In addition, beam balance is necessary in the experiment for measuring the masses, which have to be hung at the hanger. Except we have to know how to use the beam balance correctly, we should know how to minimize depletion of the balance. When we do not use the beam balance, we have to move one of masses to the right-hand sides.
Results & Calculations
Reading taken before the block begins to move:
Reading taken after the block is moving:
In the following calculations, we have made several assumptions:
- Air resistance is neglect
- The friction is evenly distributed on any surface of the sand paper (i.e. the friction should be the same over the whole sand paper.)
- The wooden block is moving in constant velocity.
Mass of the block used = 0.194 kg
From the graph, we can know the first seven readings belong to the static region while the others belong to kinetic region. So we can estimate that:
The static friction: 1.4N ± 0.05 N
The kinetic friction: 1.2N ± 0.05 N
Coefficient of static friction = static friction / normal reaction force
= 1.4 / (0.194*10)
= 0.722 (Cor. to 3 sig. Fig.)
The uncertainty = 0.05/1.4 + 0.0005/0.194 = 0.0383 (Cor. to 3 sig. Fig.)
The percentage error = 0.0383 * 100% = 3.83%
So, the coefficient of static friction = 0.722 ± 0.0383
Coefficient of kinetic friction = kinetic friction / normal reaction force
= 1.2 / (0.194*10)
= 0.619 (Cor. to 3 sig. Fig.)
The uncertainty = 0.05/1.2 + 0.0005/0.194 = 0.0442 (Cor. to 3 sig. Fig.)
The percentage error = 0.0442 * 100% = 4.42%
So, the coefficient of kinetic friction = 0.619 ± 0.0442
Part B: Coefficient of friction for various masses
Procedures
- All wooden blocks were weighed by the beam balance and labeled with numbers.
- The scale of the spring balance was set properly to zero.
- The sand paper was placed on the table.
- A wooden block was placed on the table.
- The wooden block was connected to the spring balance in series.
- The block was pulled until the block was moving.
- The reading of the static friction was recorded.
- The block was pulled to move in constant velocity.
- The reading of the kinetic friction also was recorded.
- Step 6 and 7 were repeated except increasing the numbers of the blocks that were held by the rubber band.
Precautions
In this experiment, we should keep the spring balance in horizontal position in order to ensure that only the applied force support the motion of the wooden block. If it is not in horizontal position, horizontal component of the applied force will support motion. Secondly, we should keep the wooden block that it is moving in constant velocity as much as possible; otherwise, the magnitudes of the applied force will be different from time to time. Moreover, the sand paper may make the wooden surface become smoother, and hence the static and kinetic friction may be different from the original one. So the numbers of pulling process should be minimized. On top of the above precautions, the spring balance is not connected to the wooden block firmly; it may be disconnected during the pulling process. Therefore, we should pay attention to the connection point between the spring balance and the wooden block during the experiment. As we need to increase the numbers of the blocks during the whole experiment, we should keep the way of increasing the numbers of blocks the same, for example, we may pile up the blocks throughout this experiment.
In addition, beam balance is necessary in the experiment for measuring the masses, which have to be hung at the hanger. Except we have to know how to use the beam balance correctly, we should know how to minimize depletion of the balance. When we do not use the beam balance, we have to move one of masses to the right-hand sides.
Results & Calculations
In the following calculations, we have made several assumptions:
- Air resistance is neglect
- The friction is evenly distributed on any surface of the sand paper (i.e. the friction should be the same over the whole sand paper.)
- The wooden block is moving in constant velocity.
- The mass of the rubber band is neglect.
Mass of the block 1 = 0.194 kg
Mass of the block 2 = 0.1943 kg
Mass of the block 3 = 0.1952 kg
Mass of the block 4 = 0.1976 kg
From the graphs, we find out the values of coefficient of the static and kinetic frictions: Slope of the line = coefficient of friction we have to find.
For static friction:
According to the equation fL = µs R,
The slope of the graph = value of the coefficient of the static friction.
The co-ordinate of centroid : (4.88 , 3.55)
µs = slope of the graph
µs = (3.55 – 0.0) / (4.88 - 0.0)
µs = 0.727 (Cor. to 3sig. Fig.)
Let the slopes of the two good- fit lines be m1 and m2.
m1= ( 5.0 – 3.55) / (6.5 – 4.88) = 0.895
m2= ( 5.5 - 3.55) / (8.0 – 4.88) = 0.625
Δm = [(0.895 - 0.727) + (0.625 - 0.727)] /2
= 0.033
The value of coefficient of static friction µs: 0.727 ± 0.033
The maximum error in the value of coefficient of static friction µs: 0.727 ± 0.033
Maximum percentage error in the value of coefficient of static friction µs:
= 0.033 * 100% = 3.3%
For kinetic friction:
According to the equation fk= µk R,
The slope of the graph = value of the coefficient of the static friction.
The co-ordinate of centroid : (4.88 , 2.80)
µs = slope of the graph
µs = (2.80 – 0.0) / (4.88 - 0.0)
µs = 0.574 (Cor. to 3sig. Fig.)
