Apologia Physics: Hooke's Law

Hooke's Law refers to the relationship between the force applied to a spring and the distance it stretches.  F = -k . x where F is the force, k is the relationship factor, and x is the distance.  k is negative to indicate that the spring pulls back in the opposite direction after it is pulled.  The force which pulls the spring back to its original position is call the restorative force.  A strong spring has a high k and a weak spring, the opposite.

To demonstrate Hooke's Law we set up a simple apparatus.  We attached a ruler to the end of a work table.  There must be a hole in the end of the ruler.  We used a paper clip to attach a spring to the ruler and let the spring hang straight down toward the floor.  We then attached different weights, we used coins, to the end of the spring and measured how far the spring stretched.  Plot the points with the weight on the y axis and the distance on the x axis as the UOM for k is Newtons/meter.  Fit a straight line to the data points.  The line should fit the data reasonably well as k should be linear.  We used weights of 300, 500, and 800 grams.  Be sure to use a spring that will stretch and rebound with the range of weights used.  A weak spring will stretch out and not rebound.  A strong spring will not stretch enough to measure the distance stretched.

Some springs are made to be compressed.  The coil springs on a car support the weight of the car and compress when a wheel hits a bump.  The spring absorbs some of the force from the bump on the wheel.  The spring then returns to its original height.  This makes the ride more comfortable for the passengers and allows the car to not be so upset by bumps which is especially important in a turn!

Apologia Physics: Impulse and the Egg Drop demonstration/competition

Impulse is the energy change to an object when a force is applied to an object in a short period of time.  Think about hitting a baseball with a bat. The ball changes direction and is hit out into the field owing to the application of force by the bat to the ball.  Conversely, think about dropping an egg on the floor.  The egg gains momentum as it falls to the floor and is suddenly stopped when it hits the floor.

We know that momentum is mass times velocity.  p=m.v  UOM typically kg.m/sec  There is no name for this UOM.

Newton's second law says that Force = mass.acceleration
Newton' third law says that for every action there is an equal and opposite reaction

We also know that acceleration = change in velocity/change in time
Therefore Force = m.change in velocity/change in time
which can also be stated as F=(mvfinal - mvinitial)/change in time
Force = change in momentum/change in time
which can be restated as change in momentum = Force .change in time

If you want to hit the baseball further, you swing the bat harder thus increasing force tand you also want to "follow thru" and maintain contact longer.  Both will increase momentum of the ball.

For the egg drop and egg throw, the change in momentum is the mass of the egg times the velocity at which you throw the egg or the speed of the egg as it hits the floor.  If we calculate this momentum and plug it into the impulse equation as a fixed amount, then our goal, if you don't want the egg to break is to increase the time thus decreasing the force.

The students will demonstrate this by catching a thrown egg with their bare hands, a cookie sheet, and a bed sheet.  For their Lab Report, they should give a background on impulse and momentum, procedure including how they reduced impulse so they could catch the egg without it cracking.

They will also construct an egg package which will cushion the landing of the egg.  We used bubble wrap, egg cartons, and lots of tape!  Be sure to leave a window in the container so that you can determine when the egg has cracked.  We dropped the egg from three, four, five, six, and seven feet.

Apologia Physics: Power

To start our chapter on Work and Energy we will perform the most fun lab of the year:
"Measuring your personal horsepower"

First some definitions:
Torque is the ability to perform work and is measured as newton-meters which are also called Joules.  In English measurement: foot-pounds.  Any measurement of weight and distance will do but these are the accepted units.  FYI, car guys sometimes argue over foot-pounds vs. pounds-feet.  No difference!

Work is moving some weight some distance.  No work is performed until an object has moved some distance!

Potential Energy is energy stored.  PE is a relative quantity.  If I hold a five kilogram weight two meters off the floor the PE is ten newton-meters or Joules relative to the floor.  PE = mass x gravity x height.  Unit of measure should be Newton-meters or Joules ( a Joule is Kg x M^2/sec^2)

Kinetic Energy is motion.  KE = 1/2 x mass x velocity^2   (velocity squared)

Total Energy = PE plus KE

The first law of Thermodynamics says energy cannot be created or destroyed, it can only change forms.  How is this useful?  In the design of roller coasters!

Power is work per unit of time.  Power is measured in Watts or Joules per second.

