OPENING QUESTIONS: A friend of mine teaches chemistry at a University in Illinois. Quantitative Analysis is a course where 100% of a student's grade is determined by how precisely that student measures samples in the lab.
He likes to tell the story of the time a student turned in a final analysis that concluded that a sample was 115% copper.
My friend wrote the following comment:
"That sample is unusually pure.... <grade> F"
Why did my friend fail that student?
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Now let's talk about your rotational motion quiz
Now let's revisit your labs (there were a few unanswered questions yesterday)
LEARNING OBJECTIVES:
1) I will be able to calculate the work done by a specified constant force on an object that undergoes a specified displacement after today's class.
2) I will be able to relate the work done by a force to the area under a straight line graph of constant force vs displacement graph after today's class.
3) I will be able to relate the work done by a force to the area under a curve of variable force vs displacement graph after today's class.
WORDS O' THE DAY:
- Work (Force through displacement)
- Dot Product
- Scalar Product
WORK O' THE DAY:
- Work is defined to be the force exerted on (or by) an object through a displacement
- Qualitatively: Work is defined to be the transfer of energy
- Mathematically: Work is defined as F · Displacement. Because the maximum amount of work done on an object occurs when the force is applied directly in the direction of motion (OR directly opposed to motion) we further quantify that to:
W = Fxcos(θ)
Not surprisingly (I hope) the units of measure for work are:
Nm (Newton Meters)
And, like so much of physics, once we define a new quantity we rename it. In this case the unit of measure for work is:
JOULE (J)
Take a moment to discuss that mathematical equation with your group... what is the significance of the 'cosθ' term?
Does THIS picture help?
Why is it soooo important to note that that equation only applies to the application of a CONSTANT force?
The graph of a CONSTANT force vs displacement graph would be kind of boring (notice non-trivial title, x and y labels AND units):
Talk with your group for a moment and suggest a method for determining the amount of work done on this object during 4 and 6 seconds...
ANSWER: Area under the 'curve'!
Now suggest a method for finding the amount of work done on an object when that object experiences a force that changes over time (a variable force).
Perhaps a graph will help? (Notice Trivial Title.... boo! hiss! <I found this on an IB site)
Hopefully a method quickly presents itself for finding the amount of work done at various intervels....
Now let's make a suggestion for how to handle the very non-trivial case where force and or displacement is variable in a not so linear kinda way:
Which presents WHICH sort of solution?
YES! YES! YES! Integration!!!!
This graphic comes to us from the fine folks at the University of Georgia "Hyperphysics" website (http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)
Key Thought:
Work is ALWAYS done BY a force ON an object. It is best to identify the system that supplies the force and the object that experiences the force:
"The work done by the hammer on the nail"
Work through example 7.1 on page 180:
- Read the problem description on page 180
- Write down your initial conditions
- Do a qualitative analysis on the situation
- Draw a sketch
- Solve the problem
Check the book for your answer
Do problem 3 & 5 on page 204 & 205
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- Review classwork
- Read about scalar ("dot") products