Physics AP - Friction Lab (#10)

3=E
¥=u
Background:
us is equal to tanØ just before the wooden block slips down the
surface.  uk is equal to tan0 at a constant velocity.  In general us
> uk.  u is equal to Ff/Fn.  The normal force doesn't affect the
constant (u), u depends on the material.

Problem:
To find us and uk.

Procedure:
1. Place the wooden block on top of the cardboard surface.
2. Raise the board until the wooden block moves down the surface with
   a constant velocity with a little to get the block started.
3. Measure the height of the board at that point.  Record the data as
   uk.
4. Repeat steps 1-3 three time to get an average to use for the
   equations.
5. Repeat steps 1-4 for cork, rubber, and sandpaper surfaces.
6. Place the wooden block on the top of the cardboard surface.
7. Raise the board until the block slips down.
8. Measure the height at this point.  Record data as us.
9. Repeat steps 6-8 three time to get an average for the equations. 
10. Measure the side of the board that is the hypotenuse of the
    triangle.
11. Using the pathagerism theorem to find the missing side of the
    triangle. a²+b²=c² then use the missing side and the measured
    height to find the tan-¹Ø to find the angle of the uk and us.

Data:
Surface     uk (avg)  us (avg)   Missing side (uk)  Missing side (us)
Cardboard   8.2cm     11.9cm     a²+b²=c²           a²+b²=c²
                                 8.2²+b²=19.8²      11.9²+b²-19.8²
                                 b=18.0             b=15.8
Cork        8.4cm     11.0cm     a²+b²=c²           a²+b²=c²
                                 8.4²+b²=19.8²      11.0²+b²=19.8²
                                 b=17.9             b=16.4
Rubber      7.5cm     10.0cm     a²+b²=c²           a²+b²=c²
                                 7.5²+b²=19.8²      10.0²+b²=19.8²
                                 b=18.3             b=17.1
Sandpaper   10.6cm    12.6cm     a²+b²=c²           a²+b²=c²
                                 10.6²+b²=19.8²     12.6²+b²=19.8²
                                 b=16.7             b=15.3

Surface     tan-¹Ø(uk)      tan-¹Ø(us)
Cardboard   8.2/18.0        11.9/15.8
            tan-¹Ø=46       tan-¹Ø=75
            25°             37°
Cork        8.4/17.9        11.0/16.4
            tan-¹Ø=47       tan-¹Ø=67
            25°             37°
Rubber      7.5/18.3        10.0/17.1
            tan-¹Ø=41       tan-¹Ø=58
            22°             30°
Sandpaper   10.6/16.7       12.6/15.3
            tan-¹Ø=41       tan-¹Ø=.82
            22°             39°

Conclusion/Analysis:
This lab proved that us>uk in all the cases.  Sandpaper has the most
friction of all the surfaces tested.  Rubber seemed to have the least
friction of all of the surfaces.  That makes me wonder why tires on a
car are made out of rubber.  And in the experiment the whole class
did the same result came out.  It took 2.4N on cardboard to move the
5.12kg mass (us), 3.0N on cork, 2.6N on rubber, and 7.5N on sand-
paper.