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**How do Sailboats Work? Vector Addition Brandon Hoffman General Physics**

Houghton College I am going to use a presentation on sailboats and vectors as an example of correct and incorrect ways of giving a PowerPoint presentation. Usually, the title slide is up while someone else introduces you and your talk. Therefore, little (if anything) needs to be said by you for this slide.

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**Background and Motivation Theory Experimental Procedure Results **

Outline Background and Motivation Theory Experimental Procedure Results Conclusions Here is an example of a complete failure as an outline. Every science presentation contains these sections, so it is a waste of people’s time to put this up.

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**Why Sailboats? Vector Addition Sailcart Experiment Outline**

This is a little better. Notice there are less bullets, less words, and the phrases are directly related to this presentation. However, there are no pictures on this slide, so it is still much of a waste.

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**Why Sailboats? Vector Addition Sailcart Experiment Outline B A A + B **

From these pictures, one can see how the vectors are added together and how the experiment was performed. The audience now has a good idea of what you will be talking about. This is a decent slide. BUT, if the pictures are worth more than the words, why have the words at all? 30°

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**Why Sailboats? Outline B A A + B **

Here is a reasonable outline slide. While displaying this slide, you might say: “I will start by talking about why we care about sailboats. Then I will explain head-to-tail vector addition, in the context of our experiment. Finally, I will describe the sailcart experiment and give the results of that experiment. It turns out that the acceleration of the cart is proportional to the cosine of the angle between the sail and the direction of motion, theta.” Notice what I just did there: 1. I walked over to the screen and pointed to what I was talking about. Purposeful motion pulls in your audience and gives them direction. 2. I explained what was on the screen. 3. I mentioned the results. Never be afraid to give away the ending. Your presentation is about understanding, not mystery. Once you have given the outline, its on to the motivation… 30°

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**Practice using vectors as representations of forces. **

Motivation Practice using vectors as representations of forces. Learn how vectors add together. Improve trigonometry skills. “The motivation for this experiment is to: Practice using vectors as representations of forces, Learn how vectors…” Wait!!! READING A SLIDE IS THE ABSOLUTE WORST POSSIBLE THING YOU CAN DO!!!! Of course, this would not be a temptation if the slide were not a bulleted list of sentences. Never, ever, ever do this!!! EVER!!!

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**Vector Addition Applications**

www. img.sparknotes.com www. Astronomyforbeginners.com “Sailboats are a good example for studying the addition of vectors, which is a valuable tool for measuring a great number of things, including position, motion, forces, and electric fields.” Notice a few things: 1. There were virtually no words on the motivation slide. 2. The entire motivation took less than 10 seconds. Get to the good stuff. 3. I again walked over to the screen and pointed to what I was talking about. www. free-online-private-ground-school.com

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**Theory Ftotal = Ffan on cart + Ftrack on cart**

= [(Ffan on cart + Ftrack on cart) cos()] i + [(Ffan on cart + Ftrack on cart)sin ()] j = [(Ffan on cart) cos()] i It is far too common to see lists of equations on a slide. Top scientists in your field will rarely, if ever, understand this junk! Never do this!

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**Forces on a Sailcart Fwind on cart Ftotal 30° Ftrack on cart**

“To model a sailboat, a cart with a sail was placed on a straight track. A fan blew air at an angle of 30 degrees from the plane of the sail, defined by the normal vector. The force of the wind on the sail is always along the plane of the sail. The track then keeps the cart from moving sideways by applying a force that counteracts the sideways component of the force of wind. Notice that if we position the vectors head to tail, we see that the sum of the two is pointed along the track.” Notice: the animation was simple, but brought things in as I mentioned them.

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**Addition of Vectors Ftotal = Fwind on cart + Ftrack on cart**

“Looking just at the force vectors, we see that the total force on the cart is the sum of the forces due to the wind and the track. Because these three vectors form a right triangle, we can use basic trigonometry, noticing that the magnitude of the total force, which is adjacent to theta, is equal to the hypotenuse multiplied by the cosine of theta.” Notice: 1. Virtually no words or equations were needed, only pictures. 2. The theory was described in the context of the experiment itself. 3. Again, I walked to the screen and pointed as I talked. Ftotal Ftotal = Fwind on cart + Ftrack on cart = [Fwind on cart cos()] i

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**Procedure Angle between fan and sail kept constant at 30°**

Varied angle between sail and track. Measured acceleration of cart. Compared to theoretical prediction. “For my procedure, the angle between fan and sail was kept constant at 30°. I varied the angle between…” STOP!!! Words, words words! This slide is horrifying!!! And to make it worse, I was reading it!!! Not only that, but without a good picture, I had to use hand motions! Aaaauugh!!! How about a picture of my experiment.

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**Apparatus http://webapps.lsa.umich.edu**

Whoops! This is not MY experiment.

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Apparatus This is a picture of my apparatus, but nothing is labeled. It is, therefore, completely useless.