"Measuring your personal horsepower"
We will measure a person's horsepower by running up a set of stairs.
1-measure the person's mass in KG.   I weigh 150 pounds or 68.2 kg
2-measure one step in CM   One step is 8 inches or 20 cm
3-count the number of steps bottom to top.  Our basement stairs have 13 steps
4-calculate the total height of the stairway.  13 x 20 = 260 cm or 2.6 m
5-total work accomplished by walking up the stairs:  68.2kg x 2.6m = 1737 Joules
6-time it takes to run as fast as you can up the stairs.  take three trials and average.
It took me 5.2 seconds.  1737J/5.2sec=334 Watts
There are 760 watts in one horsepower so I have the equivalent of .45 hp

Note that if you walk up the stairs or run up the stairs the quantity of work is the same.  You lifted your mass from the bottom to the top of the stairs.  It takes more horsepower to run faster up the stairs.

There are many types of energy:
Mechanical energy - movement (or potential movement) of objects
Chemical energy - ionic bonds within a molecule (potential energy). when you break these bonds you get kinetic.  For example: gasoline reacts to a spark in your car's engine. heat and carbon (and other byproducts) are released.
Electrical energy - motion (or potential motion) of charged particles
Heat energy - energy is transferred from one object to another
All of these can be PE or KE except heat which is just KE

Biology lesson:  how does food become energy in your body?
1-you eat food.  potential chemical energy of the food gets stored in cells in your body (basically fat)
2-brain tells muscle cells to convert some of that energy to electrical energy
3-which moves your muscles

Light bulbs are rated in watts
a 100 watt light bulb burns 100 Joules of energy per second

What is a calorie?  A calorie is 4.18 Joules of energy
A food calorie is really 1000 calories.
If you consume 3000 calories per day you have about 145 watts of power
3000 cal x 4.18J/cal divided by (60x60x24) seconds per day

It is interesting to follow the conversion of energy in the operation of a typical electrical power generation facility.  What type of energy (mechanical,chemical, electrical, heat) is being used and at what stages in the operation is the energy potential or kinetic?  It is helpful general knowledge for the students to understand how electricity is created on a large scale.

A typical power plant uses a fuel source (coal, oil, natural gas) to heat water and make steam.  The steam is forced through a turbine (think of a fan with many small blades).  The turbine turns a generator which creates electricity.  The fuel is potential chemical energy.  When the fuel is burned, chemical energy is converted to kinetic mechanical energy in the turning of the turbine.  The turbine turns the generator which creates kinetic electrical energy.  The only potential energy in this system is the fuel before it is burned.

A nuclear power plant is similar but it is the nuclear reaction which creates the heat.

The cooling towers you see at a power plant expel heat from the system's components just as the radiator in a car keeps the engine from overheating.  There is often a lake near the power plant as it takes a considerable amount of water to flow through the cooling system, absorb excess heat, run through the cooling towers, and not raise the temperature of the lake significantly enough to harm the plants and fish.

Apologia Physics: Static Electricity

Static Electricity

We will not study this topic until Spring as the book does not start Electricity & Magnetism for another five chapters.  However, here in Virginia, it will be warm and humid in the Spring.   Moisture in the air neutralizes static electricity so Winter is a great time to perform various demonstrations related to static electricity.

Static electricity happens when electrons are stripped off a material giving one item a positive charge (electrons stripped off) and the material a negative charge (picked up the electrons).  This electroscope lab from Exploratorium works well--use Scotch tape or a premium brand.  See the picture below.  We were able to put a charge on the tape by applying it to the table then ripping off the tape.   We were able to put a charge on the balloon by rubbing it against wool or a piece of rabbit fur.  A sweatshirt does not work very well, too much cotton.  We were able to demonstrate static electricity pushing and pulling an aluminum can across the floor. 

Static electricity is discharged by touching something that will absorb the charge.  You do this when you walk across a carpeted floor on a dry day then touch something metal.  We put a charge on a balloon and touched the metal support beam in the basement.  It was not dark enough to see the spark but it made a loud crack.

We will come back to this topic when the book gets to the topic of electricity.  We have our notes and pictures to help us remember.

Apologia Physics: Centripetal force demonstration

Centripetal force is Newton's First Law in practice!  Newton's First states that an object in motion (or at rest) will stay in motion (or at rest) unless acted upon by another force.  In the instance of circular motion, centripetal force makes an object move in a circle rather than going straight.

