Energy Storage and Transfer Model Unit 7 Energy Storage and Transfer Model

Key points Energy- a conserved, substance-like quantity with the capability to produce change in physical systems It does not come in different forms… it’s just energy. It’s stored in different containers. It can be transferred from container to container and split between them. Thinking this way diverts your attention from the changes in matter that we CAN describe.

Describing the Interaction between energy and matter Think money We have money and it’s just money, no matter how you put it But we put it, store it, in different spots- credit card, debit card, checking account, savings account, cash, coins, your wallet… It’s still all money, the only thing that changes is how it is stored. Energy is the same way

Describing the Interaction between energy and matter continued We create various "accounts" (or storage modes) in which energy can be stored in a given system It can be transferred from one account to another as some aspect of the system undergoes a change It can be transferred between system and surroundings via several mechanisms, although "working" (W) is the primary transfer mechanism used in this unit

Energy Storage Energy is not disembodied; it is either stored… In an object Labeled kinetic energy when the object is moving Labeled elastic energy when it undergoes a restorable deformation By a field Gravitational, electric, or magnetic Labeled potential energy

Kinetic Energy - EK or KE Energy stored kinetically Energy of motion Located within the moving object

Chemical Energy - EChem Energy stored chemically Stored in molecular and atomic bonds When you break the bond and form new bonds which require less energy to make, the difference is transferred to other “containers”

Gravitational Potential Energy – Ug; UG Energy stored gravitationally Where is this energy stored? Within the ball? Within Earth? Stored within the field – stored relative to GF What does GF look like? GF lines vectors pointing towards center of Earth

GPE Newtonian View Why is NULG and all other field forces modeled as an inverse square law? We live in a 3d universe, so the field will decrease in strength as you move outwards (in one dimension), but that strength must be distributed over the 2d space of a sphere – the surface area of a spatial sphere Which is 4πr2

GPE Relativistic View Mass curves/bends spacetime We still see the surface area of sphere (kind of), Newton’s calculations were pretty good but relativity gives us more accuracy (and an actual explanation for gravity)

Potential Energy in general Usubscript Energy of an object due to its position relative to a force field or due to that system’s current state relative to its rest state Others? Electric Potential Magnetic Potential Chemical Potential – this is Echem

Thermal Energy – ETherm; ETh; EInt Energy stored thermally or internally – can be described through its temperature, but it is NOT the temperature Stored in vibrations or kinetic/potential energy (movement and position) of molecules/atoms Hard to quantify without thermodynamic equations and statistics Why?

The Law of Conservation of Energy

Elastic Energy – ESpring; ES; US Energy stored elastically Potential Energy stored in configuration of material Usually deals with the deformation of the material away from its rest state https://www.youtube.com/watch?v=6TA1s1oNpbk https://www.youtube.com/watch?v=AkB81u5IM3I https://www.youtube.com/watch?v=QFlEIybC7rU

Spring F vs X graph

Hooke’s Law Think about the equation of the best fit line (y=mx+b) y is Force applied (N), m represents the spring constant (k), and x is how much the spring is stretched/compressed. We’ll ignore the y-intercept in this course. F = kx. The value of the spring constant, k, tells us how much force (in Newtons) must be applied to the spring to stretch/compress it a certain distance (in meters). So the units are N/m.

Hooke’s Law continued Sometimes Hooke’s law is formulated as F = −kx. In this expression F no longer means the applied force but rather means the equal and oppositely directed restoring force that causes elastic materials to return to their original dimensions. We won’t use it this way, it’s just good information to know.

But what else can we determine using the graph?

The area under the line seems to have meaning…

The area under the line seems to have meaning… That’s a triangle: ½ b * h So.. ½ F * x but we know F = k*x Substitute in k*x for F ½ k*x*x or Us = ½ kx2 Hooke’s Law

The area under the line seems to have meaning… The area shaded represents the spring potential energy Eel = ½ kx2 We can use this value, measured in Joules, to determine how energy is transferred to other storage accounts.

