**6. Friction, Experiment and Theory**

The lab this week investigates the frictional force and the physical interpretation of the coefficient of friction. We will make use of the concepts of the force of gravity, the normal force, the frictional force, tension, free-body diagrams, and objects sliding on an inclined plane. Recall what you know about friction before coming to the lab.

**Pre-Lab activity**

*Please complete this activity
before coming to the lab session and submit your results through Moodle.*

To study the question of friction theoretically consider the online simulation which represents two blocks connected by a string, where one block is located on the table and another block is hanging from the table. The simulation allows changing mass of each of the blocks as well as the coefficient of friction between the block and the table. Try various values for masses and friction coefficients, see what happens. Notice how acceleration of the system changes as you change these variables. Determine the unknown values for masses and coefficient of kinetic friction.

To resolve this problem as well as to perform calculations
for the real experiment, which you will perform in the lab, you have to be familiar
with how to apply

**Lab Experiment**

1.
The experimental design for the first part of
the lab will be very similar to what you saw in the online demonstration. You
will be using a block connected by a string with an additional mass hanging
from the table. You should also set up the motion sensor in such a way that it
allows you to measure the speed of the block. This way you can determine
whether or not the block is accelerating as it moves along the board. Using this
experimental setup with a horizontal surface, figure out which quantities you
should plot on the graph in order to determine the coefficient of kinetic friction
for the block sliding on the board. Hints may help to figure this out.

The provided blocks of wood have hooks for pulling
and have various materials attached to them to vary the surface in
contact. Figure out how to measure the
normal force and the frictional force while the block is sliding across the
board. See Hints for help figuring out how to do this. Vary
_{} (for at least five
values) and measure the corresponding _{} for a given block. Make a plot and have Excel calculate the
coefficient of kinetic friction from this graph.

Repeat for two more blocks. Include all three
plots on the same graph (put a legend on the graph). Which surface has the
highest_{}? Does that make
sense?

2.
Set the surface at an angle, _{}, from the horizontal. Place the object on the surface and
increase the angle until it slides. The angle
at which the object just begins to move is defined as the “angle of
repose”. Figure 1 illustrates this
situation. From the diagrams, it can be
shown that there exists a relationship between the angle of repose,_{}, and the coefficient of static friction,
_{}. Determine this relationship and solve for_{}. Note that in your case the block is just about to start
moving so it has no acceleration yet. However, to solve this problem you may
also look at the more general situation when the
block is already moving.

Using the same blocks as before, compare your
results with those for coefficients of kinetic friction, determined in Step 1.

*Figure
1.** Finding the angle of repose. *

3.
Select a block and an angle. Compute the force
required to slide (pull) the object up the inclined plane (See Fig. 2) using
the values of _{} determined in Steps 1
and 2. Carry out the experiment and compare (via %-difference) the experimental
value with the theoretical value for that type of material. Once again you can
use the motion sensor to control whether or not the block is accelerating. See Hints for help.

*Figure 2.** Sliding up an incline.*

4.
If you still have some time left try to design
and test an experimental procedure to determine the effect of surface area and
velocity upon the coefficient of friction of wood-on-wood. Discuss your results.