Lab #7
Modeling Friction Forces
Ricardo Gonzalez and Josue Luna
3-22-17
Using our understanding of friction forces and how they work, we will be conducting five experiments. Each experiment will be used to model either the coefficient of static or the coefficient of kinetic friction.
1. Introduction
Our understanding of friction is all the same. Not all surfaces are smooth therefore the two surfaces generate heat. When looking at a motion, the maximum amount of force needed to barely get an object to start moving from rest is called static friction. The amount of force required to keep an object moving at a constant velocity is called kinetic friction. Both static and kinetic friction are parallel to the motion of the object. Also. the friction force is opposite to the direction of motion, however friction may also cause motion.
We will be conducting multiple experiments. By measuring or calculating the maximum amount of force to barely get a block to begin moving we can find the coefficient of static friction. Similarly, by measuring the amount of force needed to move an object with a constant velocity, therefore no acceleration is present, we can calculate the coefficient of kinetic friction.
2. Procedure
Part 1
To measure the maximum static friction force, we will be measuring the total amount of force require to barely get a block to start moving by utilizing an ideal pulley and a hanging mass that we can measure. We placed the felt side of the block on the tables surface. Next we clamped a pulley on the corner of the table. A string was attached to the block, placed over the pulley and then tied to a hanging mass of 5 grams. We began adding 5 grams to the hanging mass until the force due to gravity of the hanging mass would begin to move the block. We repeated the process by placing 200 grams on top of the block and once again added increments of 5 grams to that hanging mass until the block barely began to move. Two more trials were conducted by adding 200 grams each time and adding increments of mass to the hanging mass.
Part 2
To measure the kinetic friction of the same block, we will move the block with a constant force and therefore moving the block at constant velocity. We first began by retrieving a laptop to utilize the logger pro software and a force sensor. We connected to the force sensor to the laptop, set the force sensor range to 10-N, held the force sensor vertically to "Zero" the force sensor on the logger pro software and placed the force sensor horizontally on our table surface to "Zero" the sensor. We tied a string from the block to the force sensor. Starting with just the mass of the block, we placed the felt-side of the block facing the ceiling. We hit "Collect" on the logger pro software and began pulling the block using the force sensor at constant velocity.
Part 3
To calculate the static friction from a sloped surface, we began by placing the block at an end of the board and placing our phones to measure the angle. As the board was raised, at a certain angle created by the board with respect to the table, the block just barely began to slide down the board.
Part 4
To find the kinetic friction from sliding a block down an incline, we raised the wooden board at an incline large enough so that we know the block will accelerate down the incline. Using the motion sensor, we can measure the acceleration of the block down the incline and also measure the angle of the inclined surface using our phones. As the block moves down the incline, an opposing force of due to kinetic friction is decelerating the motion and can be calculated.
Part 5
To predict the acceleration of a two-mass system, we can use the coefficient of kinetic friction we found in part 4 to theoretically find a value of acceleration for the system and then compare that to the experimental value measured using a motion sensor.
Run 2 = mass of block + 200 grams with the mean force applied
Run 3 = mass of block + 400 grams with the mean force applied
Run 4 = mass of block + 600 grams with the mean force applied
The acceleration = 4.79 m/s^2
4. Analysis In Part 1, we plotted the ratio of the masses. Just at the moment the block barely starts to begin moving, the force of the tension is equal to the weight of the big M (our hanging mass) and therefore the maximum static friction is equal to the weight of the hanging mass. When we solve for the coefficient of static friction, we get a ratio of the blocks mass over the hanging mass. If we think of the ratio as a slope (rise/run), then our rise (y-axis) is the mass of the block and our run (x-axis) is the mass of the hanging mass. When all points are plotted, the slope of the line gives us the coefficient of static friction between the block and the wooded board. Th coefficient of static friction from the slope was 0.435.
In Part 2, we found the mean force needed to move the block across the surface of the wooden board at constant velocity. Since there is no acceleration, then the force needed to move the object at constant velocity is equal to the kinetic friction force opposing the motion. When we solve for the coefficient of kinetic friction, we get a ratio of the Kinetic Friction Force and Normal force. When graphed, the slope of the line gives us the coefficient of kinetic for the wooden block onto the surface of the wooden board. The coefficient of kinetic friction was 0.232 which is reasonable since the coefficient of static friction should be larger that that of the coefficient of kinetic friction tat we found in part 1 to be 0.435.
