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homeschoolsciencegeek

September 2017

Students were asked to read 2.1 Seesaws in How Things Work, or Ch 11: Rotation in the Cartoon Guide to Physics and watch the following videos before class.  I really enjoy Doc Schuster’s physics videos.

Before we started the lab, I had cut out some very weird shapes out of cardboard and asked the students to find the center of mass of the shapes.  Most knew to try to balance the shape on a finger and the center of mass would be the spot above their finger when it was balanced.  But some of the shapes didn’t work for this, like the one on the left in the photo below. Another way to find the center of mass is to hang the object on a nail or tack and then let a string with a weight (plumb line) hang down as well.  The center of mass of the object will fall on this line.  If you do this from two points (2nd almost horizontal line was found by hanging the shape from the hole on the right), the center of mass can be found at the intersection of the two lines.  For this oddball shape below we see the center of mass is not in the object at all, which is why it was impossible to balance it on a finger. I also had a bird balancing toy out and handed out a paper craft from Ellen McHenry’s website, so the students could make their own balancing bird. The lab for today was one I did before, but I think we got it to work a bit better this time. Students tied a rubber stopper to a string, fed the string through an acrylic straw and then tied a weight to the other end of the string.  By holding on to the straw and letting the string slide through the straw, the students could make the stopper go in a circle of radius r, above their heads at constant speed, v (or at least that’s the goal).  The weight on the end of the string is the centripetal force and is measured using a spring scale.  For uniform circular motion  Fc = mac = mv2/r.  We can rearrange that so v2 = macr. In this lab we measures the velocity of the rubber stopper being swung around at different values of the radius, r.  To measure the speed of the stopper we need to know the distance traveled (d = 2 π r x 10) as it completes 10 revolutions and the time, t, it takes to travel that distance: v = d/t.  Since its a bit difficult to measure the time of 10 revolutions, students did each measurement 3 times and used the average time to calculate speed.  Once they had the speed, v, they found v2 and graphed it as a function of the radius, r. Data should form a line (y= mx + b, v2 = y, m(slope) =ac, x = r and b(y-intercept) = 0 ) with a slope equal to the centripetal acceleration.  The value they get from their slope should be the same as Fc / m=ac  when they plug in the force of the weights hanging on the string in Newtons and the mass of the stopper in kg (measured on a triple beam balance).

Since there were a lot of calculations in this lab, I encouraged the students to try using a spreadsheet on their tablets or smart phone.  Most had never used a spreadsheet before so its a good learning experience.  (I frequently get frustrated using Numbers  to make graphs and found this website which explained a problem I always had.) Here’s a graph of one set of data and the best line drawn through the data points and the origin. The slope of this graph is 53 m/s2 which is very close to the value of acceleration found by taking the known force and dividing by the mass of the stopper (54 m/s2).

This lab worked much better this time and I think using the acrylic straws instead of empty pens helped, as did using a larger centripetal force (0.7-1.0 N).

We started class today with the following videos:

And we can’t talk about the vomit comet and feeling weightless without watching OK Go.

For the lab I used Activity #4, Listen to gravity, like Galileo did, from “Gravity” a physics lab from Ellen McHenry’s Basement Workshop.  Students tied washers to a piece of string, either equally spaced (50 cm) or with the distance between washers increasing (10 cm, 30 cm, 50 cm, 70 cm, 90 cm) as they tied them to the string.  If you hold one end of the string up high (standing on a chair/stepstool) and let it hang to the floor, what do you think you will hear when you drop the string with equally spaced washers? Will the noises be equally spaced in time or when they the ‘dings’ get closer together as the string/washers accelerate?  What about the second string with the washers spread out at increasing distances?  Will the dings be further apart as the string falls, or when they will be equally spaced?  After the students think about it a bit… and untangle their string of washers (this took almost as much time as tying them all on to the string) they actually drop them and listen to the pattern of sound the washers make.  We dropped the string of washers on to a cookie sheet to make a nice loud ding.

The string with the equally spaced washers hit the ground at shorter and shorter time intervals since the washers that fell longer are accelerating for a longer period of time and going faster when they travel the last 50 cm before hitting the cookie sheet.  The washers that were tied at greater and greater distances hit the ground at roughly equal time intervals. Here’s a slow motion video of the string with equally spaced washers.