Energy Transfer labs Spring potential energy transferred to kinetic energy No relationship between Energy and Velocity… but if we linearize our data by squaring velocity we get the graph on the right.

Energy Transfer labs Analyze the slope: Now we have a linear relationship Slope units reduce to kilograms and the value is ½ the mass of the cart Slope unit derivation: A joule is a Newton*meter A Newton is equal to Kg*m/s2 So the slope is N*m/m2*s2 substitute in Kgm/s2 and you take reciprocal of denominator Kg*m*m*s2 / m2*s2 clearly, all the meters and seconds cancel leaving kilograms- mass.

Energy Transfer labs General equation of the line: Ek = ½ m * v2

Energy Transfer Labs Spring potential energy transferred to gravitational potential energy Analyze the slope We see the units are Joules (a N*m) divided by meters; so Newtons (N) Slope represents Force, in this case weight (m*g)

Energy Transfer Labs Ug = mgy Equation of the line tells us that energy, in this case gravitational potential energy (Ug) depends on the strength of the field and the arrangement of objects (at least two) in the field Ug = mgy where g is the strength of the gravitational field (in N/kg), and y is the height above some zero reference position. Remember, g= 9.8 N/kg

We now have 3 ways to quantitate energy storage Spring potential energy (Us) Us = ½ kx2 Gravitational potential energy (Ug) Ug = mgy Kinetic energy (Ek) Ek = ½ mv2

But… How does the spring in our experiment actually store more energy? Let’s say the force we used was constant, not changing..

What else can an F vs Δx graph tell you? Work is also area under F vs. Δx curve This area represents energy transferred into the system by work

Work = ΔE = FΔx A force does work if, when acting on a body, there is a displacement of the point of application in the direction of the force. Energy is transferred by forces that cause displacements. Force and motion must be in the same direction. On a force vs position graph, this is the area under the graph.

Units Force is measured in Newtons. Distance is measured in meters. N x m = Nm = Joules Joules and Nm are the same things.

Force and Distance must be in the same direction!! If you pick an object up, the force must be the upward force. If you slide an object sideways on a table, the force must be the sideways force. If you measure the distance up an incline, the force must be the one exerted in a direction up the incline.

Force – but no displacement Work = Zero

Displacement – but no force Work = Zero

Force – but no displacement Work = Zero

No Work Done! The force (weight) is downward. There is virtually no sideways force. The displacement is sideways. There is no downward motion. W↕ = 14 N x 0 m = 0J W ↔= 0 N x 10 m = 0J

How much work is done to lift a 15 N object upward 4 meters? When you pick an object up, you have to apply a force equal to its weight (15 N). W = F x d W = 15 N x 4 m = 60 J

How much work is done to lift a 5.00-kg object upward 4.00 meters? When you pick an object up, you have to apply a force equal to its weight (5kgx9.8m/s2=49 N). W = F x d W = 49 N x 4 m = 196 J

How much work is done to slide a 15 N object 4 How much work is done to slide a 15 N object 4.0 meters sideways if the force of friction is 3.0 N? When you slide an object sideways, you have to apply a force equal to friction (3 N). W = F x d W = 3.0N x 4.0m = 12 J

How much work is done to slide a 15 N object up an incline 4 How much work is done to slide a 15 N object up an incline 4.0 meters long if the force the person must push with is 7.0 N? When you slide an object up an incline, you have to use the force up the incline (7N). W = F x d W = 7.0N x 4.0m = 28 J

How much work is done to slide a 5. 0-kg object sideways 4 How much work is done to slide a 5.0-kg object sideways 4.0 m if the acceleration is 6.0 m/s2? F=ma F = 5-kg x 6 m/s2 F = 30-N W = F x d W = 30 N x 4 m = 120 J

Energy Bar Chart Analysis The total initial energy, plus or minus any energy transferred into or out of the system, must equal the total final energy. This is the first law of thermodynamics.

Remember The SI unit for energy is the joule (J). A joule is a or .

