16-Mar-2015 Lab 7: Modeling Friction Forces

Purpose:  To calculate static and kinetic friction and run experiments to compare calculated results.

Materials:

• Styrofoam cup - used as a weight to fill with water to calculate mass needed to move a block
• Wooden block with felt on bottom - used to calculate frictional forces
• Pulley - connecting wooden block that slides on track and water cup
• Force sensor - used to calculate the force of a pull on given masses
• Motion detector - used to calculate acceleration of blocks

Procedure:

This Lab was broken into 5 experiments:

  1)  Static friction on horizontal surface

• We measured the mass of a wooden block with a felt bottom surface and set up the block on a surface (in our case a track) attached to a styrofoam cup by a string over a pulley, similar to the following photo:

• We added water little by little to the cup until the block barely started to slide and once it barely moved, we measured the mass of the cup.  We repeated this 3 times adding one more block to the previous block(s) for each trial, taking note of the mass of each block and the mass of the cup+water, yielding these results:

• We found the normal force by multiplying the mass of the system of blocks by gravity, 9.8 m/s^2.  We then used this information to find the static friction, which is the force going against the block just strong enough to hold the block in place up until it moves the slightest bit.
• Because fstatic = μsN, μs = fstatic / N and fstatic = mass of water+cup * 9.8 m/s^2
• We used this information to plot points of normal force against static friction for each trial and found the proportional fit line, which gave us a slope that represented the coefficient of static friction, μs 

Graph of frictional force over normal force

• Slope of the line was 0.2068, our result for the coefficient of static friction

  2)  Kinetic friction on horizontal surface

• For this next experiment we used a force sensor.  After calibrating the force sensor, we took the mass of a wooden block with felt on its bottom surface, and then set it up on the track.  This time, we attached a string connecting the block to the force sensor, and pulled it horizontally at a slow, constant speed, collecting data from the force sensor.  As in the previous experiment, we found the mass of a second block, added it to the first, and repeated it 3 more times.

Results of the average force of pull from each trial.

• We used the steps from the first experiment to again plot friction (this time kinetic friction) against the normal force.  We found a proportional fit line whose slope gave us the coefficient of kinetic friction of the block, which was 0.2168. 

Unfortunately, our coefficient for kinetic friction turned out to be greater than our coefficient for static friction.  This could have been due to multiple errors, such as the horizontal pull or uneven surfaces in the track or felt.

  3)  Static friction from a sloped surface

• We set up a track with a small slope that would not allow a block to slide on it (as shown below), placed a wooden block whose mass we had collected on the track, then raised the side higher just until the block barely moved.  We measured the angle of the track at this slope.

• Using a free body diagram, along with our mass of the block and measured angle, we calculated the coefficient of static friction of this block against the track: 

  4)  Kinetic friction on a sloped surface

• Using a similar setup to the previous experiment with one side of the track elevated, we also set up a motion detector on the elevated side to track the acceleration of a block moving down the track.  

• We set up the track at an angle of 23° above the horizontal, an angle at which the block could slide freely.  Using the motion detector, we found that the acceleration of the block was 1.328 m/s^2 at this angle (slope of velocity graph).

• As in the previous experiment, we drew a free body diagram and used the mass of the block and measured angle to calculate the coefficient of kinetic friction, this time setting the force equal to mass times acceleration

  5)  Predicting the acceleration of an object

• The goal of this experiment was to use kinetic friction found from the previous experiment to calculate acceleration of a block using a hanging mass.  We would compare this calculated acceleration to the acceleration found using the motion detector and compare the two.

• To do this we set up the track horizontally with the motion detector tracking the same block from the previous experiment (same mass and kinetic friction). A string attached the block to a mass hanging over a pulley at the end of the track, heavy enough to accelerate the block.  We used a mass of 0.04 kg.  

• Before running the experiment we derived an expression for acceleration and plugged in our data using the coefficient of kinetic friction of 0.277, mass of block 0.116 kg, and hanging mass of 0.04 kg.  We created two free body diagrams and used the tension force in the hanging mass as the pull force of the block:

• Our calculated acceleration came out to be 0.506 m/s^2

• We then ran the experiment, with the motion detector recording the acceleration of the wooden block being pulled by the hanging mass.  The results of the motion detector showed that the block accelerated at a rate of 0.267 m/s^2:

• Comparing our experimental results to the derived model for acceleration, we found that they were very off from each other.  This could have been due to an error in the angle recorded in the previous experiment or placing the block on a different part of the track.