Lab 7: Modeling Frictional Forces
Chris Ceron, Amy Chung, John Choi
Purpose
To model static and kinetic frictional forces through five different experiments by using different angled surfaces.
Theory/Introduction
1 - Static Friction (flat surface)
Static friction is the the frictional force acting between two objects as they are not moving. As shown in the figure above, the magnitude of the static frictional force equals the magnitude of the opposing force until the object begins to move. Once an object moves, a constant kinetic friction between both objects applies.
The maximum point of static friction can be modeled mathematically as:
N - the normal force the surface exerts on the object
The coefficient of static friction,
, equals the maximum value of static friction between the two surfaces divided by the normal force.
The force of static friction can be modeled as:
where the static friction force can range from 0 to the maximum value of
.
M (wooden block on flat surface):
m (hanging mass):
We modeled this free body diagram by attaching a wooden block to hanging mass using string and a friction-less pulley system. We placed the linoleum surface of the wooden block on a wooden board, and increases the hanging mass in small increments (increments of 5 grams) until the wooden block began to move. We used the total of the hanging mass to calculate the maximum static friction between the block and the board.
We repeated the process four times, each time adding an increment of 200 grams to the wooden block. Using the data recorded from the four cases, we graphed the normal force of the block as y and the force of static friction as x to model the equation of a line. Then we used a linear fit to find the slope, which is now the coefficient of static friction:
The slope given by LoggerPro shows a value of 0.400.
2 - Kinetic Friction (on a flat surface)
Once the object begins to move, we see that kinetic friction remains constant and does not depend on the speed of the force. We model kinetic friction as:
To calculate kinetic friction, we tied a force sensor to our wooden block using a string. We first calibrated the sensor by a 1-kg hanging mass, which is 9.8N due to gravity. We used LoggerPro to collect the data needed as we pulled the force sensor and block at a constant speed. Since our acceleration is zero, the force applied would be equal to the force of kinetic friction. Similar to the first experiment, we recorded four different cases, each with an increment of 200 grams to the wooden block.
We graphed the normal force vs. the mean of the force obtained by the force sensor found the coefficient of kinetic friction by finding the slope of the line.
Our slope value obtained, the coefficient of kinetic friction, was 0.2769 +/- 0.0048.
3 - Static Friction from a Sloped Surface
Static friction on a sloped surface reaches is maximum when the x component of the forces are big enough to move the object. To find the maximum static friction of the block, we slowly increases the slope of the wooden board until the block began to move. Through a free body diagram, we found our x and y components of the forces acting on the block:
We used a phone application to find the slope of the wooden panel and recorded the slope when the wooden block began to move. Using the angle, we were able to calculate the static friction. The angle recorded was 33 degrees.
4 - Kinetic Friction from Sliding a Block Down an Incline
To measure the kinetic friction of the block, we held the wooden board at a slope that would cause the block to accelerate down the board. The acceleration of the block would allow for us to calculate kinetic friction. We placed a motion sensor on the top of the board and recorded the block's position vs. time, which would allow us to then calculate the acceleration of the block. We also used our phone application to record the slope of the wooden board.
The acceleration we obtained through LoggerPro is 4.071 m/s^2. The angle we used was 33 degrees. Our calculation for the coefficient of kinetic friction was:
5 - Predicting the Acceleration of a Two-Mass System
In a two-mass system (similar system to the one used in experiment one), we can add a hanging mass heavy enough to accelerate the wooden block. We attached a motion sensor to the opposite end of the table and measured the position of the block vs. time as it was being accelerated by the hanging mass.
We acceleration value obtained was 1.5 m/s^2. The hanging mass we used was 95 grams. Through our free body diagram, we obtained the following x and y component of the forces:
M:
m:
Assuming T1 is equal to T2, and using the .183kg as mass of the block, and .095 kg for the hanging mass, we can calculate the coefficient of kinetic friction.
Conclusion
There were several discrepancies in the data that caused our calculated kinetic and static friction to widely vary in between experiments. These discrepancies were given before the lab, as we knew that each repetition of the procedure would come out with different data and calculations.
Gathering of all our coefficients:
Some of the variations between the coefficients calculated from a flat and sloped surface could be due to the speed in the increment of the slope. We found that in several instances that the board would begin to slide down the sloped board at different angles. For experiments with hanging masses, we found that the block would move at different masses. There were instances where the block would begin to move when the hanging mass was up to 40 grams lighter than the case before.
Our calculated coefficient of kinetic friction in experiment 4 differed from experiments 2 and 5. This could be because the block was initially placed too close to our motion sensor.
Although there were many uncertainties in our experiments like the ones mentioned above, we were still accurately able to show that the coefficient for kinetic friction was larger than the coefficient for static friction.
 |
| Static and Kinetic Forces source: http://physics-ref.blogspot.com/2014/11/physics-9702-doubts-help-page-6.html |
1 - Static Friction (flat surface)
Static friction is the the frictional force acting between two objects as they are not moving. As shown in the figure above, the magnitude of the static frictional force equals the magnitude of the opposing force until the object begins to move. Once an object moves, a constant kinetic friction between both objects applies.
