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.