To test the coefficient of friction each of the objects including wood, plastic,sponge, and brick the following set of tools was used: a smooth wooden plank, a metre stick, miscellaneous textbooks, tape, and weights with the mass of 100g, 200g, and 500g.

The first step in testing the coefficient of friction for each object was to place the wooden plank on a flat surface (a lab bench/table top was used in this experiment) and put textbooks at the end of the wooden plank on the flat surface to prevent the object from sliding onto the floor. Each object was placed on the wooden plank one at a time starting with a block of wood. The plank was lifted on the side opposite to the textbooks until the object, in this case the wooden block, would start to move. The wooden was then held at the exact position in which the wooden blocking started to move and the rise (the line from the flat surface to the top of the wooden plank that was being held up) and the run (the line from one end of the plank to the other while the one end of the plank was being held up at the position of where the object began motion) were measured. In this case, the block of wood was tested in this way with no added mass, and then with 100g taped to the top surface of the block of wood and then so on with 200g and then 500g. Each object was tested in this way.

How do I prove that mass has no effect on the coefficient of friction using Newton's 3 laws and the equations force of friction = coefficient of friction * normal force, Net force = mass *acceleration, and Force of Gravity = mass times gravitational acceleration.