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**Apparatus fan sailcart track**

Even though everything is labeled, you still must point to and explain each part. For instance, “Here is a picture of my apparatus. The sailcart was placed on a motion track. The fan was positioned such that the wind would blow at a 30 degree angle to the plane of the sail.” Notice: I pointed to each thing as I mentioned it.

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**The Sailcart Experiment**

30° “Here is a diagram of the experiment. The wind direction was kept constant at 30 degrees from the plane of the sail. A number of trials were conducted with theta ranging between…” Angle between fan and sail held constant at 30

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**The Sailcart Experiment**

30° 30° = 90° 30° 30° 30° = -30° “…-30 degrees and 90 degrees. Let’s look at that one more time while highlighting the force of the wind on the track.” varied between -30 and 90

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**The Sailcart Experiment**

Ffan on cart Ffan on cart Ffan on cart 30° Ffan on cart 30° 30° 30° 30° 30° Ffan on cart Ffan on cart “Notice that the force of the wind on the track always points forward, even if the wind itself moves backward. This is one way that a sailboat is able to sail into the wind.” Notice: Though the animation was not necessary, it was simple and useful. A statement at the bottom brings out the whole point of the slide (this statement is borderline too long). Force of fan on cart always points forward.

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**Cart Acceleration (cm/s2)**

Results Cart Mass (kg) Sail Angle (°) Cart Acceleration (cm/s2) 0.30 -30 34.6 40.0 30 60 20.0 75 10.4 90 0.60 17.3 10.0 5.2 0.90 11.5 13.3 6.7 3.5 “Here are the results of the sailcart experiment.”

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**Conclusion Wait!!! Did you get any of that previous slide???**

If you put up a table, you must: 1. Point to and explain EVERY column and row. 2. Explain any trends or highlights that the table shows. Let’s try that again.

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**Cart Acceleration (cm/s2)**

Results Cart Mass (kg) Sail Angle (°) Cart Acceleration (cm/s2) 0.30 -30 34.6 40.0 30 60 20.0 75 10.4 90 0.60 17.3 10.0 5.2 0.90 11.5 13.3 6.7 3.5 “Here are the results of the sailcart experiment. The entire experiment was done with carts of three different masses. For each mass, the angle, theta, between the sail and the track ranged from -30 to 90 degrees. You can see that the acceleration of the cart is directly proportional to the cosine of theta and inversely proportional to the mass of the cart.” Of course, you can’t see this because this a table, which is almost always a terrible, horrible, pointless way to display data.

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**Results “Here’s a graph of the results for one mass.”**

Unfortunately, there are not titles and no units, so the whole slide is completely worthless.

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Results This one has a title, but notice how it looks like it was pasted in from Excel? By removing both borders and using a textbox for the title…

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**Acceleration of Cart vs. Angle of Sail**

You get a graph that looks much more like part of the slide. Unfortunately, still no axis titles or units, so it is completely useless.

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**Acceleration of Cart vs. Angle of Sail**

Still no units. Completely useless.

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**Acceleration of Cart vs. Angle of Sail**

Finally, a decent graph. A simple statement about the trend might be helpful…

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**Acceleration of Cart vs. Angle of Sail**

When displaying a graph you must: 1. Explain the title of the graph. 2. Point to and explain each axis, including the units. 3. If multiple curves are displayed, explain each one individually. 4. Explain any trends or highlights displayed in the graph. For instance, “Here is a graph of the acceleration of the cart as a function of the angle, theta, between the sail and the track. The y axis is the acceleration of the cart in cm/s2 and the x axis is the angle, theta, in degrees. Notice how the acceleration is proportional to the cosine of theta.” Acceleration is directly proportional to cos().

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**Acceleration of Cart vs. Angle of Sail**

Here is an alternate version. “Here is a graph of the acceleration of the cart as a function of the angle, theta, between the sail and the track that one might display. The y axis is the acceleration of the cart in cm/s2, the x axis is the cosine of the angle, theta. Notice how the acceleration is proportional to the cosine of theta.” Acceleration is directly proportional to cos ().

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Conclusions By adding the vectors representing the various forces together in head-to-tail fashion, we can calculate the total force on the sailcart. Because this force is proportional to the acceleration of the sailcart, the motion can be determined. The acceleration of sailcart is directly proportional to the cosine of the angle between the sail and the direction of motion of the cart, assuming the angle between the fan and the sail is kept constant. “In conclusion, by adding the vectors representing the various forces together in head-to-tail fashion, we can…” Aaauugh!!! More words!!! More reading!!! Yuck!!!

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**Conclusions Vector addition can be used to predict sailboat motion.**

30° Ffan on cart Ftrack on cart Ftotal Vector addition can be used to predict sailboat motion. Acceleration of sailcart has cosine dependence. “In conclusion, by adding the force vectors together in head-to-tail fashion, I was able to determine the total force and, therefore, the acceleration of the sailcart. This type of vector addition will be useful for a variety of theoretical predictions. Also, the acceleration of the sailcart was directly proportional to the cosine of the angle between the sail and the track.” Notice that I am leaving this slide up. If I have references, they could be added to the slide, but you want your audience to continue thinking about your conclusions as long as possible.