One experiences centripetal force in many ways: turning a corner in your car, going upside down on that circular ride at the amusement park, and as shown in the lab below, keeping water in the cup as the cup is upside down.

To perform the demonstration below you will need a piece of stiff cardboard.  I considered using plywood but if a student hit someone in the head that would not be good.  Drill a hole in each corner of the cardboard.  Attach a piece of string (we used acrylic yarn, strong but cheap) about 2.5 feet in length to each corner and knot together the other ends.  Place two paper cups on the cardboard and fill each with a couple ounces of water.

Swing the apparatus back and forth a few times then swing in a circle a few times.  Try swinging faster and slower.  Stop and repeat the process after adding a few more ounces of water to each cup.  Repeat again after filling each cup.

Do this outside as some students will not swing fast enough and the water will come flying out on everyone within range!

Students should be able to feel the change in centripetal force, as the tension on the string, which will be greater with more weight and also greater with more speed.

Apologia Physics: Static Friction

Static friction is the force that holds two objects that are touching each other at rest.  Kinetic friction is the force between two objects that are touching each other but are in motion.  The coefficient of friction is a measurement of the amount of friction.  We can easily measure the coefficient of static friction.

We will place a plastic car with its wheels removed on a board.  Raise the board until the car begins to move.  Measure the height of the end of the board and use the pythagorean theorem to calculate the angle of the board in relation to the floor when the car begin to move.  Also use a protractor to measure the angle as a check on your calculations.  Calculate the coefficient of friction.

Perform the test again with a light weight in the car and again with the heavier weight in the car.  Perform all three tests again with different materials attached to the board.  We used wax paper, .aluminum foil, and two grades of sandpaper.

Rank the materials in order of their coefficients of friction.  The material with the lower coefficient is more slippery.  The sandpaper is abrasive.  It has a high coefficient of friction.

How do you calculate the friction?  The gravitational force that runs parallel to an inclined surface is equal to the weight of the object times the sine of the incline angle.  The gravitational force that runs perpendicular to the incline surface is equal to the weight of the object times the cosine of the incline angle.  The normal force of the board pushing up against the car offsets the force of the car pushing down on the board.  Therefore the frictional force that is offset when the car begins to move is equal to the coefficient of friction times weight times the cosine of the angle.  The force that keeps the car from sliding down the board is equal to the weight times the sine of the angle.  Since these forces are equal until the car begins to slide, the coefficient of friction times weight times cosine of the angle equals weight times sine of the angle.  The coefficient equals the weight times sine divided by weight times cosine.  The weight cancels out!  The coefficient of friction is equal to the sine divided by the cosine of the angle or more simply the tangent of the angle.  Putting weight in the car does not affect the coefficient of static friction.  None of this applies to the coefficient of kinetic friction that will be addressed in a future chapter of the book.

Another way to calculate the angle is to take the inverse sine of the height divided by the length of the board.  Use this calculation to check the angle measured by the protractor.

Apologia Physics: Torque and First Class Levers

Our class did a lab Torque and First-Class Levers from NSTA's Take Home Physics book. 

Rotational torque equals the product of weight and distance from the axis of rotation.  The lab above is an easy way to demonstrate this calculation.

Materials include a ruler with a hole in the middle, some string, washers, and paperclips.
Construct the apparatus as shown in the lab.  We found that the hole in the middle of the ruler was not exactly in the middle so we taped a small washer on the back of the ruler in a location that would balance the ruler.  The ruler should hang horizontally before you start!

Record the number of washers you hang on the left side of the ruler at the distance prescribed in the lab.  Balance the ruler by adding the number of washers on the right side of the ruler, as prescribed in the lab, then record the distance the washers needed to be from the axis to balance the ruler.

Multiply the number of washers times the distance from the axis.  The resulting number should be equal.  Calculate the margin of error.  The students had margins of error of ten percent or less.

Apologia Physics: Module 7 Measuring Tension

The object of this demonstration is to determine the tension on two strings on which hangs a weight.
The students obtained a weight from a balance scale.  They measured the weight to be 147.5 grams.  They hung weight from a spring scale determine its accuracy. 
Next they hung the weight from two springs as shown below.  First they hung the weight so that it was in between the two scales such that the angle of the scale and string to the base board is equal on both sides.  Then they hung the weight such that it was to the left of center.  The angle of the scales and string to the base board were therefore not equal.
Using the equations from Example 7.2 in the book, they will calculate the tension on the string in each situation for both sides and compare to the reading they took on the spring scales.