Slow motion video of the second string, with washers at increasing distances but hitting the pan at almost equal time intervals.

Its kind of hard to hear when you’re doing the actual experiment so having someone take a movie so you can watch/listen in slow motion is useful.

I wanted to make sure the students understood gravitational potential energy and kinetic energy so I had them measure the potential energy and kinetic energy of a pendulum bob at different times during its swing.  When the pendulum bob is at its highest point, A, then all its energy is potential energy (PE = mgh) because its velocity is zero (and therefore its KE = 0)  for the split second before it falls back down again.  At point C, the pendulum is moving at the greatest velocity and therefore has its maximum kinetic energy (1/2 m v2).  It also has its lowest potential energy at  point C, equal to zero if we choose that position as our origin (x=0,y=0).  So at point A all the energy is potential energy and as the pendulum swings through point B it will have both potential and kinetic energy, but by the time it reaches point C all the potential energy has been converted to kinetic energy. Data recorded with Video Physics App.

The top graph below shows the horizontal, x (red), and vertical, (blue), positions as a function of time. The bottom graph shows the velocities in the (red) and (blue) directions. I marked the location of points A, B and C on the graph – again you can see at point A that the velocities are zero and the positions are at their maximum/minimum values and at point C the positions are both zero but the velocity in the x direction is at its maximum.  The velocity in the y or vertical direction is also zero at point C because the pendulum bob is really only moving horizontally at that moment. At point B, and you can pick any point between A and C, the pendulum has both potential and kinetic energies. In the graphical analysis app you can click on a data point and the app shows you the values – those are the numbers in the white boxes. This is handy when trying to read values off the graph, especially when the app doesn’t label the tick marks.

Students made a table in their lab books and recorded the height (y) of the pendulum at the three points, as well as the velocities (x & y).  Then they calculated the potential energy at each point (mgh) and the kinetic energy (1/2 m v2), m = mass of the pendulum bob which was 0.05 kg.  Finally they calculated the total energy (PE + KE) at each point and hopefully found the numbers to be roughly the same.  For the data shown above we got 0.074J for the total energy at each point.

This is a nice lab but the students get really confused looking at the graphs and confusing position for velocity, x for y, etc.  Another problem that popped up in a couple of groups was students didn’t put the origin at the bottom of the swing (C),  so when the pendulum was at C the graph showed a nonzero y-position.  You also need to make sure you mark enough points (Video Physics app)  to catch the pendulum turning around (A) and coming back through the lowest point (C).

Without even doing any math, but just looking at the graphs and realizing that the data for the height of the pendulum, y (blue dots), is proportional to the PE, reaches its maximum at the same time the velocities, and therefore KE, both go to zero.  As the horizontal velocity (red data in bottom graph) reaches its maximum value, and therefore KE will be its maximum, you can see the height (and therefore PE)  is also zero.  As one goes up the other goes down.  I guess one way to simple the graphs would have been to have them just plot vertical position (y) and horizontal velocity as a function of time and just do points A and C.  Something to think about the next time I do this lab.

I asked the students to watch these videos before class.

Lesson 3 in Science Fusion Module I is about forces and Newton’s Laws of Motion so I started class by talking about forces and showing a few videos.  The first two lego stop motion movies were made by students (not mine).

I also showed this video of Felix Baumgartner and pointed out his velocity to the students and we watched as it quickly increased to over 800 mph.  But after a few minutes he started to slow down until he reached about 130 mph and he stayed roughly at that speed until he opened his parachute.

I asked the students why did his speed slow down as he was falling?  We talked about air resistance and how the thickness of the air and therefore the force of air resistance changes with altitude.  The force of air resistance also depends on your speed – think about trying to run in waist high water versus walking slowly, its much more difficult to run through the water than walk – same thing with air resistance.  At some point as you fall the force of gravity and the force of air resistance balance out so that the net force on you is zero, therefore you’re acceleration is zero (F=ma)  and you fall at constant velocity.