Let the slopes of the two good- fit lines be m1 and m2.
m1= ( 1.50 – 2.80) / (3.00 – 4.88) = 0.691
m2= ( 3.95 – 2.80) / (6.95 – 4.88) = 0.556
Δm = [(0.691 - 0.574) + (0.556 - 0.574)] /2
= 0.0495 (Cor. 3 sig. Fig.)
The value of coefficient of kinetic friction µk: 0.574 ± 0.050
The maximum error in the value of coefficient of kinetic friction µk: 0.574 ± 0.050
Maximum percentage error in the value of coefficient of static friction µl:
= 0.050 * 100% = 5.0%
Part C: Contact surface area
Procedures
- All wooden blocks were weighed by the beam balance and labeled with numbers.
- The scale of the spring balance was set properly to zero.
- The sand paper was placed on the table.
- Two wooden blocks were piled up and placed on the table.
- The blocks were held by rubber band.
- The wooden blocks were connected to the spring balance in series.
- The block was pulled to move in constant velocity.
- The reading of the kinetic friction also was recorded.
- Step 6 and 7 were repeated except that the two blocks were placed side by side.
- Step 4 to 9 were repeated except increasing the numbers of the wooden block by one.
Precautions
In this experiment, we should keep the spring balance in horizontal position in order to ensure that only the applied force support the motion of the wooden block. If it is not in horizontal position, horizontal component of the applied force will support motion. Secondly, we should keep the wooden block that it is moving in constant velocity as much as possible; otherwise, the magnitudes of the applied force will be different from time to time. Moreover, the sand paper may make the wooden surface become smoother, and hence the static and kinetic friction may be different from the original one. So the numbers of pulling process should be minimized. On top of the above precautions, the spring balance is not connected to the wooden block firmly; it may be disconnected during the pulling process. Therefore, we should pay attention to the connection point between the spring balance and the wooden block during the experiment.
In addition, beam balance is necessary in the experiment for measuring the masses, which have to be hung at the hanger. Except we have to know how to use the beam balance correctly, we should know how to minimize depletion of the balance. When we do not use the beam balance, we have to move one of masses to the right-hand sides.
Results & Calculations
In the experiment, we have made several assumptions:
- Air resistance is neglect
- The friction is evenly distributed on any surface of the sand paper (i.e. the friction should be the same over the whole sand paper.)
- The wooden block is moving in constant velocity.
- All blocks are moving at the same time.
- The mass of the rubber band is neglect.
Errors and Accuracy
In this experiment, we had made several experimental errors, we can improve the experiment with the following the improvements:
First of all, the blocks were not moving in constant velocity during experiment. As the block had to move on the sand paper which have a large friction, it is difficult for students to move the blocks in constant velocity. If the blocks are not moving in constant velocity, the applied force will be different from time to time; the values of coefficient of the static and kinetic friction will be inaccurate. To get rid of such error, we should pull the block in constant velocity as much as possible; in addition, we can carry out the experiment for several times to obtain a more reliable result.
Secondly, the spring balance was exactly in horizontal position. The component of the applied force supports the motion of the blocks. In this way, we cannot study the effect of the normal reaction force on the friction. To do away with this error, except we can hold the spring balance in horizontal position as much as possible, we also can measure the degree of the direction of the applied force to the horizontal by using the projector.
Besides, the roughness of the sand paper is not the same over the whole sand paper. The friction produced between the block surface and the sand paper is different from place to place. As the friction is different over the whole surface of the sand paper, according to the formula, the values of the coefficient of static and kinetic frictions will not be constant. It is difficult for students to study the effect f the normal reaction force on the friction, as the coefficient of the friction is not constant. To avoid such error, we should choose the sand paper that the roughness is evenly distributed over the whole sand paper.
Moreover, sometimes the wooden blocks may have some wooden fragments out of the surface of the blocks. The fragments may provide extra friction acting on the block, according to the formula; the normal reaction force should increase when the friction increases. In this way, we cannot study the effect of normal reaction force on the friction. In addition, the fragments are easily removed during the pulling process; it may produce different frictional force acting on the block. Therefore, we should make sure that no wooden fragment is out of the surface of the wooden block. If it is present, we should remove all of them before we start the experiment.
On top of that, it is very difficult for human eyes to take the readings from spring balance, as the reading of the balance is not constant throughout the whole experiment. The scale of the spring balance is not firmly attached to the balance. When we pull the spring balance and hence the blocks, there must be vibration of the balance. The scale then is not set to zero. The reading we taken will be inaccurate and then inaccurate calculated values of the coefficient of the static and kinetic friction will be obtained. To prevent the error to occur, we should use glue to attach the scale firmly to the balance. As it is firmly attached, the vibration cannot make the scale leave its original position.
In addition, we pull the wooden blocks to move; the sand paper also is moved. In this way, we have to supply external force to fix the sand paper in position. The external force we supplied may cause an increase in the magnitude of the applied force. Inaccurate static and kinetic friction are obtained and hence the calculated coefficient of the static and kinetic friction will also be inaccurate. We should use the adhesive paper to fix the sand paper in position, in this way; no external force is acted on the system.