Statistics: Sampling with and without replacement

How do they count the number of deer in a wooded area?  Can they round up all the deer in the woods and count them?  If so, how would you know you had all the deer?  Scientists do a catch, mark, and release process.

We simulated this process by counting white beans.  Each student was given a cup about 2/3 full.  Each student had between 400 and 500 beans.  Pull 15 beans and mark them with a marker. Return the marked beans to the cup and mix well.  Pull a sample of 10 to 25 beans and record the total number of beans in your sample and the number marked.  Return the sample to the cup and mix well.  Repeat this process ten times.  This is called sampling with replacement.  

Add the number of beans in the samples and the number marked.  Set up a ratio to estimate the number of beans in the total population and then record the percent error.

Repeat the process but do not return the samples to the total population.  Perform the same calculations.

Which method was more accurate?  What could be done to make the process more accurate?

Mark and Recapture Lab

Apologia Physics: Module 6: Friction and Inertia

Friction Lab

We are studying friction.  To move an object requires a force.  This force is equal to the friction coefficient (Greek letter mu) times the Normal Force (mass times gravity expressed in Newtons).  To demonstrate the friction coefficient of different materials we placed an object on a wooden ramp and raised the ramp until the object started to slide.  We then recorded the angle of the board.  We repeated the same exercise with different materials taped to the board including: aluminum foil, parchment paper, light or fine grade sandpaper (high grit number) and rough or heavy grade sandpaper (low grit number).  Interesting fact: the grading of sandpaper is based on the number of holes per square inch in the screen used when sieving the grains of of grit during sandpaper manufacture.  Thus fewer holes are bigger holes which allow larger grains to pass through.

Results: aluminum foil is smoother than wood, parchment paper smoother than foil.  Large grit is rougher than small grit sandpaper and both had a higher coefficient of friction than the wood.

To calculate the static coefficient of friction, find the formula in module 7. 
The coefficient of static friction is the tangent of the angle.  This is not true for the coefficient of kinetic friction!  Why is the mass or weight (mass times gravity) not used in this calculation?
The mass determines how much force is pushing the object down the slope.  The mass also determines how much the object is pushing down on the board.  The additional force pushing the object down the slope is offset by the additional static friction.

Apologia Physics: Projectiles with Vernier's Video Physics App

Last Thursday we made catapults from popsicle sticks and rubber bands.  We launched a ping pong ball and video recorded the projectile's path.  Today we used Vernier's Video Physics, see below for link, to draw a graph of the trajectory including time of flight and the distance traveled in both the vertical and horizontal directions.  The students picked six points from the graph and entered the x and y coordinates into their TI83/84 calculators.  We now have the quadratic equation for the line of the trajectory.  The students' assignment for next week is to use the formulas in module five of the physics book to determine the initial velocity of the ping pong ball and also the angle of flight.








Vernier's Video Physics app

Graph Image 1
Graph Image 2
Graph Image 3

Apologia Physics: Catapults or Projectile Motion Module 5

Module 5 topic is projectile motion.  Today we built a trebuchet and a catapult.  We fired a projectile, a ping pong ball, from the catapult and recorded the motion with Verneer's video app.  During the next class we will analyze the videos, graph the projectile movement, and separate the forces that act upon the ping pong ball, horizontal and vertical.  The paper trebuchet worked but did not send a projectile, a paper clip, more than a foot at best so we will not use that data but what we built will serve as a good model.

These are the links to the project descriptions:

Paper Trebuchet  and Craft Stick Catapult

Statistics: Graphing Absolute Zero

The Stats class used Flinn's Charles' Law Lab instructions today.  I wanted a real life example of collecting data and using the data to extrapolate.  We measured the volume of air (gas) in a syringe at different temperatures.  Basically, the syringes are in yogurt containers filled with ice water, boiling water, and room temperature water.  I had the kids mix the hot water with cold to get at least four or five data points.  We used 10 mL and 30 mL plastic, oral syringes with caps.

We found that the 30 mL syringes didn't work.  I insisted I needed 30 mL syringes--not just 10 mL syringes.  Guess what?  The 10 mL syringes worked better.  The results were surprising.


