LEARNING OBJECTIVES:

1) I will be able to use the concept of gravitational potential energy to solve basic energy equations after today's class.

WORDS O' THE DAY:

• Work (Force through displacement)
• Dot Product ("scalar product")
• Work ("Newton meter (Nm)" or "Joule (J) ")
• RESTORATIVE force (results in acceleration in the opposite direction of the applied force)

FORMULAE OBJECTUS:

• Work = fdcosθ (including the integral form)
• F = -kx (note the negative sign)
• Potential Energy of a spring = 1/2kx²
• Kinetic Energy of an object = 1/2mv²
• Gravitational Potential Energy = U = mgh

A change and/or transfer of energy requires WORK, or to put it perhaps a bit more succinctly, WORK is defined as a transfer of ENERGY

WORK O' THE DAY:

Let's take a moment to revisit the spring-between-two-blocks part of last Friday's homework.

The question really boils down to.... what?

Also, let's take a gander at why it is so helpful (AND expedient!!) to solve problems using the isolate/substitute/solve model.

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Recall from the previous unit that the Newton's Second is often written quantitatively as F = ma.

Also note that from last week we learned that the energy exerted on a spring (to compress it) or by a spring (as it decompresses) is Hooke's Law: F = -kx

Is the "F" in each equation the same sort of F.

In otherwords, can we substitute one equation in for the other on an "as needed" sorta basis?

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ANSWER:

YES... force is force is force...

One of the things that often befuddles Newbies in physics is the seemingly ad hoc way that we sometimes substitute one equation for another.

Get used to that.

One of the keys to understanding physics is to 'cross over' from one application (for example Newton's Laws (dynamics) with the motion of a spring (as shown by Hooke's Law) or even gravitational attraction or rotational dynamics.

The important thing to keep track of is that there are certain equations that will weave their way in and out of our conversations of physics.

If I were you, I'd have a special page in my notes that says something like:

HERE BE THE GONZO EQUATIONS OF PHYSICS:

Type	Equation (1)	Equation (2)	Equation (3)
Motion (kinematics)	yf = yi + viyt+ 1/2aty2	vf = vi + aty	v2f - v2i =2ay
You should be VERY cofortable understanding those are Y dimension equations and that the x direction equations have exactly the same format
Forces (dynamics)	∑F = max	∑F = may
Work	Work = F ∙ r (for constant force and constant displacement)	Work = ∫F dr (for variable forces and/or variable displacements
You should be *VERY* comfortable explaining why the "dot" product for calculating work takes the form ABcosθ
Hooke's Law	F = -kx	W =1/2kix2-1/2kfx2

NEW STUFF

Potential Energy is defined to exist when a system exists where energy can be stored.

Discuss with your groups please...Give an everyday example where energy is stored...

 

 

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Energy can be stored in:

• a battery (chemical potential energy)
• a compressed spring
• water stored behind a dam

Now let's consider the last example:

How is the POTENTIAL energy of the water stored behind a damn converted into actual energy for us when we plug in our microwave to burn popcorn (electrical energy)

Of particular interest to us in this unit is GRAVITATIONAL POTENTIAL ENERGY...

Let's have someone come up and lead our conversation....

Energy created in this fashion is fairly cheap to produce (unless of course you're a salmon, but that's another story), and very plentiful inthe Northwest.

Take a look at the Grand Coulee Power Plant:

The falling water (converted from Gravitational Potential Energy of the water just sitting behind the damn into kinetic energy of falling water) spins the blades of the turbine (and as we'll see next semester) transfers that kinetic energy into electric energy that then flows down the wires to our homes.

If you're interested, here are the specs.

Those turbines generate 6800 million watts of energy (we'll talk about watts very soon, but for now think of a watt as Nm/sec or Joules/sec)

As a general rule of thumb, one megawatt (1 million watts) is enough energy to power about 2500 average American homes.

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ANYWHO.....

Gravitational Potential Energy is found very easily by the following equation:

U_g = mgy

I HAVE NO IDEA who came up with "U" to describe potential energy, but we're stuck with it, so add it to your GONZO list.

Not surprisingly (I hope)

When the only work done on or by a system involves potential energy, the change in potential energy of an object in that system is given as:

W = mgy_f - mgy_i

where y is the change in the displacement of the object in meters

or, more succinctly:

W = ∆U

Take a gander at the equation 7.8 on page 193.

1. Do a sketch of the situation
2. Write down the initial conditions
3. Close the book
4. Write a quick qualitative analysis of the situation
5. Write down the formula that governs this situation
6. Substitute your initial conditions into your formula
7. Solve the problem
8. Check your answer in the book

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HOMEWORK

• Objective problems starting on page 203: problem 16
• Problems for 7.5 starting on page 206: problems 31, 35, 38