“Useful” Energy Energy is defined as the ability to cause change, and, like the money analogy, some forms of energy are more useful or effective in causing change than others. Kinetic and potential energies are useful energies. Thermal is not – why? Rub your hands together – where did your chemical energy go? Now, use that thermal energy to cause more change. Very hard to – in fact, it is impossible. This will ultimately lead to the Entropic Heat Death of the Universe.

Conservative vs. Non-conservative A conservative force is a force for which its total net work does not depend on the path taken. Gravity is conservative; total work will only depend on initial and final positions Friction is non-conservative; the longer the path, the more work friction does and the more energy goes into the non-useable container Conservative Forces Non-conservative Forces Gravity Friction Elastic Air resistance Electric Tension Magnetic Propulsion by rocket or motor Push/pull by a person

The difference between conservative and non-conservative forces: Non-conservative forces transfer energy to non-useful containers I can’t really use thermal energy to do much in terms of motion Consider a possible definition of “useful energy”: the ability to do work Gravitational potential energy can be used to do work Thermal energy cannot be used to do work Thus gravity is a conservative force, because this force maintains the usefulness of the energy as it stores it potentially Friction is a non-conservative force, because this force does not maintain the usefulness of energy as it stores it thermally

You push down with a force of 10 N on your friend’s car which is stuck in the snow. By pushing down you increase the normal force and, therefore, the friction force. The car is now able to get out and moves a distance 5m. How much work did you do? None! There was a force but no Δx! If you change the FN (push down) you change the frictional force

A B C D Rank the amount of work done from positive to negative. 𝐹 𝐹 𝐹 Δ𝑥 Δ𝑥 Δ𝑥 Δ𝑥 cadb

When the rubber bands are stretched, which rubber band has more elastic energy or are they the same?

Imagine a ball on a track where no energy is transferred between the ball and the track or between the ball and the air around it (frictionless/air resistanceless).  The ball starts from rest at the position labeled Start and moves along the track toward Positions 1, 2, and 3. What is the highest position the ball achieves?

Same question – air resistanceless and frictionless environment Same question – air resistanceless and frictionless environment. Does the ball make it to position 2?

Which book has less gravitational potential energy or are they the same? (Consider the reference point to be the floor.) Which is faster if dropped?

Law of Conservation of Energy and the Work – Energy Principle Total Work (due to only conservative forces; frictionless/air resistanceless environments) always equals zero Essentially… Initial Energy = Final Energy

Complete this in your notes A 70 kg skier starts from rest from the top of a frictionless 35° incline with a vertical height of 20 m. What is the skier’s speed just before she enters the plane? Draw a energy bar chart to help you organize your energy storage accounts. Set Einitial = Efinal 19.8 m/s

By how much will the spring compress? Draw a energy bar chart to help you organize your energy storage accounts. Set Einitial = Efinal 0.54 m

The rate at which work is done or energy is consumed. Power The rate at which work is done or energy is consumed.

Which does the most work? Which is the most powerful?

Power = Work / time

Units Work is measured in Joules. Time is measure in seconds.

Common Metric Prefixes

No matter what the problem says, you must use “standard” units in the equation. Distance – meters (m) Time – seconds (s) Force – Newtons (N) Mass – kilograms (kg) Velocity – meters per second (m/s) Power – Watts (W) Work – Joules (J)

James Watt

Watts The unit was names for James Watt, the inventor of the steam engine. Watts engine was better than the current method getting work done (horses). To help sell engines, Watt developed a way to “rate” their abilities.

Rearranging the Power Formula The power formula can be rearranged into three common forms. They are mathematically equal, but they look different and contain different variables. They are useful for different problems, depending on what is “given” in the problem.

Relates Power to Work and Time. Relates Power to Force, Distance and Time. Relates Power to Force and Velocity.

How long will it take a motor, rated at 200 W, to do 1800 Joules of work?

How much power is used to lift a 15 N object upward 4 meters in 20 seconds?

At what speed can a 1000 W motor lift a 25-kg mass?

FYI 1 N is about ¼ pound May be helpful someday