Here is one student's, Anna's, data:
Temp  (C)   Vol (change in volume mL)
19.5              5.5
13.3              5.0
9.4                5.5
63.8               7.0
30.6              6.25


Next the kids plotted, calculated, and graphed the linear regression with their TI 83/84 calculators.  Then, the kids went to the Window in the calc and extended the range: Xmin -300, Xmax 100, Ymin 0, Ymax 10.

Lastly the kids extrapolated to see the temperature at 0 volume.  Anna's 0 volume y-intercept was -360C.  Absolute zero is -273.15.  Her percent error is 32%.  Not bad at all!  We had a couple students with less than five percent error.  That was excellent and unexpected.  Remember we used syringes in yogurt cups for the water bath.

The lab coincides with Chapter 4 in Stats.  How do you collect, organize, graph, and present your data?

I'll post a lab report when the kids finish.

Statistics:Chapter 3: Part 2

The kids are working on worksheets from Chapter 3 activities from Mrs. Daniel's Stats blog.  I spent my class time explaining linear regressions and the LSRL, the least squares regression line. 

Apologia Physics: Module 4

Today, the kids did on your own problems for Module 4.  They are working on the test questions for Tuesday.  Tommy is having trouble drawing the vector.  We'll work on this skill.

Statistics: Chapter 3 Correlations

The kids worked on TI84 graphing exercises on p.186 and p.219 before class began.  (They're doing the same exercises again as homework to ensure the kids can do the exercise.)  (The variables are located in Vars Statistics or Y-Vars Functions.)  We went over half the slides in Mrs. Daniel's powerpoint 3.1--just before the formula to calculate r, correlation coefficient.  The kids can enter data in the stat function of the graphing calculator, calculate linreg, and graph linreg.  We reviewed those skills last time.  Be sure to practice entering data and graphing. 

Apologia Physics

Today the class worked on Vectors: The Vector Voyage and Walking Vectors activities.  The Walking Vectors should have been done outside, rather than in the basement. The kids ran into walls.  The point was you can shuffle the order of the vectors and still end up in the same spot.  I made five or six cards.  The kids did the activity, shuffled the cards and repeated it.  The walking did not work because, the kids ran into obstacles, such as walls and tables.  We drew the instructions from the cards on to graph paper.  That worked.

We did not begin the Vector Voyage; the kids are completing it for homework.

Statistics: Chapter 2 and Linear Regression

At the beginning of class, the kids did example 3.9 (p.200 textbook) Does Fidgeting keep you slim?  The class entered the data into L1 and L2, graphed the data, calculated the linear regression and displayed the regression with the data.  The kids learned how to turn on Diagnostic or r coefficient.

Do linear regression models frequently or the kids will forget how to enter, graph, calculate, and display linear regressions. 

We reviewed the Mrs. Daniel's WS 2.2  The homework for Tuesday is the Chapter 2 test.  Yes, the worksheet took most of the class period.

Statistics: Two new videos for the Normal Curve

One of the students took two hours to create two videos with instructions for graphing a normal curve and shading under the curve with a TI 84.  Take a look!

Statistics: Normal Curve

Update: There are two new videos with explanations how to graph the normal curve and shade under the curve here.

The first thing we did in class was graph normalpdf, normalcdf, and shadenorm with the graphing calculator.  The point was to understand how to shade different areas under the normal curve by setting upper bound, lower bound, mean, and standard deviation with these exercises or examples.    These examples have the screen shots.  This powerpoint has good instructions.

We spent about 30 minutes explaining that normalpdf (x) must be defined under y=, 1E99 or -1E99 represent infinity on the TI84, normalpdf graphing a standard curve or normal curve, shadenorm uses lower bound, upper bound, mean, and SD, and normal cdf converts a z score into a percentage.  Largely, we set the window and practiced shading.  We only spent a few minutes converting z score to a percentage or percentile.  The point was to learn how to enter the data.  The screen shots provide the answers.

For the remainder of the class, the laptop died.  We talked about a normal curve, defined z score, introduced the z score equation, talked about comparing scores with the SAT and ACT as an example of standardizing two scores with different scales.  Their homework is to complete the overview and summary and the 2.1 worksheet for Friday.


We have a back-up Thinkpad for the seemingly dead laptop up and running.  Fingers crossed it works on Friday.  I am wed to the powerpoint slideshows.