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.