Eric Chong
Lab 7: Physics 4A Lab -- Modeling Friction Forces
Lab Partners: Lynel Ornedo and Harvey Thai
Purpose: The goal of this lab is to model the trends of static friction and kinetic friction in five different experiments.
Introduction/Theory: Friction is a force that has two parts: static and kinetic. Static friction is friction that occurs when an object is stationary. It is harder to move an object when it is initially stationary than when it is already in motion. This is due to the irregularities between the surface the object is touching and the electrical charges on the surface. It takes more energy to move the object from rest than to keep it in motion. This is why static friction is a stronger force than its counterpart, kinetic friction. Kinetic friction is friction that occurs when an object is moving. Although its a weaker force, its effect is still visible. Many times objects slow down to a halt, and this is due to kinetic friction. When calculating for the friction force, there are friction coefficients that result from the surfaces of objects, and each one is different, depending of the type of surface. The equation for friction is this:
Ffriction = μN
(Note: N is the normal force applied to the object, and mu has different values depending on the type of friction and the type of surface)
Since the friction force relies on the normal force, it is expected for heavier objects on a surface to experience a greater amount of friction. By calculating the gravitational force on the object, and whether the object is on an inclined slope, we can find the normal force applied on the object. Furthermore, by calculating the amount of force needed to get an object to start moving, we can also deduce the static friction coefficient of that object and the surface. Lastly, once an object starts moving, we can apply a constant force on the object and have the object move at a constant speed in order to infer the coefficient of kinetic friction.
Procedure: 1) Static Friction
For this experiment, we set up a block, that has a mass of 175 g, connected to a string that is also connected to a hanging mass on the other end. The string is set upon on a pulley, with the felt side of the block on the table, and the hanging mass hanging in mid air from the edge of the table. This gives us the complete setup in order to find the force needed to get the block to move. Here is a picture of the setup:
After completing the setup, we then added some masses on the hanging mass until the hanging mass and the block started moving. The mass we measured on the hanging mass is a total of 90 g. Afterwards, we added more 200 g more on the block itself. This should increase the mass needed on the hanging mass in order to move the block. The measured mass for this trial is 200 g. We then did 2 more trials, each time adding 200 g more to the block. The results are 255 g and 420 g respectively. Here is a data table to summarize the results:
From here, we can find the force of static friction for each trial. To do this, we used a graph of the forces calculated from the mass of the hanging mass. We calculated the normal force by setting the normal force equal to the gravitational force. We also calculated the force of friction by calculating the gravitational force of the hanging mass. Here are the results and the graph:
From observation, the line is linear, and the reason this is so is that the equation of the force of friction resembles a line equation. Compare y=mx+b to Ffriction = μN. For this case, mu would be the slope of the graph, and the normal force is the x value inputted into the equation. From this logic, the slope of the line is the coefficient of static friction. Our value of the coefficient of static friction is 0.5105 +/- 0.02551. Now that we have the coefficient, we can find any value of the maximum force of static friction of the block by calculating its normal force.
2) Kinetic Friction
For this experiment, we attached a force sensor to the string that is connected to the block. We then connected the force sensor to LoggerPro and measured the force needed to keep the block moving at constant speed by pulling the block with the force sensor connected to the string. Here is a picture of the setup:
Once we measured the force, we then analyzed the average force on the graph and it looks like this:
From the data, the mean force is 0.4246 N. This gives us the force that will keep the block moving at constant speed.
We then added 200 g more to the block like we did in the first experiment, and pulled the string with the force sensor. We did this 3 times, for a total of 600 g in the third time, and measured the force each time. Here are the data from the trials:
From the data, we can see the averages of the force in each trial. The averages for each trial (4 in total) from least to greatest mass are 0.4246 N, 0.9319 N, 1.263 N, and 1.912 N. We then calculated the normal force on the block for each trial just like we did in the first experiment. Here is a data table to summarize the data:
We then graphed these results and looked at the slope of the line created. Here is the graph:
The slope of the graph, which is also the coefficient of kinetic friction in this case, is 0.2529 +/- 0.001228. From here, we can calculate any value of the maximum force of kinetic friction by calculating for the normal force applied to the block.
