Coefficient of Friction

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```					IB SL Physics                           Coefficient of Friction                                 Bertossa

DISCUSSION

The system below is composed of a cart that is free to move on an inclined track. The earth pulls
the cart downward giving it an acceleration (although the acceleration will not be -9.8 m/s2). If the
cart is given a gentle push up the ramp, it will slow on its way up in response to gravity. After
reaching its highest point on the track, it will speed up on its way down, again in response to
gravity. If no friction or air resistance act on the cart, the acceleration of the cart as it moves up the
ramp and as it moves down the ramp will be exactly the same. There is, however, a small frictional
force acting on the cart and this causes the upward and downward accelerations to be slightly
different. The purpose of this investigation is to find an estimate of the coefficient of friction, ,
between the wheels of the cart and the ramp. This coefficient should be found by measuring both
the upward and downward acceleration of the cart and then by applying force statements to both the
upward and downward motion of the cart.

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PROCEDURE

1.      Set the steel track on an incline of not more than 10. Carefully measure the angle of
incline with the greatest precision possible.

2.      Place the motion detector at the top of the ramp, facing the cart.

3.      Open the Logger Pro software from the shortcut on the desktop of your computer. Choose
the file “04 Determining g.xmbl” from the Physics with Computers folder. This should
provide you with a split screen showing a position vs. time graph and a velocity vs. time
graph. Start the motion detector by choosing       .

4.      Practice pushing the cart up the ramp in such a way that the cart consistently reaches a point
approximately 40 cm from the motion detector. Be very careful not to push the cart so hard
as to have it hit the motion detector.

5.      Continue to run trials until you achieve a VERY linear velocity versus time graph. Be
certain that your angle of incline on the steel track does not vary during the data
collection process.
6.     Use the software’s capabilities to find the slope of the velocity versus time graph and an
average value from the acceleration versus time graph. Click and drag the mouse along the
velocity time graph to define the limits of the constant acceleration upward portion of
the motion. Select Analyze from the pull down menu and choose Linear Fit. This will
place a box in the upper left corner of the v-t graph that shows the slope and y intercept of
the region of the graph you’ve identified. Next, define the same region on the acceleration
versus time graph with the click and drag mouse operation. Select Statistics from the pull
down menu under Analyze and this will place a box on the a-t graph that lists the mean
value of the acceleration for the portion of the graph you’ve highlighted. Repeat this
process to find this information (slope of v-t graph and mean value of a-t graph) for the
constant acceleration motion of the downward portion of your trial.

7.     Make certain that the boxes (there should be four total) which include the slope and average
values are all clearly visible on the graph along with the highlighted portions of the graphs
that they represent. Save your graphs on your H drive and print the file on the printer in the
front right corner of the room.

8.     If time permits, change the angle of incline and repeat the entire process.

ANALYSIS

Draw a Free Body Diagram of the cart showing ALL the forces (perpendicular and parallel) acting
on the cart. Write force equations for both the perpendicular and parallel forces acting on the cart.
There should be a parallel force statement for the upward motion and a slightly different statement
for the downward motion to account for the different accelerations. Solve your force equations to
determine the coefficient of friction between the ramp and the wheels. Find an average value for
the coefficient of friction using your group’s values as well as all data collected by other groups.
Determine the deviation in each measured value (both absolute and fractional) and find the average
deviation. Finally, state the average value along with its average deviation found by the class.
Although you will not have a table value with which to compare your calculated value, you should
still discuss your results including possible sources of error and suggestions for
modifications/extensions to this investigation. Comment on the importance of the mass of the cart
in this experiment. You will not be required to submit a full write-up. Your work will be assessed
based on IB’s requirements for Data Collection and Processing, and Conclusion and Evaluation.

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