In part 3, we set up a sum of forces in the x and y direction and solved for the coefficient of static friction between the block and the surface of the wooden board. This is only achievable when we utilize the maximum angle the block can be raised at an incline just before the block begins to accelerate down the incline. When we solved for the coefficient of static friction , we got 0.445 which is just about the same as the coefficient of static friction we calculated in part 1 which was 0.435.
In part 4, we raised the block on an incline at an angle we know the block would accelerate down the incline. When we found the acceleration of the block using a motion sensor, we were able to a sum of forces that accelerated the block and solved for the coefficient of kinetic friction. Surprisingly, the coefficient of kinetic friction was 0.323, different from the number we calculated in part two which was 0.232.
In part 5, we can theoretically calculate the acceleration of a block with a two mass system, if we add a large enough mass to accelerate the block from rest. Using the coefficient pf kinetic friction found in part 4, we theoretically found the acceleration to be 4.79 m/s^2. We did not manage to conduct the experiment and so we do not have a real life value for the acceleration to compare too.
5. Conclusion
In conclusion, we can use our current knowledge of forces to calculate both the coefficient of static and kinetic frictions. Not so simple is to be able to interpret, the ratio of masses as it is not so obviously seen. Through the calculations, we can conclude that the values for kinetic friction were within reasonable values between parts 2 and 4. However, the coeffiecients of static friction between parts 1 and 3 there was a differnce of nearly 40 percent between the two values calculated. A reason for this is simply becasue in part 1, the coefficient of static friction relied on a ratio of masses as opposed to in part 3 where the coefficient of static friction was reliant on the angle itself.
1. Introduction
Our understanding of friction is all the same. Not all surfaces are smooth therefore the two surfaces generate heat. When looking at a motion, the maximum amount of force needed to barely get an object to start moving from rest is called static friction. The amount of force required to keep an object moving at a constant velocity is called kinetic friction. Both static and kinetic friction are parallel to the motion of the object. Also. the friction force is opposite to the direction of motion, however friction may also cause motion.
We will be conducting multiple experiments. By measuring or calculating the maximum amount of force to barely get a block to begin moving we can find the coefficient of static friction. Similarly, by measuring the amount of force needed to move an object with a constant velocity, therefore no acceleration is present, we can calculate the coefficient of kinetic friction.
2. Procedure
Part 1
To measure the maximum static friction force, we will be measuring the total amount of force require to barely get a block to start moving by utilizing an ideal pulley and a hanging mass that we can measure. We placed the felt side of the block on the tables surface. Next we clamped a pulley on the corner of the table. A string was attached to the block, placed over the pulley and then tied to a hanging mass of 5 grams. We began adding 5 grams to the hanging mass until the force due to gravity of the hanging mass would begin to move the block. We repeated the process by placing 200 grams on top of the block and once again added increments of 5 grams to that hanging mass until the block barely began to move. Two more trials were conducted by adding 200 grams each time and adding increments of mass to the hanging mass.
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| Here is a two-dimensional representation of our apparatus. |
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| Here is a photo of our experiment for Part 1 |
To measure the kinetic friction of the same block, we will move the block with a constant force and therefore moving the block at constant velocity. We first began by retrieving a laptop to utilize the logger pro software and a force sensor. We connected to the force sensor to the laptop, set the force sensor range to 10-N, held the force sensor vertically to "Zero" the force sensor on the logger pro software and placed the force sensor horizontally on our table surface to "Zero" the sensor. We tied a string from the block to the force sensor. Starting with just the mass of the block, we placed the felt-side of the block facing the ceiling. We hit "Collect" on the logger pro software and began pulling the block using the force sensor at constant velocity.
We stored the latest run, we placed 200 grams on top of the block and repeated the process by pulling the block at constant velocity.
We then repeated the process with 400 grams and 600 grams placed on top of the block.
Part 3
To calculate the static friction from a sloped surface, we began by placing the block at an end of the board and placing our phones to measure the angle. As the board was raised, at a certain angle created by the board with respect to the table, the block just barely began to slide down the board.
Part 4
To find the kinetic friction from sliding a block down an incline, we raised the wooden board at an incline large enough so that we know the block will accelerate down the incline. Using the motion sensor, we can measure the acceleration of the block down the incline and also measure the angle of the inclined surface using our phones. As the block moves down the incline, an opposing force of due to kinetic friction is decelerating the motion and can be calculated.