To demonstrate Newton’s 1st law I built a lego car with a smooth top so the minifigure sitting on top could move easily.  I gave the car a push and when it hits a rock the passenger continues traveling until she hits the rock herself.  I took the video below with the video physics app and if you play it at a slower speed (hit settings and put play speed at 0.5) you can see the motion a little easier.  The red dots show you the position of the minifigure’s head in each frame. We did Unit 1, Lesson 3 S.T.E.M. lab, Newton’s Laws of Motion, which means we built straw rockets.   Students wrapped paper around a stiff plastic straw and then taped the paper to make the body of the rocket.  They then twisted the end to make a  cone on one end.  Some added fins and other stuff to their rockets.  They also tried using more or less paper, thicker paper, etc.  To launch the rockets we had stiff straws in plastic bottles with clay holding them in place and blocking air flow, so that when you squeeze the bottle air shoots out of the straw.  We had a variety of plastic bottles to try.  The goal was to get their rocket to travel the furthest.  I believe the longest flight was 140 some inches. The student above has put fins on his rocket and is about to launch it by squeezing the air out of the bottle.  The air exits the bottle and pushes on the front end of the straw rocket accelerating it.

I actually spent the first hour of today’s class lecturing.  I wanted to make sure the students really understood velocity and acceleration so we did a few more problems with falling objects, talked about Felix Baumgartner free falling from 39,000 meters (video was in last R2 Physics post) and why his velocity actually decreased as he fell once hit the atmosphere (air resistance).  We also talked about projectiles and since most of the class is also in my 4H Archery project we calculated how much an arrow falls when traveling from a bow to the target. If we shoot the arrow so it leaves the bow only with a horizontal velocity – aimed straight at the center of the target, then the amount of time the arrow is in flight only depends on it’s initial velocity and the distance to the target.  A typical arrow speed for an arrow shot from a recurve bow is 50 m/s and for a compound bow (like the one shown in the photo), arrow speeds are closer to 110 m/s.  For this problem we put the target 30 meters from the archer (same as in the photo).  If the arrow is traveling with a constant 50m/s in the horizontal direction, it will take  t = x/v = 30m/(50m/s)  = 0.6 s for the arrow to reach the target.  Now we can consider the vertical problem, if we drop an arrow, how far does it fall in 0.6 seconds?  y =  1/2 a t2 = 1/2 (9.8 m/s2 ) (0.6s)2 = 1.7 m. So an arrow shot from a recurve at 50m/s will drop from the horizontal 1.7 meters before hitting the target at 30 meters, which means it will probably hit the ground before it hits the target! A compound shooting an arrow at 110 m/s fairs a bit better dropping only 0.4 meters before it hits the target. I actually found a website that goes into this detail: Arrow Flight Fact or Fiction: one pin to 40 yards.

Then we moved on section 1.3 in the text, How Things Work: The Physics of Everyday Life by Bloomfield and talked about potential energy, kinetic energy and work.  I sent the following videos for students to watch before class.

I found this Inclined Plane Lab on the web – the link will download the pdf.  We used my dry erase boards as the ramps and some wooden blocks with eye hooks screwed into them.  I also have a variety of spring scales that students could use to measure the force on the blocks, including a new digital one from Vernier, Go Direct Force and Acceleration Sensor.The Go Direct sensor works directly with the Graphical Anaylsis App so you can record the force measured by the sensor as you pull it up the ramp.   In the photo below you can see a student pulling the block with a spring scale.  Go Direct Force & Acceleration Sensor

Students measured the force required to pull the block up a ramp at different heights (10, 20, 30, 40 and 50 cm).  They also used the spring scales to measure the force of gravity (weight) by just hanging the block from the spring scale.  As the steepness of the ramp increased they found they needed  a larger force to pull the block up the ramp.  Students also calculated the force that was required to pull the block and found it was smaller than the force actually required.  This was because we ignored friction in our calculation, so the difference between the measured and calculated forces was due to the force of friction between the block and the board.  Once they had all their data they plotted both the measured and calculated forces as a function of ramp height. HOLLYWOOD ( and all that )

hanging out and hanging on in life and the movies (listening to great music)

Learn from Yesterday, live for today, hope for tomorrow. The important thing is not stop questioning ~Albert Einstein

graph paper diaries

because some of us need a few more lines to keep everything straight

Evan's Space

Wonders of Physics

Gas station without pumps

musings on life as a university professor

George Lakoff

George Lakoff has retired as Distinguished Professor of Cognitive Science and Linguistics at the University of California at Berkeley. He is now Director of the Center for the Neural Mind & Society (cnms.berkeley.edu).