (change in X)
Energy Pie Charts
Say a car is pushed with a spring up a slightly inclined hill. As the car moves, up the hill, where does its energy go?
(Total circle contains Eel) (Half Eel, 1/4 Ek, 1/4 Eg) (Half Eg, Half Ek)
Graphs and Elastic Energy
When using a graph, the elastic energy can be determined by using the formula for the area of a triangle. The area of a triangle is 1/2 base x height, and then you add the length x width to get the full elastic energy.
Bar Graph Key Points
(I'm sorry, it's not letting me upload pictures so I am unable to show bar graphs as examples)
- make sure you list all components in the system. If you miss out on one, you may mistake energy as work instead of chemical (for example).
- when friction is included, there is a very large chance that Ediss or Etherm is going to be used in the end.
- make sure you label how many boxes you have used for each graph, because the amount of energy you start with is exactly the same as the amount that you end with.
- if two back to back problems have the same idea, but one just asks for friction, use the same ratio of boxes concerning the height of the object if it is being thrown up/ moving up.
- you only really use Echem when the energy comes from a person, and if the person is part of the system. If the person is not part of the system, but is still putting energy into the object, you would call that Work.
Quick Problems!
1) How much kinetic energy does a 2000kg SUV traveling 50 mph have?
Ek = 1/2mv^2
Ek = 1/2 (2000) (50)^2
Ek = 1000 (2500)
Ek = 250,000J
2) How much energy is stored when a railroad cart spring is compressed to 10cm? (The spring requires about 10,000 newtons to be compressed 3 cm).
Eel = 1/2Kx^2
Eel = 1/2 (333333) (0.1)^2
Eel - 1666.6 J
*Finding the spring constant given newtons and distance:
Fel = Kx
10,000 = K(0.03)
333333 = K
3)Determine the final velocity of a rollercoaster with a mass of 40kg, assuming a 10% loss to friction, that is 5m above the ground.
Energy conservation equation -> Ek = Eg
Eg = mgh
Eg = (40) (10) (5)
Eg = 2000J
10% of 2000 is 200, and 2000-200 = 1800J
Ek = 1/2mv^2
1800 = 1/2 (40) (v^2)
1800 = 20v^2
90 = v^2
v = 9.5m/s
4) A student eats a breakfast before school that contains 350 calories. (One food calorie = 4186 joules). While he is working on classwork during school, he radiates about 150 joules per second. How long would the student have to work on classwork to radiate all of the energy from breakfast?
350 x 4186 = 1,465,100
1,465,100 / 150 = 9767 seconds = 1.62 hours
Power
- power = energy transferred / time
- measured in watts
- the quicker you are at transferring energy, the more powerful you are
1) Bob pulls on a rope to lift a 12kg pail out of a deep, dark well. She lifts the pail straight up for a total of 10 meters at constant speed. How much power is required to complete this task in 5 seconds?
Eg = mgh
Eg = (12) (10) (10)
Eg = 1200J
power = energy transferred / time
power = 1200 / 5
power = 240 watts
