16-Mar-2015: Modeling Friction Forces

Purpose: For this lab we had 5 different experiments that all involved friction. We wanted to physically see the properties of static and kinetic friction in different systems.

Part 1: Static Friction

Procedure: Static friction is the friction force acting between two bodies when they are not moving relative to one another. For this part of the lab we are going to measure the maximum static friction of a block on a table top being pulled by cup of water on a pulley. We kept adding water to the cup until the weight surpassed the maximum static friction from the block. The threshold of motion in the experiment can be characterized by u(static) = f(static, maximum)/Normal. We weighed a block with felt on one side, tied a string on it and and put the string over a pulley to a paperclip attached to a cup. We patiently added water to the cup (very little at a time) until the block started to slide. Then recorded the mass in of the cup required to move the block. We weighed another block and added to the first block and repeated the steps all the up to four blocks.

lab apparatus with four blocks

Results/Analysis:  Our results were put into a data chart and converted into a friction/Normal graph. When we applied the linear fit you can see that the slope of the linear fit is very consistent with the points on the graph. The slope of the graph is our coefficient of static friction. Below you can see that our u(static) was A = .2912, which is a reasonable number for a coefficient of static friction.

Graph of friction (static)/ Normal force. also data table and slope

Part 2: For part two we wanted to measure the kinetic friction of an object by building a model that is in motion. The kinetic friction of an object can be measured with the equation f(kinetic) = u(kinetic)/Normal. In our model, the kinetic friction force is a fixed value for a given N, regardless of the speed of the motion. Like static friction, the coefficient of kinetic friction is not dependent on weight or area of contact, but the on the surface material.

For this lab we needed a force sensor tied to a block, and required us to apply a pull force onto the block with a constant speed along the surface of the table. First we calibrated the force sensor by hanging a 500 N mass on the end. Then we measured the mass of the wooden block. with a horizontal pull applied, we hit collect and and stored the run under from the experiment menu. Using the analyze menu and choosing statistics, we recorded the mean value of the pulling force for the block while it moved horizontally on the surface. We then repeated the steps with a second, third, and fourth block.

4 Blocks tied to a force sensor

After saving our four runs, we were able to find the mean value of the pulling force so that we can plot the friction force over the normal force in another graph.

Graphs of force/time for the four runs

Below you can see we were able to find the coefficient of kinetic friction by using the linear fit and looking at the slope of the graph.

graph of kinetic friction/ Normal force

Part 3: The next part of the lab required us to put the block on a dynamic surface where we could have it horizontal initially and slowly raise one side of the surface until the block breaks static friction and slides down the surface. We carefully measured the angle at which the block surpassed the threshold for maximum static friction with our phone app. We were then able to solve for the coefficient of static friction of the block using the mass of the block and the angle theta of the slope. Notice how our result is similar to that of the static friction for the first block in the first experiment.

Diagram of experiment of static to static friction

Part 4: Here we wanted to measure kinetic friction from sliding a block down an incline. Using a motion detector fixed at the top of the ramp, we recorded the position of the block as it slid down the ramp over a period of time. we measured the weight of the block, the angle of the incline and also found the acceleration of the block as it slid down the ramp. We found that the acceleration of the block was .4164 m/s^2 at a 19.3 degree incline. 

block sliding down incline with motion sensor

Below shows our calculations that we did analytically using our values of mass and the angle of the incline. We wanted to find the answer for the coefficient of static friction analytically and compare it to the results on our graph .

calculating coefficient of kinetic friction

Part 5: The final part of our lab required us to predict the acceleration of a two mass system. Using our coefficient for kinetic friction from part 4, we were tasked to to derive an expression for what the acceleration of the block would be if we used the hanging mass sufficiently heavy enough to accelerate the system down.

lab setup for two mass system

We drew the system up in order to understand the forces being applied to the block so we can solve for the acceleration. we created an equation and plugged in our values and figured out that theoretically our acceleration of the mass should be around 0.459 m/s^2. We want to compare this answer to what we get from our graphs formed by the motion sensor and logger pro.

calculating acceleration of the block

graph of position/time and velocity/time. shows slope which is the acceleration

Above are the results of both our calculated results and the results from the motion sensor. Our calculated answer was only 1/100ths of a decimal off, which showed that we were very accurate with our prediction.

Conclusion/Uncertainty: Through this experiment, we were able to confirm friction in action and relate our calculated results with results from our lab equipment. Our results showed that the coefficient of static friction is always greater than that of the kinetic friction. This is inline with how it should work theoretically and in the real world because it should be harder to move something that is still than to move something that is already in motion. Also the coefficients of friction are always under 1 because it the friction was greater than the normal force being applied, the system would not move. Our results also proved that the coefficient of friction is only affected by the surface of the objects and not the speed of the object or the weight. 

Uncertainties in our lab experiments include things such as our measuring tools, which are not precise to the third or fourth decimal place. also the table at times could very in smoothness and texture. Things like the air resistance are ignored when pulling our objects down inclines so our answers are not exact.