Materials
- Binders, cardboard, sheet metal, plastic, cardboard, sandpaper, glass etc. Any book sized flat surface for students to investigate the co-efficient of friction of
- Protractors, one per group
- Objects to place on the books (like their sneakers) pens, pencils, erasers, rulers, ice cubes etc.
Procedure
- Have the students place one end of their flat object on the table and hold the other end at a slight angle
- Place the other sliding object (like the student’s sneaker) on top of the flat object
- Lift the end of the flat object until the sliding object just begins to slide on the surface
- Have the students measure the angle between the flat object and the table
- Have students calculate mu (μ)
Calculations
First break the gravitational force into components.
Since the board is lifted until object just begins to slide, the student is finding the angle at which the co efficient of static friction is at its maximum value. Therefore Ff = μFN
Since the object is at rest, all the forces balance out. Therefore the net force of the x components is zero and the net force of the y components is zero
X-component:
Fnet = 0 = mg sinθ – Ff
therefore
mg sinθ = Ff
Y-component:
Fnet = 0 = mg cosθ – FN
mg cosθ = FN
Since Ff = μ FN and mg sinθ = Ff
then
mg sinθ = μ FN
Since mg cosθ = FN and mg sinθ = μ FN
mg sinθ = μ mg cosθ
mg cancels on both sides
solving for μ equals
μ = tan θ
Therefore, for the students to find the maximum coefficient of static friction, the students need to use the above equation and the angle of the board from the table
Reinforcement Activities
Students can study free body diagrams and vectors easily using force tables. Have students hang different size masses from nearly frictionless pulleys and get the forces to balance. Tables have the angles clearly and easily labeled for students to take measurements and make calculations
Another classic physics problem using friction and free body diagrams is the ladder leaning against the wall, use “The Learning Ladder” to investigate this problem more completely.
Use friction blocks and spring scales to more quantitatively come up with a value for mu. Instead of just taking one reading, have students take several readings by pulling blocks of different masses along a surface. The blocks have different surfaces that students can investigate.
