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Experiment 5:Friction and the Inclined PlanePhysics 1730June 15, 2020AbstractThe main purpose of this experiment was to measure the coefficient of friction and to determine the various factors that influence the coefficient of friction. This experiment was done in two parts and under several differe...

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Experiment 5: Friction and the Inclined Plane

Physics 1730 June 15, 2020

Abstract

The main purpose of this experiment was to measure the coefficient of friction and to determine the various factors that influence the coefficient of friction. This experiment was done in two parts and under several different angles to find the coefficient of friction. The results show that the surface area did not affect the coefficient of friction, and the angle required for the block to slide down the inclined plane decreased as the weight of the block was increased. The data presented show small inconsistency relating the measurements, though caused by human error does it not contribute to the conclusion as a whole. The average result in Part A for the narrow and the wide side gives the coefficient of Kinetic friction to be 0.212. The coefficient of Kinetic friction in part A with varying angles and constant mass is 0.242. In part B the average result of coefficient of kinetic friction is 0.2579. The calculation for the error in the result was not possible due to the fact that the actual or universal coefficient of kinetic friction between the block and the plane was not given.

Introduction When one body slides over another there is always a force between them that opposes their relative motion between them. This force is called the frictional resistance, or simply friction. Friction between two objects that opposes the relative motion when one object slides over another is known as the kinetic friction. Static friction is the friction that occurs between a stationary object and the surface on which it is resting. It is important to understand that the coefficient friction(µ) is defined as the ratio between the force needed to overcome friction i.e. frictional force(f) to the normal force(N). The equation for the coefficient of kinetic friction, µk=ff/N where µk is the coefficient of kinetic friction, fk is the kinetic frictional force in dynes, and N is the normal force in dynes. For the second method to determine the coefficient of friction, an inclined plane will be used. Using the angle of the inclined plane θ, the coefficient of kinetic friction(µ) is calculated from the height of the plane(h) to the base(b). This ratio is called the tangent of the angle θ between the inclined plane to the horizontal. µ= h/b= tanθ If we slide an object up a frictionless plane, the exerted force needed would have to be equal to the weight (W) times the sine of the angle that the plane makes with the horizontal (θ). P=W sin θ When a body slides down an inclined plane at a constant velocity, the weight component that is parallel to the surface of the inclined plane, P, just balances the frictional resistance, f. The angle of the uniform slip or angle of repose is the angle which the inclined plane makes with the horizontal, θ. The weight component that is perpendicular to the plane is just balanced by the normal for N. At the angle of uniform slip, the coefficient of friction becomes μ= W sinθ/N= h/b with h being the height of the end of the plane above the tabletop and b the length of the base of the plane along the tabletop. If the object is going up an inclined plane, the total force would be,

Fup=W sin θ+f While if the object is going down the inclined plane, the total force would be, Fdown=W sin θ− f

Apparatus 

1 adjustable inclined plane



Multiple gram weights to put of the sliding block and the weight hanger. This includes half kilograms and 1-kilogram mass. 1-meter stick to measure the length and height of the plane for the coefficient of friction calculations. 1 weight hanger for the gram weight placement. 1-meter long string that can be attached from the hanger over the pulley to the mass block. The rationale behind using the pulley is to reduce the friction, thereby collecting more accurate friction measurements. A wooden block that has an indentation inside for holding weights. This block also needs to be non-uniform in length for testing the wide and narrow sides.

   

Experimental Procedure The procedure of the experiment consists of two parts. In Part A, the block was tested at four different angles 0°, 15°, 30°, and 45°. In the 0° conditions, the block was tested in the narrow side as well as the wide side and the half kilogram and one-kilogram weights were placed on the wooden block, hence a total of six trails were measured for this degree condition. We first set the plane degree to 0, and placed string over the pulley such that the top of the pulley was at the same height as the eyelet on the wooden block and connected it to the weight hanger. The block was connected to the pulley in order to reduce the friction between the wooden surface and the string. The first set of readings was conducted using the wider side of the block, first without any weight, then a half kilogram weight, and then a one-kilogram weight. To observe whether the blocks would move, we placed gram weights on the weight hanger and gave a gentle push on the wooden block to notice whether there was a forward direction of motion. At the weight, the block begins moving with a constant velocity its value will be noted and the pulling force will be calculated. Then, 500 grams and kilogram blocks were added on top of the block and the same procedure described for the initial trial was implemented for the rest of the wide trials. We then proceeded with our trial of the narrow side following the same steps as mentioned above. After the trials for the 0 degree plane were completed we then proceeded to conduct trials using the