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**How do Sailboats Work? Vector Addition Brandon Hoffman General Physics**

Houghton College I am going to use a presentation on sailboats and vectors as an example of correct and incorrect ways of giving a PowerPoint presentation. Usually, the title slide is up while someone else introduces you and your talk. Therefore, little (if anything) needs to be said by you for this slide.

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**Why Sailboats? Outline B A A + B **

Here is a reasonable outline slide. While displaying this slide, you might say: “I will start by talking about why we care about sailboats. Then I will explain head-to-tail vector addition, in the context of our experiment. Finally, I will describe the sailcart experiment and give the results of that experiment. It turns out that the acceleration of the cart is proportional to the angle between the sail and the direction of motion, theta.” Notice what I just did there: 1. I walked over to the screen and pointed to what I was talking about. Purposeful motion pulls in your audience and gives them direction. 2. I explained what was on the screen. 3. I mentioned the results. Never be afraid to give away the ending. Your presentation is about understanding, not mystery. Once you have given the outline, its on to the motivation… 30°

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**Everybody Loves Sailing**

“Because so many people go sailing each year, it would be a good idea to know how sailboats work.”

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**Vector Addition Applications**

www. img.sparknotes.com www. Astronomyforbeginners.com “Also, sailboats are a good example for studying the addition of vectors, which is a valuable tool for measuring a great number of things, including position, motion, forces, and electric fields.” Notice a few things: 1. There were virtually no words on the motivation slides. 2. The entire motivation took less than 20 seconds. Get to the good stuff. 3. I again walked over to the screen and pointed to what I was talking about. www. free-online-private-ground-school.com

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**Forces on a Sailcart Fwind on cart Ftotal 30° Ftrack on cart**

“To model a sailboat, a cart with a sail was placed on a straight track. A fan blew air at an angle of 30 degrees from the plane of the sail. The force of the wind on the sail is always along the plane of the sail. The track then keeps the cart from moving sideways by applying a force that counteracts the sideways component of the force of wind. Notice that if we position the vectors head to tail, we see that the sum of the two is pointed along the track.” Notice: the animation was simple, but brought things in as I mentioned them.

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**Addition of Vectors Ftotal = Fwind on cart + Ftrack on cart**

“Looking just at the force vectors, we see that the total force on the cart is the sum of the forces due to the wind and the track. Because these three vectors form a right triangle, we can use basic trigonometry, noticing that the magnitude of the total force, which is adjacent to theta, is equal to the hypotenuse multiplied by the cosine of theta.” Notice: 1. Virtually no words or equations were needed, only pictures. 2. The theory was described in the context of the experiment itself. 3. Again, I walked to the screen and pointed as I talked. Ftotal Ftotal = Fwind on cart + Ftrack on cart = [Fwind on cart cos()] i

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**Apparatus fan sailcart track**

Even though everything is labeled, you still must point to and explain each part. For instance, “Here is a picture of my apparatus. The sailcart was placed on a motion track. The fan was positioned such that the wind would blow at a 30 degree angle to the plane of the sail.” Notice: I pointed to each thing as I mentioned it. track

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**The Sailcart Experiment**

30° “Here is a diagram of the experiment. The wind direction was kept constant at 30 degrees from the plane of the sail. A number of trials were conducted with theta ranging between…”

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**The Sailcart Experiment**

30° 30° = 90° 30° 30° 30° = -30° “…-30 degrees and 90 degrees. Let’s look at that one more time while highlighting the force of the wind on the track.”

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**The Sailcart Experiment**

Ffan on cart Ffan on cart Ffan on cart 30° Ffan on cart 30° 30° 30° 30° 30° Ffan on cart Ffan on cart “Notice that the force of the wind on the track always points forward, even if the wind itself moves backward. This is how a sailboat is able to sail into the wind.” Notice: Though the animation was not necessary, it was simple and useful. A statement at the bottom brings out the whole point of the slide (this statement is borderline too long). Force of fan on cart always points forward.

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**Acceleration of Cart vs. Angle of Sail**

Here is an alternate version. “Here is a graph of the acceleration of the cart as a function of the angle, theta, between the sail and the track that one might display. The y axis is the acceleration of the cart in cm/s2, the x axis is the cosine of the angle, theta. Notice how the acceleration is proportional to the cosine of theta.” Acceleration is directly proportional to cos ().

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**Conclusions Vector addition can be used to predict sailboat motion.**

30° Ffan on cart Ftrack on cart Ftotal Vector addition can be used to predict sailboat motion. Acceleration of sailcart has cosine dependence. “In conclusion, by adding the force vectors together in head-to-tail fashion, I was able to determine the total force and, therefore, the acceleration of the sailcart. This type of vector addition will be useful for a variety of theoretical predictions. Also, the acceleration of the sailcart was directly proportional to the cosine of the angle between the sail and the track.” Notice that I am leaving this slide up. If I have references, they could be added to the slide as an animation, but you want your audience to continue thinking about your conclusions as long as possible.

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