Let's start by changing teams please write down the country that you would MOST like to visit, anywhere on the planet on a small strip of paper.
OPENING QUESTIONS: Work is defined in physics to be a force acting through a displacement.
With that in mind, please work (get it?) with your NEW team to answer the following questions:
What are the UNITS of work?
How do you suppose WORK might be related to ENERGY? (at least in the physics sense).
What are the UNITS of energy?
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 during 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 during today's class.
WORDS O' THE DAY:
- Work (Force through displacement, usually measured in Nm)
- Energy (measured in Joules)
Power (measured in Joules/sec = Watts)
FORMULAE OBJECTUS:
Work = ∆E = Fd = Fdcosθ
KE = 1/2mv2
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 = F·cosθ
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Moving Right Along!
Not surprisingly (I hope) the units of measure for work are:
Nm (Newton meters)
Do please make sure to note the upper/lower cases!
Notice that if we break down down Newton meters we get:
(kgm/s2)(m)
Which equals:
(kgm2/s2)
Which equals Joules.... right?
Well, not really.
We typically (but not always... *sigh*) refer to work done in terms of Nm and energy gained, lost or expended in terms of Joules (J).
Take a moment to discuss that mathematical equation with your group... what is the significance of the 'cosθ' term?
Does THIS picture help?
Let's put some data to those pictures and see what's what:
a) A person exerts 2.5 N of force on the eraser at an angle of 65 degrees to the horizontal for a total of .575 meters. How much work did that person do?
b) A person exerts 2.5 N of force on the eraser at angle of 35 degrees to the horizontal for a total of .575 meters. How much work did that person do?
c) A person exerts 2.5 N of force directly downwards on the eraser for 15 seconds. How much work did the person do?
d) Use ONE of the above as a starting point. Do a quick sketch or write a description to show how you can exert force on that eraser, move the eraser and yet do no work at all.
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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 meters...
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ANSWER: Area under the 'curve'!
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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 intervals.... Let's give it a try. Work with your group to calculate the TOTAL work done on the object shown in the graph above.
For those of you with calculus in your future, we can actually find the area under a curve using integration (not to worry, we won't get into that in this course)
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Let's say you are helping some friends build a wall on their back 40. You push a VERY heavy load of concrete 110 meters to the east. Your friend apologizes but notes that you went the wrong way, so you have to push the wheelbarrow 110 meters back to the west.
Using physics terms, explain why you did no work at all!
Let's say that you just built a 3.00 meter wall and you have to hold it up for 14 hours to let it cure. Being a good friend you struggle mightily and (somehow) manage to hold up the wall. Your arms and legs are shaking, you're breathing hard and you feel like you're going to pass out.
Using physics terms, explain why you did no work at all!
What are the Standard International (SI) units for work?
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This graphic comes to us from the fine folks at the University of Georgia "Hyperphysics" web site (http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html). It *can* get a wee bit dicey so take away JUST AS MUCH info as makes sense to you!
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:
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COURSEWORK (problems #1 - #5 on the physics classroom):
Notes:
The author typically does NOT include angles in sig figs but WE do!
- Problems #1 & #2 are fairly basic
- Problem #3 introduces the concept of negative work
- Problem #4 is fairly basic
- Problem #5 requires a CLOSE READING of the problem
- Problems #6 & 7 are fairly basic
- Problem #8 is fairly tough
- Problem #9 is an elegant beast
And my worked solutions are HERE