The Mass-Dependence of Friction

•  Set up the equipment as for the kinematics experiment, where you detected the motion of a cart on a slightly sloped track. Open today’s Logger Pro file.

•   Determine the angle of the track using a ruler and your knowledge of trigonometry.  Enter the value into the table in the worksheet.  It is easiest to keep the angle of the track the same; enter the angle into all three rows corresponding to the three trials you are about to do.

•   Your cart might or might not have one or two additional masses screwed to it, as in the pictures below.  Measure the mass of your cart using a mass balance, as in the right-hand picture.  The masses are attached to the cart by means of a bolt and wing-nut.  Your lab instructor can show you the easiest way to secure them.  Upon removing a mass, please replace the bolt in the hole and tighten the wing-nut so that these small parts do not get lost.
 

  

Left: cart and masses on track; right: cart and masses on mass balance.

 
•   Measure the accelerations of the cart as it moves up and down the slope, as you did for the kinematics experiment, in which you found acceleration as the slope of a Linear Fit (“R=” button in the upper toolbar) to the velocity.  Display the standard deviation of the slope by right-clicking on the data box and choosing Show Uncertainty.  Do this for the cart with no additional mass, one additional mass, and two additional masses.
 
•  You may do the three measurements in any order.  The accelerations for up and down the slope should be slightly different.  (Do you understand why?)

•   Copy and paste your graphs into Question 4 of the worksheet, making sure that you can see the data and read the data boxes, with standard deviations.  You might need to decrease the size of the plots, such that the data boxes consume a larger portion of them.  Fill in the table with the three mass values and the six accelerations.  Type in the relevant units within the square brackets at the top of each column.  Calculate N, f, and μ based on your equations.  All values in the table should have four significant digits.  Find the average of the three measurements for N, f, and μ.

•   Logger Pro calculates the "sample standard deviations" of linear and quadratic fits.  We have not yet told you how they are calculated.  The equation is

sd = SQRT { [ ∑_i (x_i - x_ave)² ] / (n-1) },

where x_i is an individual measurement, x_ave the average of the measurements, and n the number of measurements.  Compute the standard deviation for the columns N, f, and μ, and then determine the fractional uncertainties, sd/ave.  Of the three variables, two should have large fractional uncertainties, and one should have a small fractional uncertainty, less than 0.100.  (Why?)
 
•   In reporting your results for the last question on the worksheet, remember to follow the standard form that you learned in Part I of the uncertainties experiment. Please answer the last question individually, in your own words.