bjective:
The objective of this experiment was to determine the coefficient of static friction and the
coefficient of kinetic friction of a mass using three different methods. A specific analysis will be done on the peak static friction and kinetic friction. Moreover, this lab was conducted to determine the relationship between the static/kinetic friction force and the acceleration of an object, as well as its mass and whether they are dependent on each other.
In order to stop an object in motion, a force must be exerted on that object that is equal in magnitude, but opposite in direction. This force is called the force of friction (Knight, 2008).There are two different types of friction; static and kinetic. Static friction is the force that prevents an object from moving (keeps it stationary) (Knight, 2008). Once the object starts to move, kinetic friction takes over. This is the friction force that acts in the opposite direction of the movement while the object is in motion (Knight, 2008). More specifically, it is always harder to start the motion of an object than to keep it in motion. This is due to the fact that static friction is always greater than kinetic friction (Knight, 2008). Moreover, increasing the roughness of the surface results in increasing the friction force (Knight, 2008). This leads to a higher static friction and kinetic friction, showing that friction is dependent upon the surface.
For this lab, a wooden block will be pulled with different masses and the maximum static friction and kinetic friction will be measured. Moreover, the block will be pushed with different masses and then the kinetic friction will be measured. It is hypothesized for this experiment that the static and kinetic friction forces are depended on the mass of the object. Increasing the mass of an object results in increasing the friction force.
Theory:
In this lab, an experiment has been conducted to determine whether the static and kinetic friction
forces are depended on the mass of the object. Both static and kinetic friction are proportional to the coefficient of friction and the magnitude of the normal force (Knight, 2008). The normal force is the contact force that is perpendicular to a surface where two objects are in contact with each other. Force of friction is the force that resists the motion and acts in the opposite direction (Knight, 2008). The normal force can be calculated using the following formula:
F = m.g
Where:
F is the normal force (N)
m is the mass of the object (kg)
g is the gravitational acceleration 9.8 m/s2
A force vs. time graph can be used to determine the value of the peak static friction. Static friction is the force required to start the motion of the object, meaning that it is the highest value on the graph. Furthermore, there are two ways to determine the kinetic friction. One way to find the kinetic friction is from the force vs. time graph, where the linear part can be analyzed to find the mean (which is the value of kinetic friction). Another way to calculate it is mathematically using Newton’s second law formula:
Ff=k*FN Where:
μk is the coefficient of kinetic friction Ff is the force of friction (N)
FN is the normal force (N)
To calculate the coefficient of kinetic friction, the following formula can be used:
μk= Ff/ N
Where:
μk is the coefficient of kinetic friction Ff is the force of friction (N)
N is the normal force (N)
Procedure:
Method 1
1.) The force sensor was connected to channel one of LabPro. The force sensor was then calibrated
and ensured that its range was 10N.
2.) Using hooks, a wooden block was hung to the force sensor. The sensor was held as vertical as
possible and data was calculated. This data was used to calculate the mass of the block
3.) The block and sensor, held together by hooks, were placed on a horizontal track. The sensor was
zeroed.
4.) The force sensor was slowly pulled until the wooden block began to move. Constant force was
applied for 2-3 seconds and data was recorded in the table.
5.) This process was repeated using a 500g block, and a 1kg block
Method 2:
6.) The motion sensor was set to cart mode
7.) The motion sensor was placed at the end of the track, and the wooden block was also placed on
the track with the hook facing away from the motion sensor
8.) The wooden block was pushed towards the motion detector, and its velocity was recorded with
LoggerPro. This was used to calculate the acceleration of the block.
9.) This process was repeated using a 500g block, and a 1kg block.
Method 3:
10.) The track was attached to a retort stand and placed at an angle as shown in figure 1.
11.) The 1kg mass was placed inside the wooden block and placed at the bottom of the ramp.
12.) The block was slowly pulled up the ramp using the force sensor. The process used here is similar
to the process in method 1.
13.) The height of the ramp, and the length of the ramp was measured. This was used to determine the angle of inclination.
