Apologia Physics: Module 7 Sum of Vectors Lab

Sum of Vectors Lab

Module 7 covers various applications of Newton's Second Law.   Force = mass x acceleration.
Calculations are straight forward when the forces are acting in a straight line.  When forces are acting at angles, we have to separate the forces into the x and y directions (x and y axis on a graph).  The above lab is a great demonstration.

I drew on the board a picture hanging from a nail.  With one piece of wire attaching the picture to the nail, the tension on the wire has to be equal to the weight of the picture.  If the picture is too heavy for the wire, the wire will break.  One of the students asked if the picture could be hung with two nails and two pieces of wire.  This would distribute the weight evenly and you could therefore use wire with less capacity as the weight on each nail is half the total weight of the picture.

It is when you use one nail and two attachments to the picture that the calculations get complicated.  On an x and y axis graph, the wire now has tension in both directions.  Therefore the forces on the wire is greater in total than just the weight of the picture because there is now horizontal force as well as vertical to take into account.

We will also do a lab to demonstrate the coefficient of friction of various materials.
Materials: one by four board a meter long, tape, aluminum foil, wax paper, sandpaper, box with weights.
Hypothesis: which material has the highest and lowest coefficient of friction?
Procedure: weigh the box with some weights inside.  Weights can be coins, washers, etc.  Use enough weight that the box slides when you raise the board.  Apply one of the above (aluminum foil, wax paper, sandpaper) to the board, place the weighted box on the material being tested, raise the board and measure the height of the board when the box moves.  Repeat three times.  Then repeat with another surface.  Using the height of the board, draw a picture of the board leaning at the height observed when the box moved, measure and calculate the angle of the board to the flat surface, then calculate the coefficient of friction. Note: you can measure the angle of the board with a protractor or by measuring the length of the board and the height at which the weight moved.  The angle is the inverse sine of the height/length.

We also took the same board, placed a box weighted with a few quarters, and measured the coefficient of friction as above.  Then we added weight to the box by adding another twenty quarters.
What do you think will happen?  The resulting coefficient  of friction was the same.  Although the additional weight made the box more difficult to move in a horizontal direction, when the board was raised, there was more potential energy owing to the height of the board.  Therefore, the box started to slide down the board at the same angle despite the additional weight in the box.  The additional weight pushing down, the y coordinate, was offset by the additional force on the x coordinate.

To confirm this we put two boxes weighted as above, one lighter and one heavier, and ran them side by side on the same board.  A good old American drag race!  It was difficult to demonstrate that the boxes would move at the same time as we discovered various imperfections in the board.  The box in the right lane of the board always moved last despite the different weights as there were some ridges in the wood.  We then covered the wood in aluminum foil and got more consistent results.