16-Mar-2015: Modeling friction forces

     The purpose of this experiment was to model friction forces. It was split into five different parts. The first part asked to find the coefficient of static friction between a block and the lab table. The second part asked to find the coefficient of kinetic friction. The third part asked to find the coefficient of static friction from a sloped surface. The fourth part asked to find the coefficient of kinetic friction from a sloped surface. Finally, the fifth part asked to predict the acceleration of a two-mass system.

Part 1

     The first part of the experiment was to find a coefficient of static friction between a block and a lab table. The setup had a block resting on a table, with a piece of string attached to it. The piece of string went over a pulley at the end of the table and was attached to a cup hanging off the table.

Setup for experiment 1.

     The mass of the block was weighed. Then, water was poured into the hanging cup until the block moved the slightest bit. The mass of the cup plus water was weighed.This was done three more times for a total of four blocks on top of each other. The resulting data was plugged into a table in Logger Pro.

Since it is known that static friction force is proportional to the normal force of an object by equation,

then the coefficient of static friction must be the slope of a friction vs normal force graph given by,

     So, the friction force and normal force needed to be found and plotted. In this case, the normal force of the blocks is equal to the weight of the blocks (mg) and the friction force is equal to the weight of the cup plus water (mg). Doing the calculations gives a new table of:

Taking the values of friction and normal force and plotting them gives a graph of:

And a linear fit with an equation of y=Ax, similar to the friction force equation, where A is the slope.

                                             

This means the coefficient of static friction between the block and the table was found to be:

coefficient of static friction=0.3093.

Part 2

     The second part of the experiment asked to find the coefficient of kinetic friction between the same block and table. This was achieved by using the same block and string but this time the end of the string was attached to a force sensor. The force sensor was connected to the Logger Pro system. The force sensor was calibrated by hanging a known mass from it and telling the computer what the mass was. The Force sensor was then held horizontally and zeroed out. The block was then pulled horizontally at a constant speed by the person holding the force sensor. Logger Pro recorded the data and produced a graph. This was repeated for up to 5 blocks sitting on top of each other.

The graphs of all five trials were stored.

     Each graph was then analyzed using the statistics tool in Logger Pro. The mean value of the pulling force of each individual graph was recorded. Since it was assumed there was no acceleration in the system, the pulling force was equal to the friction force. This means if a graph of friction vs normal force is plotted then the slope of the line is the coefficient of kinetic friction. Much like the static friction in the first part of the experiment. 

The friction force seen in the table is the mean of each force graph (analyzed above). The normal force is equal to the weight of each mass of blocks. With this data a graph of friction vs normal force was produced:

with a best fit line that produces an equation y=Ax, with A being the slope which is the coefficient of kinetic friction.

This means the coefficient of kinetic friction was between the block and table was found to be:

coefficient of kinetic friction=0.2531.

This value is lower than the coefficient of static friction, which agrees with the model of friction.

Part 3

     The third part of the experiment asked to find the coefficient of static friction from a sloped surface. The block was placed on one end of a horizontal track. The end of the track where the block was placed was lifted up, slowly, until the block starts to slip. The angle the track made with the horizontal was then measured and used to calculate the coefficient of static friction.

The angle was measured to be 24 degrees. The mass of the block was measured to be .111kg.

 A free-body diagram and the sum of forces were needed to find the coefficient of static friction.

free body diagram of the block on a sloped surface.

Below are the sum of forces and the steps taken to solve for the coefficient of static friction.

Plugging in the angle of 24 degrees into the above equation yields a coefficient of static friction of: 0.445

Part 4

     Part four of the experiment asked to find the coefficient of kinetic friction from sliding a block down an incline. The setup was much the same as part 3, except this time there was a motion sensor attached to the ramp and the ramp was already inclined enough so that the block would automatically slide down. 

     To find the coefficient of kinetic friction, the acceleration of the block and the angle of the slope was needed. The motion sensor was used to find the acceleration. The motion sensor was setup with Logger Pro. When it was activated, the block was released. The following position vs time and velocity vs time graphs were produced:

The velocity vs time graph was analyzed with a linear fit to produce a slope, which is the acceleration of the block.

An acceleration of 0.3377 m/s^2 was recorded. The slope was measured with a smart phone to be 16 degrees.

     After the acceleration and slope was found, the sum of forces was found to solve for the coefficient of kinetic friction.The free-body diagram was the same as the one in part 3, but the sum of forces in the x-direction were slightly different. Here are the steps that were taken to solve for the coefficient of kinetic friction:

     Since the block was moving this time, the sum of the forces in the x-direction were equal to (ma). After solving for the coefficient of kinetic friction and plugging in the measured angle and the acceleration, a value of 0.251 was found.

Part 5

     Part five of the experiment asked to predict the acceleration of the block when attached to some amount of mass over a pulley. After the prediction, it asked to test the experiment with a motion sensor to find the acceleration. Since the same mass was being used on the same surface as part 4, the mass measurement and coefficient of kinetic friction values would be used. The hanging mass was simply weighed on a scale to find its value. In this trial, a hanging mass of 0.08kg, a block mass of .111kg, and a coefficient of kinetic friction value of .251 was used.

     The first thing that needed to be done was draw the free body diagrams of the block, string, and hanging mass. Then, the sum of forces needed to be found. Solving for acceleration and simply plugging in numbers was the last step. Here are those steps:

Free-body diagrams for each mass.

     The sum of forces were found and solved for acceleration. The acceleration of the system was then predicted by plugging in the masses into the derived acceleration equation. Then the trial run was done. A graph on logger pro popped up and a linear fit was done for the velocity vs time graph. The slope of the line gave the acceleration of the system. The predicted acceleration was not close to the actual acceleration. Each trial gave a sloppy velocity vs time graph so a best fit line had a poor correlation. This might have been caused by the surface of the ramp not being smooth enough.