above-mentioned procedure with the wider side of the block by setting the angle of the plane to 15°, 30°, and 45° with only the block weight. That concludes part A. For part B, we were required to observe the wooden block moving with a constant velocity and the inclined plane with our own angles. This trial will be conducted with the wooded block's wider side facing down and with half kilogram weight and one-kilogram weight. When the block begins moving for the first set with no weights measure the angle of the inclined plane the height(h) of the inclined plane to the base and the length of the base. Once completed, repeat the above mention steps by added half kilogram weight and one-kilogram weight. This concludes part B.

Data Table 1 Object moved

Weight W(dynes)

Side Used

Angle (θ)

Block only 189434 wide 0° 680414 wide 0° Block + 500 g wide 0° Block + 1 kg 1170414 Block only 189434 narrow 0° 680414 narrow 0° Block + 500 g narrow 0° Block + 1 kg 1170414 Table 1. Table describing values for the 0° angle condition.

Pulling Force F(dynes)

Coefficient of Friction µk = fk/N

39200 151900

0.207 0.223

240100 39200 151900

0.207 0.223

240100

0.205

Table 2 Frictional Force f= F – Wsin θ Block only 86240 15° 182979.19 49029.13 37210.87 Block only 132300 30° 164054.66 94717.00 37583 Block only 173460 45° 133950.07 133950.07 39509.93 Table 2. Table describing values for the 15°, 30°, and 45°-degree conditions. Object moved

Pulling Force F (dynes)

Angle (θ)

Normal Force N = Wcosθ

Parallel Force W sin θ

Coefficien t of Friction µk = fk/N 0.203 0.229 0.295

Table 3 Object moved

Weight W (dynes )

Angle θ (θ )

h (cm)

b (cm)

μk h/b

µk = tan θ

Block 189434 16 17.5 69.0 0.2536 0.2867 only Block + 680414 15 16.5 70.0 0.2357 0.2679 500g Block + 1170414 15 16.5 70.0 0.2357 0.2679 1kg Table 3. Table listing values for variable angle set-up with new coefficient of friction values.

Data

Frictional force Vs Pulling force µk=ff/N 300000

Pulling Force F (dyne)

250000 200000 150000 100000 50000 0

0

200000

400000

600000

800000

1000000

1200000

1400000

Normal Force N(Dyne)

Table 1. This graph represents the relationship between the coefficient of kinetic friction and the surface area of the block against the plane. Since the values of the wide and narrow coincide one line series is represented. As you can see this line is not consistent since there is an increase in the pulling force. Using the data recorded from Table 1 Calculations for Coefficient of Friction: Equation used: μk = Fk / N; where µk is the coefficient of kinetic friction, Fk is the frictional force, and N is the normal force of the block.

Wide Side: Block only: μk = 39200 dyne /189434 dyne = .207 Block + 500 g: μk = 151900 dyne /680414 dyne = .223 Block + 1 kg: μk = 240100 dyne /1170414 dyne = .205 Narrow Side: Block only: μk = 39200 dyne /189434 dyne = .207 Block + 500 g: μk = 151900 dyne /680414 dyne = .223 Block + 1 kg: μk = 240100 dyne /1170414 dyne = .205 Average µk= (0.207+ 0.223+ 0.205+ 0.207+ 0.223+ 0.207)/ 6= 0.212

Frictional force Vs Pulling force µk=ff/N 40000

Pulling force N=W cos θ (dyne)

39500 39000 38500 38000 37500 37000 36500 36000 130000

140000

150000

160000

170000

180000

190000

Frictional force Fk = F - W sin θ (dyne)

Table 2. For the inclined plane, you can see we remained with a consistent coefficient of friction. This graph should show that no matter what angle is used, the friction of the plane will remain the same. The line should be linear, but because of the inconsistencies in the wood it made it hard for us to gather precise measurements.