Furthermore, the length of the sand paper is not long enough and then the blocks just move in a very short time. It is difficult for students to take the readings from the spring-balance, as the time for the blocks to move is very short. To get rid of this error, we should increase the length of the sand paper or replace the sand paper with larger size.
Finally, there must be zero error of the apparatus in the experiment, the only thing we can do is to replace the apparatus with a smaller zero error.
Discussion
In this experiment, there are some assumptions we had made. Firstly, we assume that the air resistance is neglect. If the air resistance is not neglect, extra frictional force will be acted on the wooden blocks. This frictional force is difficult to measure by the common experimental apparatus. This extra frictional force may affect the values of the coefficient of static and kinetic friction calculated. Secondly, one of the assumptions is that the wooden blocks are moving in a constant velocity. If the bung is not moving in a constant velocity, the applied force will be different from time to time. The next assumption is that the friction is evenly distributed over the whole sand paper. If we do not assume that, the frictional force acted on the blocks will be different all the times. The coefficient of the static and kinetic friction will also be different over the whole sand paper. Next is that the mass of the rubber band is neglected. As the one rubber band has a very small mass. It just causes a very very small change in the weight of the blocks. So it can be neglected. The last assumption is that all blocks are moving at the same when we place the wooden blocks side by side.
The experimental errors can be divided into two errors, systematic errors and random errors. The zero errors of the spring balance and the beam balance are belonged to the systematic errors. All other experimental errors mentioned in the above section are the random errors. An experiment with small systematic and random errors is more precise.
Questions
- The friction acted on the block increases when the applied force increases in the static region. It shows that the magnitude of static friction increases when we apply a larger force in the opposite direction. The static friction is direct proportional to the applied force. The static friction balances the applied force until it reaches the limiting friction which is the highest point of the graph. After reaching the limiting friction, the kinetic friction then is acted on the block instead of the static friction. The graph then drops for a small value and then levels off as the block is moving in constant velocity.
- This case is totally wrong. If the applied force is smaller than the static friction, there will be a net force in the direction f the static friction that is opposite to the direction of the applied force. By the Newton’s second law of motion, the block will move in the opposite direction of the applied force. So this case is impossible. In the reality, the static friction is direct proportional to the applied force. The static friction always is equal to the applied force until it reaches the limiting friction.
- According to the Newton’s first law, the object maintains its motion in constant velocity or remains at rest unless a net force is acted on it. So we need a larger applied force to accelerate the blocks as it is initially at rest. Hence, a larger static friction exists. When the block is moving the in constant velocity, inertia also helps the block maintain its motion of moving in constant velocity. So a smaller net force also can be maintain the motion of the block. A smaller kinetic friction exists. By the formula of the static and kinetic friction, the coefficient of the kinetic friction is smaller than that of the static friction.
- The contact surface does not affect the kinetic friction as the difference between the two ways of placing the wooden blocks is small. It can be neglected. The kinetic friction acted on the two blocks which was piled up is 2.6N while the two blocks which was placed side by side is also 2.6 N. The kinetic friction acted on the three blocks which was piled up is 3.2N while the three blocks which was placed side by side is also 3.8 N. The kinetic friction acted on the four blocks which was piled up is 4.6N while the four blocks which was placed side by side is also 5.2 N. The difference between the placing way of the blocks is small. Therefore, The size of the contact force does not cause any significant change to the kinetic friction. However, the small difference is caused by the uneven roughness distributed over the sand paper and the experimental errors mentioned above.
Conclusion
In the three parts of the experiment, we can find out the effect of normal reaction force and contact surface on the kinetic friction and estimate the coefficient of static friction and kinetic friction.
In part A, we can find out the relationship between the friction and the applied force. When the applied force increases, the static friction also increases and it is direct proportional to the applied force which can be seen from the graph. So it can balance the applied force to make the block remain at rest. However, when the applied force further increases and overcome the maximum limiting friction which is the peak of the graph. After reaching the limiting friction, the graph drops and levels off. It shows that the block obeys the Newton’s first law. The applied force is same as the kinetic friction but in opposite direction. From graph, it shows that the static friction is smaller than the kinetic friction.
In part B, we can study the effect of normal reaction force on the static and kinetic friction and estimate the coefficient of static and kinetic friction from the graph, From the graph plotted, we can conclude that the normal reaction force is direct proportional to the static and kinetic friction from the graph. We also can estimate the coefficient of the static and kinetic friction by finding out the slope of the graphs. So the coefficients of static friction and the kinetic friction are 0.727 ± 0.033 and 0.574 ± 0.050 respectively.
In part C, we study the effect of contact surface on the friction. From the experimental result, we can conclude that the size of the contact surface does not cause significant change to the kinetic friction. The difference between the ways of placing the blocks is caused by the experimental errors discussed above. However, we can further investigate how the nature of the contact surface affects the kinetic friction such the metal surface.
References
Wikipedia (Friction)
http://en.wikipedia.org/wiki/Friction
New Way Physics for advanced level Mechanics