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.