The maximum point of static friction can be modeled mathematically as:
N - the normal force the surface exerts on the object
The coefficient of static friction,
The force of static friction can be modeled as:
where the static friction force can range from 0 to the maximum value of
 |
| Free body diagram for the set up of experiment one |
m (hanging mass):
We modeled this free body diagram by attaching a wooden block to hanging mass using string and a friction-less pulley system. We placed the linoleum surface of the wooden block on a wooden board, and increases the hanging mass in small increments (increments of 5 grams) until the wooden block began to move. We used the total of the hanging mass to calculate the maximum static friction between the block and the board.
We repeated the process four times, each time adding an increment of 200 grams to the wooden block. Using the data recorded from the four cases, we graphed the normal force of the block as y and the force of static friction as x to model the equation of a line. Then we used a linear fit to find the slope, which is now the coefficient of static friction:
The slope given by LoggerPro shows a value of 0.400.
2 - Kinetic Friction (on a flat surface)
Once the object begins to move, we see that kinetic friction remains constant and does not depend on the speed of the force. We model kinetic friction as:
To calculate kinetic friction, we tied a force sensor to our wooden block using a string. We first calibrated the sensor by a 1-kg hanging mass, which is 9.8N due to gravity. We used LoggerPro to collect the data needed as we pulled the force sensor and block at a constant speed. Since our acceleration is zero, the force applied would be equal to the force of kinetic friction. Similar to the first experiment, we recorded four different cases, each with an increment of 200 grams to the wooden block.
We graphed the normal force vs. the mean of the force obtained by the force sensor found the coefficient of kinetic friction by finding the slope of the line.
Our slope value obtained, the coefficient of kinetic friction, was 0.2769 +/- 0.0048.
3 - Static Friction from a Sloped Surface
Static friction on a sloped surface reaches is maximum when the x component of the forces are big enough to move the object. To find the maximum static friction of the block, we slowly increases the slope of the wooden board until the block began to move. Through a free body diagram, we found our x and y components of the forces acting on the block:
We used a phone application to find the slope of the wooden panel and recorded the slope when the wooden block began to move. Using the angle, we were able to calculate the static friction. The angle recorded was 33 degrees.
4 - Kinetic Friction from Sliding a Block Down an Incline
To measure the kinetic friction of the block, we held the wooden board at a slope that would cause the block to accelerate down the board. The acceleration of the block would allow for us to calculate kinetic friction. We placed a motion sensor on the top of the board and recorded the block's position vs. time, which would allow us to then calculate the acceleration of the block. We also used our phone application to record the slope of the wooden board.
The acceleration we obtained through LoggerPro is 4.071 m/s^2. The angle we used was 33 degrees. Our calculation for the coefficient of kinetic friction was:
5 - Predicting the Acceleration of a Two-Mass System
In a two-mass system (similar system to the one used in experiment one), we can add a hanging mass heavy enough to accelerate the wooden block. We attached a motion sensor to the opposite end of the table and measured the position of the block vs. time as it was being accelerated by the hanging mass.
We acceleration value obtained was 1.5 m/s^2. The hanging mass we used was 95 grams. Through our free body diagram, we obtained the following x and y component of the forces:
M:
m:
Assuming T1 is equal to T2, and using the .183kg as mass of the block, and .095 kg for the hanging mass, we can calculate the coefficient of kinetic friction.
Conclusion
There were several discrepancies in the data that caused our calculated kinetic and static friction to widely vary in between experiments. These discrepancies were given before the lab, as we knew that each repetition of the procedure would come out with different data and calculations.
Gathering of all our coefficients:
| µ (k or s) | |
| Experiment 1 | 0.400 (s) |
| Experiment 2 | 0.2769 (k) |
| Experiment 3 | 0.65 (s) |
| Experiment 4 | 0.154 (k) |
| Experiment 5 | 0.287 (k) |
Some of the variations between the coefficients calculated from a flat and sloped surface could be due to the speed in the increment of the slope. We found that in several instances that the board would begin to slide down the sloped board at different angles. For experiments with hanging masses, we found that the block would move at different masses. There were instances where the block would begin to move when the hanging mass was up to 40 grams lighter than the case before.
Our calculated coefficient of kinetic friction in experiment 4 differed from experiments 2 and 5. This could be because the block was initially placed too close to our motion sensor.
Although there were many uncertainties in our experiments like the ones mentioned above, we were still accurately able to show that the coefficient for kinetic friction was larger than the coefficient for static friction.
"Some of the variations between the coefficients calculated from a flat and sloped surface could be due to the speed in the increment of the slope."
ReplyDelete--I don't know what that last part means.
..still accurately able to show that the coefficient for kinetic friction was larger than the coefficient for static friction.
--should be the other way around.