14.) Repeat this process using two different inclinations
Figure 1: This shows how the ramp would look, along with the block placed on the ramp. The inclination would change every time the ramp was adjusted
Results:
Method 1:
To begin the experiment, the sensor and wooden block were held up as vertical as possible. Data was recorded, and the force was calculated. This was divided by the force of gravity, to give the mass of the wooden block. The calculations are shown below:
Fnet=m*a
Fnet/a=m
Fnet= 2.458 N 10 N a=9.8 m/s2
m=2.458N/9.8 m/s2 m=0.25 kg
After this, the block and the sensor were laid on a horizonal track. The force sensor was used to pull the wooden block across the track, and to see the magnitude of force needed to pull it across the track. LoggerPro was used to determine these values. The highest peak of the graph represents the peak static friction value, while the linear portion represents the kinetic friction. Figure 2 illustrates the results of one graph below, for the 1kg mass.
Figure 2: Determining peak and constant friction
This graph shows the static and kinetic friction when there is a 1kg mass placed on the wooden block. The peak in the graph represents the static friction, and the value of the static friction is 7.81 N. The mean of the data after the peak value represents the kinetic friction acting on the block, which was 6.03 N. The static friction shows that there needed to be a value of 7.81N to allow the block to start moving, while a force of 6.03 N was needed to keep it in motion.
Following this, the peak force values for the different masses was put into a graph and the slope of the graph was calculated. The slope of the graph represents coefficient of static friction. Moreover, the mean values for the different masses was also put into the graph, and the slope of that line represented the coefficient of kinetic friction. Figure 3 shows the graphical results:
Figure 3: This graph shows the results for the peak force v mass graph, and the kinetic friction force v mass graph. As the results show, the peak force has a steeper slope, while the kinetic force has a lower force. The coefficient of static friction was shown to be 5.93 1.088, while the coefficient of kinetic friction was 5.02 0.9786.
Once these values were obtained, they were divided by the force of gravity. The reason for this is, the slope of figure 3 is force of friction over mass. The equation for the coefficient of friction is the force of
friction/mass*gravity. Thus, in order to get the true coefficient of friction, the slope of the two lines in the graph must be divided by gravity. Below are sample calculations for how the coefficient was calculated: Sample calculations for calculating coefficient of friction
k= Force/mass*gravity
k= slope of figure 3/gravity k= 5.02 𝑁/𝑘𝑔
9.80 𝑚/𝑠2
k= 0.512
s= peak slope of figure 3/gravity
s= 5.93 𝑁/𝑘𝑔 9.8 𝑚/𝑠2
s= 0.605
Table one also shows the results of the graph in a table format:
Table 1: Masses and their peak force/kinetic force:
This table shows the results of the method 1. As the mass increases, the static and kinetic force increases as well. These results make sense due to the formula Fk=*m*g, showing that the peak force, and the kinetic force is directly proportional to the mass. The highest peak force was 7.81 N, while the lowest was 1.92 N. This contrasts with the kinetic force, which has a maximum of 6.03N at 1.25 kg, and a minimum of 1.05 at 0.25 kg.
Therefore, as shown through the graph, the force needed to start the movement of the object is always greater than the force needed to keep the object in movement. Regardless of the changes in the mass of the object, the static force is always going to be greater than the kinetic. The reason for this is Newton’s first law, the law of inertia. An object that is at rest will like to remain at rest, and will resist a change in motion (Knight, 2013). The initial movement will be harder to overcome, and when the object is already in motion it will be easier to overcome the friction forces and continue the motion since the object is
Mass (kg)
Peak force (N)
Kinetic force (N)
0.250
1.92
1.05
0.725
3.39
2.22
1.25
7.81
6.03
already in motion and wants to stay that way. Moreover, what was also discovered is that as the mass of the object increases, force needed to move it increases. Thus, the coefficient of static friction is always greater than the coefficient of kinetic friction, and both the static/kinetic friction force increases with mass.
