Friction and the Inclined Plane

Student’s Name 

Date 

Abstract: The objective of the study is to compute the coefficient of friction using the two methods, including the incline plane. In addition the study also looks into the factors affecting coefficient of friction. Aside from the weight of the block, the study agrees with the theoretical concepts about kinetic and static friction. 

Introduction 

Kinetic friction is the force that resists relative motion between two objects in contact. On the other hand, static friction is the friction that occurs between two stationary objects. Frictional force is always oppositive to the direction of motion. The ratio between the force required to resist friction and the normal force is known as the coefficient of friction ( Barrett, 2014 ). While friction acts parallel to the plane of the surface of contact, normal force acts at right angle to the plane of the surface of contact. 

The equation for kinetic friction is: 

Equation 1

Where  is the coefficient of kinetic friction,  is friction, and N is the normal force. 

Static friction is mathematically represented as: 

Equation 2

Where  is the coefficient of static friction,  is friction, and N is the normal force. 

Coefficient of friction can also be computed using an inclined plane. From the angle of an inclined plane (Ɵ), measured from when the block moves down the inclined plane at a constant speed, the coefficient of friction can be computed by identifying the ratio of the height (h) to the base (b) of the inclined plane. Mathematically, coefficient of friction using the incline plane model is: 

= tan Ɵ­ c

Equation 3

Apparatus 

The experiment requires the following: adjustable inclined plane, set of gram weights, two meter sticks, one 1 kg mass, weigh hanger, 1 meter long string, wooden block with precut holes for holding weight, and one 500 gram mass. 

Procedure 

Setup Procedure 

The measured wooden block was placed on the inclined plane with its wide side facing down. The plane, which was parallel to the table top, was positioned in a manner that allowed the pulley to extend over the edge of the table. The height of the pulley was then adjusted until it was the same height as the precut hole on the wooden block. The weight hanger was then placed on the string. The subsequent set up was the same, except for the inclined plane which was raised to different angles. The angle adjustments that were made on the inclined plane in the subsequent setup were 15 °, 30°, and 45°. 

Experimental Procedure 

After setting up the apparatus, weights were added on the weigh hanger until the block moved with a constant velocity. The total weight of the weight hanger along with the weights added were recorded in Table 1. An additional mass of 500 grams was then added on the block of wood, after which the aforementioned procedure were repeated. Again, the 500 grams mass was replaced a 1 kilogram mass. The setup procedure along with the addition of weights on the weight hanger was repeated. Upon the completion of the aforementioned procedures with the wide side of the block facing down, the setup was adjusted with the narrow end of the block facing down this time round. The loading procedure was repeated with the weights required to overcome static friction being recorded. In the subsequent procedures, the setup’s angle of inclination was gradually adjusted for 0 ° to 45° with constant increments of 15°. The loading procedures described above were repeated with the weights required to overcome static friction being recorded. 

In part B of the experiment, the wooden block on the inclined plane was setup with its wide side facing down. The inclined plane was then slowly raised until the block moved at a constant speed upon overcoming the static friction. The angle was recorded on Table 3. The heigh and the base of the inclined plane was also measured and recorded on table three as h and b, respectively. The aforementioned procedure was repeated with a a 500 grams and 1 kilogram wooden block. 

Data 

Part A 

Table 1 

Object moved	Weight W(dynes)	Side Used	Angle    ( θ )	Pulling Force F(dynes)	Coefficient of Friction µ k = f/N
Block only	189434	Wide	0	39200	0.21
Block + 500 g	680414	Wide	0	151900	0.22
Block + 1 kg	1170414	Wide	0	240100	0.21
Block only	189434	Narrow	0	39200	0.21
Block + 500 g	680414	Narrow	0	151900	0.22
Block + 1 kg	1170414	Narrow	0	240100	0.21

Table 2 

Object moved	Pulling Force F (dynes)	Angle ( θ )	Normal Force N = W cos θ	Parallel Force W sin θ	Frictional Force f = F – W sin θ	Coefficient of Friction µk = f/N
Block only	86240	15°	182979	49029	37211	0.203
Block only	132300	30°	164054	94717	37583	0.229
Block only	173460	45°	133950	133950	39510	0.295

Part B 

Table 3 

Object moved	Weight W (dynes)	Angle  θ  ( θ )	h (cm)	b (cm)	μ k	µ k  = tan θ
Block only	189434	16	17.5	69.0	0.254	0.287
Block + 500g	680414	15	16.5	70.0	0.236	0.268
Block + 1kg	1170414	15	16.5	70.0	0.236	0.268

Calculation and Graphs 

Figure 1 : The above graph compares the relationship between friction and normal forces for the wide and narrow faces of the block as per Table 1. 

According to the graph above, a change in the surface area of contact does not affect the coefficient of friction in anyway; the gradient for the graphs, which represents the coefficient of friction, does not change with area. 

Figure 2: The graph above compares the change in the angle of inclination to coefficient of friction as per Table 2. 

According to the graph, as the angle of inclination increases, coefficient of gravity also increases. 

Figure 3: The graph above compares the coefficient of friction to the weights. As the weight increases, the coefficient of gravity reduces. 

Discussion 

According to the experiment outcome, the frictional force, and the subsequent coefficient of friction is independent of the contact area between the two surfaces. Although Figure 3 shows a small drop in the coefficient of friction as mass increases, the coefficient of friction does not depend on the mass of an object ( Halliday et al., 2013 ). The variation between the theoretical and the practical outcome may have been as a result of systematic errors. However, as the angle of inclination increases, the coefficient of friction increases. 

Conclusion 

The primary objective of the study was to determine the coefficient of friction using the two methods. In addition, the study intended to analyze the various factors affecting the coefficient of friction. The study was a success since these objectives were achieved. 

References  

Halliday, D., Resnick, R., & Walker, J. (2013).  Fundamentals of physics . John Wiley & Sons. 

Barrett, T. E. (2014).  A study guide to accompany Fundamentals of physics . Wiley.