3) Static Friction from a Sloped Surface
For this experiment, we had an inclined slope and placed the block on the slope. We then lifted one end of the slope until the moment the block started to slip. At this moment, we measured the angle the slope makes with the table. The angle we got turned out to be 23.2 degrees. From here we can deduce the coefficient of static friction with calculations. Here are the necessary calculations:
By drawing a free body diagram, making the x and y-axis parallel and perpendicular to the direction of acceleration, and noticing that the Force of Static Friction is equal to the x-component of the gravitational force, we can solve for the coefficient of static friction, which turned out to be 0.43.
4) Kinetic Friction from sliding a block down an incline
For this experiment, we raised the incline slightly above the angle that we measured from the previous experiment. The angle we used was 25 degrees. We placed a motion detector at the top of the incline and connected it to LoggerPro. To ensure that the motion detector could see the block's movement, we taped an index card on one end of the block. Here is a picture of the setup:
After completing the necessary setup, we ran the experiment and measured the block's motion as it slid down the incline. Here is a picture of the data measured:
For this part, we looked at the slope of the velocity and took that as the acceleration of the block. The acceleration for our case is 1.519 m/s^2. The acceleration can be used to find the coefficient of kinetic friction through calculations, similar to the calculation of static friction. Here is a picture of the necessary calculations:
Through drawing the free body diagram and realizing that the summation of the x-components add up to the quantity of mass and acceleration, we can solve for the coefficient of kinetic friction, which turned out to be 0.30
5) Predicting the acceleration of a two-mass system
For this final part of the lab, we used the coefficient of kinetic friction we calculated from the previous part in order to derive an equation of acceleration. The derivation is this:
From here, we measured the mass of the hanging mass that moves the block. The mass of the hanging mass is 0.100 kg. Finally, we can use the measurements of the block mass, the hanging mass, and the kinetic coefficient in order to find the theoretical acceleration of the system. Here is the calculation:
The theoretical acceleration turns out to be 1.6945 m/s^2. Here is the experimental acceleration measured:
The experimental acceleration is actually 1.561 m/s^2. From observation, the experimental acceleration is less than the theoretical acceleration.
Conclusion: Through all five of these experiments, we were able to manipulate equations and derivations in order to give us the coefficients of static or kinetic friction for our models. From our models, we can find the maximum force of friction depending on the normal forces applied to the objects. Though this experiment was largely a learning purpose in order for us to see how friction works with the other forces, the lab was still prone to uncertainties, and this may extend to experiments in the future. Some sources of uncertainty were the surfaces. The surface of the block was very unsteady and could easily slip and slide from a single touch. By slightly shaking the table, or even due to the positioning of the block, the block was prone to slipping and ruin the calculated force needed to get it to start moving. Another source of uncertainty was the pulley itself. It is very possible that the pulley manipulated the tension and swayed the calculations. Since tension was very important in most of these calculations, this is the uncertainty that is crucial to our calculations. Perhaps using a more ideal pulley would make it better. And specifically in experiment 2, perhaps a source of uncertainty would be the pulling of the block, since it was largely unstable in the 4 trials we ran, which may have altered slightly our data, though we tried to combat this by taking the average. Overall, this lab was an endeavor to capture the mindset of how forces work with one another, specifically friction. Friction is reliant on the static or kinetic friction, depending on the type of surface and whether the object is moving, and the normal force applied to the object. The normal force is changed by whether the object is on an inclined slope at an angle. By drawing free body diagrams and looking at the x and y components, we can solve for the unknown variables and plug them into the other equations and find the value we are looking for. Friction is a force that occurs in everyday life, and by knowing how it functions, we can have a better understanding of how our lives work.
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