Method 2:
In this part, the acceleration of the block was measured by giving the block a push towards the motion detector. Data was collected using LoggerPro, and a velocity versus time graph was created based on the push. To obtain the acceleration of the block, the slope of the v-t graph was obtained. A sample graph of one of the velocity-time graphs is shown below:
Figure 4: This v-t graph highlights the velocity of the block as it is pushed towards the motion sensor. The mass of the block was 1.25kg, and the acceleration at this point was 3.55 m/s2 .
Trials were done for each mass, starting from just the wooden block, to the wooden block with the 1kg of weight. Once the acceleration was determined, the force of kinetic friction would be determined by multiplying the mass by the acceleration. Upon finding the force of kinetic friction, the coefficient of friction was determined by diving the force by the product of mass and gravity.
Table 2 shows the results:
Mass (kg)
Acceleration (m/s2)
Force of Kinetic friction (N)
k
0.250
2.02 0.765
0.505
0.206
0.750
2.82 0.765
2.12
0.288
1.25
3.55 0.765
4.44
0.362
Table 2 displays the acceleration determined by the graph on LoggerPro. The mass and the acceleration were multiplied to get the Force of kinetic friction, which then opened up the opportunity to obtain the values for the coefficient of friction.
As shown in table 2, as the mass of the object increased, the coefficient of kinetic friction increased as well. Moreover, when the mass of the object increased, the acceleration of the object increased, showing a proportional relationship. Sample calculations for the values obtained in the table are shown below: Sample calculation for kinetic force:
Fnet = (mass)(acceleration)
Fk =(mass)(acceleration)
Fk=(0.250 kg)(2.02 m/s2)
Fk=0.505 N
Sample calculation for Coefficient of friction:
Fk=k(mass)(gravity)
k =Fk/(mass)(gravity)
0.505N/(0.250 kg)(9.8m/s2)=k
k=0.206
Average force of kinetic friction:
Avgk= (k1+k2+k3)/3
Avgk= (0.206+0.288+0.362)/3
Avgk=0.285
Shown through the equation above, the coefficient of friction is not dependent upon the speed of the object. The reason for this is, the only thing the coefficient of friction is dependent upon is the force of friction divided by the normal force. In ideal conditions, other factors such as the speed don’t impact it, but only the two forces acting on the object do (Knight, 2008).
In method one and two, the coefficients of kinetic friction were calculated. Method 2 is the more realistic result as there was one swift push with no change in force applied. In method one, the force is applied for 2-3 seconds and even though it is said to apply constant force, it is tough to apply that in practice. Moreover, in method one two calculations must occur, first the slope of the line in the graph, and secondly the result of that must be divided by gravity. More calculations mean there is a higher chance for error due to rounding, and thus method 1 has a higher chance of error. A percent error calculation between both methods is shown below. Method two is deemed the more accurate results, thus it is referred to as the expected value.
Percent difference calculations:
Error %= |𝑒𝑥𝑝𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒−𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒| *100 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒
Error%= 0.227 *100 0.285
Error %= 79.6
Therefore, the error difference between both methods is 79.6%, showing a drastic difference between the
results obtained in method one and those obtained in method 2.
Method 3:
During method 3, the track was put onto a retort stand and as a result put on an angle of inclination. The wooden block with a 1kg mass was placed at the bottom of the track, and the block was slowly pulled up the ramp similar to method 1 with its data being recorded on LoggerPro. A graph below depicts the force needed during the experiment.
Figure 5: This graph shows the force needed to pull the cart up the incline. To begin, it needed a high amount of force to begin the motion, about 7.83 N. Afterwards, the force needed began to decrease as the cart was in a constant motion. Upon reaching the top of the track at about 4.5 seconds, the force needed lowers significantly as the cart reached the max height.
The angle of inclination was changed two more times and the process was repeated, with the peak static force being recorded both times. The peak forces were then put into a table along with their angle, and a peak force vs sin graph was created.