Using the data recorded from Table 2 Calculations for Coefficient of Frictions: Equations used: N=W cos θ; Fparallel = W sin θ; Fk = F - W sin θ; μk = Fk / N;

where µk is the coefficient of kinetic friction, W is the weight of the block, Fparallel is the force need to slide the block down the plane, Fk is the frictional force, N is the normal force of the block, and θ is the angle of the inclined plane. 15°:

N = 189434 dyne* .9659 = 182979.19 dyne Fparallel = 189434 dyne* .2588 = 49029.13 dyne Fk = 86240 dyne - 49029.13 dyne = 37210.87 dyne μk = 37210.87dyne /189434 dyne = 0.203

30°:

N = 680414 dyne * .8660 = 164054.66 dyne Fparallel = 680414 dyne * .5000 = 94717.00 dyne Fk = 132300 dyne - 94717.00 = 37583.00 dyne μk = 37583.00 dyne / 164054.66 dyne = 0.229

45°:

N = 1170414 dyne * .7071 = 133950.07 dyne Fparallel = 1170414 dyne * .7071 = 133950.07 dyne Fk = 173460 dyne - 133950.07 dyne = 54337.00 dyne μk = 54337.00 dyne / 133950.07 dyne = 0.295

Average µk= (0.203+ 0.229+ 0.295)/ 3= 0.242

Normal Force Vs Angle μk=tan θ 16.2 16 15.8

Angle θ

15.6 15.4 15.2 15 14.8 14.6 14.4

0

200000

400000

600000

800000

1000000

1200000

1400000

Normal Force F(dyne)

Table 3. This graph should remain linear showing that the change in mass of the object does not change the coefficient of linear friction, but due to the inconsistencies in our measurements we can see that the graph is not linear.

Using the data recorded from Table 3 Calculations for the Coefficients of Friction: Equations used: μk =h/b; μk = tan θ; where µk is the coefficient of kinetic friction, h is the height of the Inclined plane to the base, b is the length of the base of the inclined plane, and θ is the angle at which the plane is inclined. Block only: μk = 17.5cm / 69.0cm = 0.2536 μk = tan (16°) = 0.2867 Block + 500 g: μk = 16.5cm/ 70.0cm = 0.2357 μk = tan (15°) = 0.2679 Block + 1 kg: μk = 16.5cm/ 70.0cm = 0.2357 μk = tan (15°) = 0.2679 Average μk= (0.2536+ 0.2357+ 0.2357+ 0.2867+ 0.2679+ 0.2679)/ 6= 0.2579

Discussion of Results and Error Analysis From Part A of the experiment, the coefficient of friction from the wide side of the block was equivalent to the coefficient of friction from the narrow side of the block. Given that these values are identical, it can be concluded that the surface area of the block in contact with the surface plane does not affect the coefficient of friction. In part A we see that a pulley with a string attached the block with weights hanging at the opposite end, this is due to the presence of Static friction, which known to be greater than kinetic friction. Static friction is the friction that keeps an object in place. This Static friction must be overcome to move the object. Because of a combination of surface irregularities, the effort needed to move the static object is greater. We can see the huge variation of results in part A where the angle changes from 15° to 30° to 45°. The result varies from 0.203 to 0.229 to 0.295, respectively. This issue could be resolved if the force required to overcome the additional friction so that, when pushed, the block slides with a constant velocity is measured more accurately that is we can put the exact weight for the pulling force in the weight hanger. In part B for measuring the angle of the inclined plane when the object starts moving with a constant velocity, it is seen that the angle for the block with half a kilogram and the block with one-kilogram is the same 15°, one would expect the object with heavier weight to start moving at a lower angle but in this experiment, it remained the same this can mean the error could be caused by the inconsistency with the surface of the block and the inclined plane. Hence with the height of the inclined plane and the length of the base remain the same for the two.

Conclusion From the experiments taken place in this lab, the errors lie within the quality of material the block and apparatus, as well as the measuring devices, although the majority of the error in our experiment can be attributed toward human error means. To analyze these problems more in-depth, more testing must be performed using different apparatuses and block materials, as well as more precise measuring devices. Although these errors may have occurred, through consistent trends of the experiment, it can be concluded that the surface area of the block in contact with the surface plane has no effect on the coefficient of friction, and the angle required for the block to slide down the inclined plane decreases as the weight of the block increases....