Unit 7: Energy Notes
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1 Unit 7: Energy Notes Energy is a conserved, substance-like quantity with the capability to produce change. Energy is conserved, neither created nor destroyed. = (Law of conservation of energy) Εnergy is always stored in something and does not exist on its own ( pure energy ). Modes of energy storage: (1) Kinetic Energy (Ek) - energy of motion - stored in the moving object (2) Gravitational Potential Energy (Eg) - energy of height or potential to fall - stored in the gravitational field (g-field) (3) Elastic Potential Energy (Eel) - potential to spring back to its original form - stored in a stretched or compressed elastic object (4) Chemical Potential Energy (Echem) - stored in chemical bonds (5) Electrical Potential Energy (Ee) - stored in the electric field (e-field) (6) Magnetic Potential Energy (Em) - stored in the magnetic field (m-field) (7) Internal Kinetic Energy (Eint) - describes the kinetic energy of molecules - transfer of causes a temperature or phase change - only 2 ways to form it: 1. Friction 2. Deformation (change in shape) Where energy is stored when it is (1) Ek = (2) Eg = (3) Eel = (4) Echem = (5) Ee = (6) Em = (7) Eint =
2 The first step in all energy analysis problems, is to define a system. A system is simply the objects being included in the analysis. Write this out to the side of each problem unless it s given to you. Hint: The more inclusive the system, the simpler the analysis is (generally) Pie Charts Showing Energy Storage: We can use qualitative pie charts to analyze energy storage (not transfer) at specific times. The size of the pie indicates the total amount of energy of the system at that time. The labeled divisions in the pie show the relative amounts of each energy storage mode. Never put Eint in your first pie. The underlying concept here is that energy is conserved, neither created nor destroyed. (Law of conservation of energy) Example 1: a spring-launched ball is propelled upward (neglect air & spring deformation) System: spring, g-field and ball Example 2: A ball rolling on the floor, coming to a stop due to friction System: ball and floor
3 Energy Transfer The relationship between energy storage and transfer is known as the 1 st Law of Thermodynamics: ΔE = W + Q + R (where ΔE = E f - E i = ΔE k + ΔE g + ΔE el + ΔE chem + ΔE int ) W = working transfer (involves forces) Q = heating transfer R = radiating transfer These are the 3 methods of energy transfer. They are positive when going into the system and negative when going out. 1 st Law in words: The total amount of energy in the universe is constant. Energy can neither be created nor destroyed! Einitial = Efinal 2 nd Law of Thermodynamics: The available energy in the universe is diminishing. (This internal energy is called entropy.) Bar Graphs & System Circles ( LOL ) showing energy storage & transfer: Example 1: A person pushes a box at rest across a floor System = box + surface
4 Example 2: A person pushes a box up a ramp to a stop. System = box + surface of ramp + g-field Example 3: Buffy tosses a water balloon on Biff s head. System = water balloon + g-field + Biff
5 Energy (E) is measured in Joules (J). Equations: Ek = ½ mv 2 Eel = ½ kδx 2 Eg = mgh E = W + Q + R W = E = FII(Δx) Q = mc T Quantifying Energy & Power (k = spring constant) (h = height) Review: F = ma & Ff = μ(fn) Quantitative Bar graph Problems: (FII is the force parallel to the Δx that is causing the E) Example 1: A 2 kg ball is propelled upward by a spring with a spring constant of 120 N/m that s been compressed 0.2m (neglect air friction & spring deformation). How high does the ball go? System: spring, g-field and ball Example 2: A 2 kg ball rolling on the floor at 3 m/s comes to a stop due to friction. (a) How much internal energy is produced total? (b) If the ball rolls 5 m, how large was the force of friction on the ball? System: ball
6 Power: Power is the time rate of changing energy or the rate at which work was done. P = E / Δt or P = W / Δt Power is measured in Watts (or horsepower = 746 Watts) An alternate equation for power is P = FII ( vv ) (since W = FII(Δx) and vv = Δx/Δt) Power Problems: Example 1: A person pushes a box at rest across a floor with a force of 75 N with a power rating of 200 W. How much time does it take to move it 8 meters? Example 2: A 2 kg ball rolling on the floor at 3 m/s comes to a stop due to friction. If this took 2 seconds, how much power was required?
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