Figure 6: This graph shows the peak forces compared to the angle they were at. As the green line shows, when the angle increased, the peak force also increased, making it harder for the block to go up the track. The slope of this line was taken to determine the coefficient of static friction. Upon taking the slope, it was determined the coefficient of static friction was 22.7 0.1655.
The coefficient obtained in the graph above used the formula static force/sin ()= s. This formula isn’t entirely correct as the formula for finding the static friction on an incline is S= FS/(mass)(gravity)( sin
()). Thus, the slope obtained in the graph above will be divided by m*g to obtain a more accurate coefficient of static friction. Below is the sample calculation for obtaining the coefficient of static friction:
S= 𝑆𝑙𝑜𝑝𝑒 𝑜𝑓 𝑡h𝑒 𝑔𝑟𝑎𝑝h (𝑀𝑎𝑠𝑠)(𝐺𝑟𝑎𝑣𝑖𝑡𝑦)
S= 22.7 𝑁
1.25 𝑘𝑔∗9.8 𝑚/𝑠2
S= 1.85
Upon discovering the coefficient of static friction in method 3, it was compared to the coefficient of static
friction in method 1. The two methods differ in the way they used to find the coefficient of static friction.
Method 1 changed the mass of the block while maintaining a constant track, while method 3 changed the
angle of inclination while keeping a constant mass. Method 1 was better because it computes a more
realistic coefficient of static friction (0.605). A coefficient of 1.85 is very high and requires the force of
static friction to be higher than the normal force, which is not common. Moreover, method one allowed
less source of error due to it being easier to maintain constant force on a horizontal track rather than at an
incline. When taking something up an incline the likelihood of someone accidentally increasing force is
high due to the ramp increasing in height, thus it’s not the best method. The percent difference between
method one and 3 was calculated to see the difference between the results. Method 1 is the expected value
since it’s deemed to be the more accurate value.
Error %= |𝑒𝑥𝑝𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒−𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒| *100
𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒
Error%= 1.85−0.605 *100 0.605
Error%= 206% Thus, the percent error for method 3 was determined to be 206%.
Uncertainty calculations:
There were no uncertainty calculations for this lab as everything was done on the computer, thus the RSME values were taken for the uncertainties.
Conclusion
This lab has been conducted to determine the coefficient of static and kinetic friction of a wooden
block carrying different masses. Moreover, this lab was done to determine whether increasing the mass of an object has effects on the friction force that is resisting the motion of the object. It was hypothesized that the friction force and the mass of the object are directly proportional to each other; increasing the mass of the object results in a stronger frictional force.
The results showed multiple key ideas and trends. One trend it displayed was that the coefficient of static friction will always be greater than the coefficient of kinetic friction. This is shown through figure 3, where the slope of the kinetic friction graph was less than the static friction graph, indicating it has a lower coefficient. This general principle can be applied to every situation in physics, as the force needed to take an object out of inertia (static force) is larger than the force needed to keep it in motion (kinetic force).
Moreover, another trend that was observed is that as the mass of an object increases, its kinetic and static force increases. As shown in tables 1 and 2, when the mass was raised from 0.250kg to 0.750 kg, and then 1.25 kg, the peak force and kinetic force needed also increased. This is because both friction forces are dependent on the push, also known as the applied force. The magnitude of the force of friction is equal to the magnitude of the applied force. Thus, when you apply more force, the force of friction will increase as well. Since the weight was increased, more force will be required to push the object since more weight is harder to push. As a result of this, since the friction force is equal in magnitude to the applied force, it increases as mass increases.
