OPENING QUESTIONS:

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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 = mg

WORK O' THE DAY:

HERE BE THE EQUATIONS OF PHYSICS SO FAR:

Type	Equation (1)	Equation (2)	Equation (3)
Motion (kinematics)	y_f = y_i + v_iyt+ 1/2at_y²	v_f = v_i + at_y	v²_f - v_²i=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 = ma_x	∑F = ma_y
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 =1/2k_ix²-1/2k_fx²

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WORK O' THE DAY:

Consider the case of equation 7.24 (page 197):

W_int = U_i - U_f = - ∆U

With equation 7.20 (on page 192)

W_ext = ∆U

There is some obvious confusion here... let's see if we can zero in on that.

Those two equations consider whether the work done on the object is directed from OUTSIDE the system (external) or occurs INSIDE the system in question (internal)

Soo.... what the heck does THAT mean???

What is a very good place to go when we have frustrations of such a nature?

KHAN ACADEMY!!!>

Yay!

Personally I *much* prefer figuring out the physics of the situation and assigning positive or negative values based on my understanding.... that is just what the Khan Academy video suggests...

However, a more *standard* <yechhh> view of things follows:

Internal work represents work done by members of a closed system on each other...

External work represents word done on a system by an "agent" OUTSIDE of that system...

CONSERVATIVE FORCES:

Take a moment to read about Conservative Forces on page 197.

Get ready to brief the class and answer questions on that.

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Let's take a gander at THIS (courtesy of http://tutor4physics.com/positivenegativework.htm:)

Note: Color emphasis and paragraph formatting are mine

Positive and Negative Work

We have seen the situations when the work done is zero. Work done can also be positive or negative. When 0^o <= θ < 90^o, work done is positive as Cos θ is positive.

Work done by a force is positive if the applied force has a component in the direction of the displacement.

When a body is falling down, the force of gravitation is acting in the downward direction. The displacement is also in the downward direction. Thus the work done by the gravitational force on the body is positive.

Consider the same body being lifted in the upward direction. In this case, the force of gravity is acting in the downward direction. But, the displacement of the body is in the upward direction. Since the angle between the force and displacement is 180^o, the work done by the gravitational force on the body is negative.

Note, that in this case the work done by the applied force which is lifting the body up is positive since the angle between the applied force and displacement is positive.

Thus work done by the applied force which is lifting up the body is positive since the angle between the applied force and displacement is positive. Thus work done is negative when 90^o < θ <= 180^o as Cos θ is negative. We can also say that work done by a force is negative if the applied force has a component in a direction opposite to the displacement.

Similarly, frictional force is always opposing the relative motion of the body. When a body is dragged along a rough surface, the frictional force will be acting in the direction opposite to the displacement. The angle between the frictional force and the displacement of the body will be 180^o. Thus, the work done by the frictional force will be negative.

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Let's see if we can turn that into everyday English:

A conservative force acting on an object is universally consistent with whatever path that object takes.

For example, gravity is a conservative force because it really doesn't matter how we get to the top of a building... the potential energy we have at the top of the building is still the same.

Friction is NOT a conservative force because the path we take DOES change how the energy is transferred between the sliding object and the surface it slides over

So... in summary:

The work generated (or energy transferred) by a conservative force or against a conservative force is path independant (think gravity)

The work generated (or energy transferred) by a non-conservative force or against a non-conservative force is very path dependant (think friction)

THEREFORE: When work is done by a conservative force that work represents the transfer of energy between two parts of the same system: (see equation 7.26 & 7.29).

Continue to think of the situation independently... if we take away energy from an object, we've done negative work. If we add energy to an object we do positive work.

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HOMEWORK:

Problems for 7.8 starting on page 208: problems 48, 49, 51 (hint: when you see a mathematical equation-- be prepared to use calc (not always true but a good hint nonetheless)

ANSWERS:

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