Part 5
To predict the acceleration of a two-mass system, we can use the coefficient of kinetic friction we found in part 4 to theoretically find a value of acceleration for the system and then compare that to the experimental value measured using a motion sensor.
3. Measured Data/Results
Part 1
The coefficient of static friction = m/M
- Mass of block = 0.189 kg
hanging mass = 0.075 kg
-Mass (Total) of block = 0.389 kg
hanging mass = 0.125 kg
- Mass (Total) of block = 0.589 kg
hanging mass = 0.225 kg
-Mass (Total) of block = 0.789 kg
hanging mass = 0.39 kg
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| Notice, we graphed the ratio of the masses in terms of grams. Whether in grams or kilograms, the ratio, or the slope, is unaffected. |
Part 2
The Kinetic Friction Force = Coefficient of Kinetic Friction x Normal Force
Therefore, the Coefficient of Kinetic Friction = Kinetic Friction Force/Normal force
Here we measured the forces resulted from pulling the block.
Run 1 = mass of just the block with the mean force applied. Run 2 = mass of block + 200 grams with the mean force applied
Run 3 = mass of block + 400 grams with the mean force applied
Run 4 = mass of block + 600 grams with the mean force applied
Below is a graph of the mean force vs the Force from kinetic friction.
Part 3
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| By drawing the forces on the system, we can find the sum of the forces in the x direction, the y direction, and then simplify for the coefficient of static friction between the block and the wooden board at the maximum angle. |
Part 4
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| Here is a graph for our motions velocity vs time |
Coefficient of kinetic friction 0.323
Part 5
4. Analysis In Part 1, we plotted the ratio of the masses. Just at the moment the block barely starts to begin moving, the force of the tension is equal to the weight of the big M (our hanging mass) and therefore the maximum static friction is equal to the weight of the hanging mass. When we solve for the coefficient of static friction, we get a ratio of the blocks mass over the hanging mass. If we think of the ratio as a slope (rise/run), then our rise (y-axis) is the mass of the block and our run (x-axis) is the mass of the hanging mass. When all points are plotted, the slope of the line gives us the coefficient of static friction between the block and the wooded board. Th coefficient of static friction from the slope was 0.435.
In Part 2, we found the mean force needed to move the block across the surface of the wooden board at constant velocity. Since there is no acceleration, then the force needed to move the object at constant velocity is equal to the kinetic friction force opposing the motion. When we solve for the coefficient of kinetic friction, we get a ratio of the Kinetic Friction Force and Normal force. When graphed, the slope of the line gives us the coefficient of kinetic for the wooden block onto the surface of the wooden board. The coefficient of kinetic friction was 0.232 which is reasonable since the coefficient of static friction should be larger that that of the coefficient of kinetic friction tat we found in part 1 to be 0.435.
In part 3, we set up a sum of forces in the x and y direction and solved for the coefficient of static friction between the block and the surface of the wooden board. This is only achievable when we utilize the maximum angle the block can be raised at an incline just before the block begins to accelerate down the incline. When we solved for the coefficient of static friction , we got 0.445 which is just about the same as the coefficient of static friction we calculated in part 1 which was 0.435.
In part 4, we raised the block on an incline at an angle we know the block would accelerate down the incline. When we found the acceleration of the block using a motion sensor, we were able to a sum of forces that accelerated the block and solved for the coefficient of kinetic friction. Surprisingly, the coefficient of kinetic friction was 0.323, different from the number we calculated in part two which was 0.232.
In part 5, we can theoretically calculate the acceleration of a block with a two mass system, if we add a large enough mass to accelerate the block from rest. Using the coefficient pf kinetic friction found in part 4, we theoretically found the acceleration to be 4.79 m/s^2. We did not manage to conduct the experiment and so we do not have a real life value for the acceleration to compare too.
5. Conclusion
In conclusion, we can use our current knowledge of forces to calculate both the coefficient of static and kinetic frictions. Not so simple is to be able to interpret, the ratio of masses as it is not so obviously seen. Through the calculations, we can conclude that the values for kinetic friction were within reasonable values between parts 2 and 4. However, the coeffiecients of static friction between parts 1 and 3 there was a differnce of nearly 40 percent between the two values calculated. A reason for this is simply becasue in part 1, the coefficient of static friction relied on a ratio of masses as opposed to in part 3 where the coefficient of static friction was reliant on the angle itself.
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