The Coefficient of Kinetic Friction Between a Block and an Include Plane

Objectives of the Experiment

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There were three objectives in this experiment. The first objective was to determine the coefficient of kinetic friction between a block and an include plane. The second objective was to determine the coefficient of static friction between a block and an inclined plane. The third objective was to examine compare the coefficients of kinetic and static friction were also compared.

Experimental Data

Part 1: Static Friction

In this experiment for static friction, there were two parts. The first part involved placement of the cart on a horizontal plane and the second part involved the placement of the cart on an inclined plane. Data was collected for both the experiments involving placement of the cart on a horizontal track and an inclined plane. The data obtained were recorded as shown in Part 1(a) and Part 1(b).

1(a). Cart on the horizontal track

Mass of the cart, M = 650g = 0.650kg

Mass of the hanger, m = 50g = 0.050kg

Mass on the hanger, mw = 70g = 0.070kg

Total mass of the hanger, mh = 120g = 0.120kg

1(b). Cart on an inclined plane

Trial Critical angle (Th)

1 10.3 0

2 10.3 0

3 10.30

Mass of the cart, M = 650g = 0.650kg.

Part 2: Kinetic Friction

In this experiment for kinetic friction, there were two parts. The first part involved placement of the cart on a horizontal plane and the second part involved the placement of the cart on an inclined plane. Data was collected for both the experiments involving placement of the cart on a horizontal track and an inclined plane. The data obtained were recorded as shown in Part 2(a) and Part 2(b).

2(a). Cart on the horizontal track

Mass of the cart M = 650g = 0.650kg

Mass of the hanger, m = 50g = 0.050kg

Run Acceleration, a

1 -0.02m/s

2 0.13m/s^2

2(b). Cart on an inclined plane

Run acceleration, a

1 0.02m/s

2 -0.32m/s^2

Mass of the cart, M = 550g = 0.550kg

Data Analysis

Part 1: Static Friction

1(a). Cart on the horizontal track

The experimental value of the coefficient of the static friction us calculated as follows:

Theoretical value=mwM =0.0700.650=0.108ms=experimental value-theoretical valuetheoretical value 100%Therefore, ms=0.185-0.1080.108 100% =71.3%The discrepancy between the experimentally determined us and its actual given value has been calculated to be:

=experimental value-actual valueactual value 100% =0.185-0.180.18100%=2.78%.1(b). Cart on an inclined plane

The experimental value of the coefficient of static friction us is calculated with equation (4) as follows:

The theoretical value is 10.30, for which us = 0.1817

Determine the discrepancy between the above-calculated value and the given one to compare them: 100%* (|calc. value expect. value| / expect. value).

=calculated value-expected valueexpected value 100%=0.1817-0.180.18100%=0.96%.Part 2: Kinetic Friction

2(a). Cart on the horizontal track

For run 1 the coefficient of kinetic friction mk is calculated as follows:

mk=FkF.= -0.101x 2=-0.202

For run 2 the coefficient of kinetic friction mk is calculated as follows:

mk=FkF.= 0.066*2=0.13

The average values of coefficient of kinetic friction mk from both runs is:

mk=0.202+0.132=0.07The discrepancy between the experimental and theoretical values is:

Discrepancy=0.07+0.090.09100%=22.2%2(b). Cart on an inclined plane

For run 1 the coefficient of kinetic friction mk is calculated as follows:

mk1=sin50+0.02cos50=0.11For run 2 the coefficient of kinetic friction mk is calculated as follows:

mk2=sin70+(-0.32)cos70=0.14The average values of coefficient of kinetic friction mk from both runs is:

mk=mk1+mk22mk=0.11+0.142=0.25The discrepancy between the experimental and theoretical values is:

Discrepancy=experimental value-theoretical valuetheoretical value100%Discrepancy=0.25-0.090.09100%=177.8%Discussion and Conclusion

There were three objectives in this experiment. The first objective was to determine the coefficient of kinetic friction between a block and an inclined plane. The second objective was to determine the coefficient of static friction between a block and an inclined plane. The third objective was to examine compare the coefficients of kinetic and static friction were also compared. The experiment tested the theory of friction. Friction is said to occur when two surfaces are brought into contact with each other. When two surfaces come into contact, they become cold-welded. To move the sources, the cold welds must first be broken. The force of Friction is a non-conservative force. Once the force applied is used to overcome frictional force and allow the object to move the force is dissipated into heat energy and it will never come back to the system even if the movements stops.

The results obtained in the experiment are consistent with the principles being investigated in the lab. Overall, the findings of the experiment supported physics theories about the coefficient of friction for both the static and kinetic friction. From the findings, it was found out that the theoretical value of the coefficient of friction is smaller than the experimental value. For example, while the theoretical value for the coefficient of static friction was 0.108, the experimental value was 0.185. A comparison between discrepancies between the experimental values suggests that the discrepancies are very small for static friction while discrepancies for kinetic friction are big. In a horizontal and inclined plane, the discrepancies for static friction are 2.78% and 0.96% respectively. However, the discrepancies for kinetic friction in the horizontal and inclined plane are 22.2% and 177.8% respectively. A comparison between coefficients of friction for static and kinetic friction show they are also different. For the kinetic friction, the coefficient of friction on a horizontal plane is 0.07 while that of an inclined plane is 0.25. For the static friction, the coefficient of friction for a horizontal plane is 0.185 while on an inclined plane is 0.181. In Fig 1 and 2, the displacement versus time graph shows that they are different from Fig 3 and 4. For horizontal friction, the graphs are more curved unlike for kinetic friction where the graphs are straighter.

Frictional forces have been shown to depend on not only the surface roughness of the bodies in contact but also the surface area. In this experiment, frictional forces also suggest it depends on the angle of inclination of the plane. This is because the coefficient of frictional forces for both the horizontal and inclined surfaces are different. But there were errors involved in the experiment, especially on measurements. It was difficult to maintain a steady speed of the cart to find the value of the coefficient of friction. The surface roughness of the cart was constantly changing. Accurate results would be obtained in perfectly even surfaces with materials hose surface roughness do not change with distance moved. Measuring of the angles of inclination is a challenge especially when human eyes are used. These errors can be reduced by employing more accurate measurement methods.