Furthermore, it was discovered that the surface area did not impact the coefficient of kinetic friction. This is shown throughout the experiment, as nowhere in the lab did it specify to push the block for a certain length. The only time height was required was to calculate the angle of inclination. Surface area does not impact the coefficient of friction, as shown through the equation mk=Fk/(mass)(gravity). This equation shows there is no dependence on the displacement, or surface area of the object. Instead, the coefficient of kinetic friction is only dependent upon the force of friction (which is equal in magnitude
to the applied force), and the normal force being exerted on the object. Moreover, while it is true that a larger contact area leads to a larger source of frictional forces, those forces are cancelled out due to a reduction in the pressure of the systems holding the two objects together. Pressure multiplied by surface area equals force, and thus when the surface area increases, the pressure decreases leading to the same amount of force of friction (physlink, 2018). A way to test if this theory is correct is by taking two equal masses on the same surface and pushing them with the same force. One mass should be pushed for 2 meters, and the other for 4 meters. Then, the values of the coefficients of static/kinetic friction should be compared on LoggerPro to see if surface area does not impact the coefficient of friction.
In all of the force vs time graphs shown in the report, the beginning force does not equal 0 at time 0, and instead equals a number greater. This should not be the case as when the time is at 0, no forces should be acting on the object. This is because when the time is 0, the object should not be in motion, If the object is not in motion, no forces are acting on it and the net force is 0, as shown through Newton’s first law (Knight, 2013). A possible reason as to why the results have the initial force being greater than 0 can be due to human error. The individual moving the cart could have accidentally began to apply a force onto the cart before the force sensor began recording, thus causing an initial force being applied on the cart. This would lead to the graph showing an initial force value greater than 0, displaying the error.
During method 3 of the lab, when pulling the block up the track, the track would sometimes slide before the block began to move. This can be explained through the coefficients of static friction the two objects have. The coefficient of static friction between the track and the table is smaller than the coefficient of friction between the track and the block. This is because it required less force to cause the track to move, in comparison to the block. When minimal force was applied on the block, it wouldn’t move, but when the same force was being exerted on the track it would begin to slide. Thus, the force of friction is less on the track than the block, which means the coefficient of static friction is less on the track than the block since the force and coefficient are proportional through the equation Fk=mk(mass)(gravity).
To determine the minimum angle at which the block will not be able to stay stationary, a FBD diagram of the block can be drawn and Newton’s second law of motion can be used to analyze the forces acting on the block. In the x-axis, only two forces are acting on the block, Fg, and FF. By setting the equation equal to zero (in order to keep the block stationary), the result will give f*FN=m.g. sin(1). The same analysis can be done on the y-axis, the resulted equation will be FN=m.g. cos (2). Dividing equation (2) by (1) will give the following formula tan=f. Therefore =tan -1(f). Using the coefficient of kinetic friction calculated in method 3 (1.85), will be 61.6. At this angle, the block will not slide, however, any angle that is higher than this value will cause the block to slide.
The percent error was calculated for this experiment and it was determined to be 79.6% when comparing method 1 and 2 and was 206% when comparing method 1 and 3. Some sources of error may have happened and caused the margin of error indicated above. For example, the block might have experienced either a very strong or very weak applied force. If the block was pulled/pushed very hard, the applied force would easily resist the force of friction. Moreover, the applied force has been done by a human hand, which means keeping the block at a constant velocity might not be very accurate. This could have affected the experiment and gave inaccurate results. In order to improve this experiment next time, more trials can be done when pulling/pushing the block. By doing so, more data can be collected, and the accurate ones can be chosen. In addition, being more careful when pulling the block at a constant velocity, which can give more accurate results when selecting the linear portion from the graph to analyze.
In conclusion, the friction force is the force that resists the motion of an object and acts in the opposite direction of the motion. Static and kinetic are the two different types of friction. Static friction is the force that keeps the object stationary, while kinetic friction acts on the object while it is in motion. For this lab, the coefficient of static and kinetic friction was determined by pushing/pulling a wooden block with different masses. Results show that increasing the mass of the object causes an increase in the frictional force. Furthermore, results also indicate that static friction is higher in value than kinetic friction, meaning that static friction requires more input of applied force that it does for kinetic friction.
Knight, Randall D. Physics for Scientists and Engineers: A Strategic Approach . 3rd ed., Pearson
Education , 2013.
References
Skorucak, A. (n.d.). Friction and Surface Area. Retrieved October 17, 2018, from