Friction Lab Report

FACULTY OF ENGINEERING & TECHNOLOGY

LAB REPORT

EME 1016 APPLIED STATICS

TRIMESTER 1 (2015/2016)

EXPERIMRNT 1: FRICTION

Name: Teng Shieh Maine ID: 1141327023 Name: Tee Fang Ying ID: 1141327369 Lab group: Group 8

DATE:27/7/2015

Abstract The purpose of this experiment is to examine and compare the static and sliding friction forces (Fs and Fk). We carried out one set of three friction tests as a function of area, weight, material, and force of gravity. We also made a comparison between the rolling and sliding friction forces (Fr and Fk) as a function of weight. In Set 1 of the experiment, we pulled a wooden blocks of varying sizes across the experiment surface to determine the effects of the the surface area of the block, the weight of the block and the type of surface on friction force, Ff. In Set 2, we pulled a large block with additional weights across the experiment surface to determine how the weight of an object affects friction force, Ff and to find the coefficient of friction, µ. In Set 3, stand rods were aligned next to each other to act as the experiment surface. We pulled a wooden block with additional weights horizontally and parallel to the rod axes to determine the rolling friction force, Fr and sliding friction force, Fk respectively. We found that the surface area did not appear to affect friction force, F and the coefficient of friction, µ. Weight affects friction force, Ff but does not affect coefficient of friction, µ. However, the type of materials in contact directly affects friction force, F and, coefficient of friction µ. The type of surface produced the largest percentage difference in values of coefficient of friction µ, 75.8% for the change in coefficient of static friction,μs and 86.2% for the change in coefficient of sliding friction, μk.

Introduction The purpose of this experiment is to examine static and sliding friction forces (Fs and Fk) and the factors that affect it. The factors that are examined within this experiment are the surface area of the object, the type of surfaces in contact with one another, and the force of gravity (weight). All of these will be tested and compared to see how they affect the value of friction forces. Friction is a force that always opposes the motion of an object. According to velocity, friction may be classified into static friction force, Fs (when velocity = 0) and sliding friction force, Fk (when velocity ≠ 0). Static friction force, Fs is a force between two objects that are not moving relative to one another. For example, an object resting on a slope, but not sliding down the slope, is kept in its position by this friction. Static friction force, Fs must be overcome to cause an object to move across a surface. Once enough force has been applied to an object, it will begin to slide across a surface and sliding friction force, Fk will then act on the object. Sliding friction force, Fk occurs when two objects are moving relative to one another with one object sliding across the surface of the other and it opposes the motion of the object. Both types of friction are described by different coefficients. These values are known as the coefficients of static and sliding friction (µs and µk) respectively and they are dimensionless.[1] The coefficient of static friction, µs is usually higher than coefficient of sliding friction, µk. Coefficients of friction, µ is a measure of how easily one object moves in relationship to another. When you have a high coefficient of friction, µ, you have a lot of friction between the materials. Every object in the universe that has mass that exerts a gravitational pull, or force, on every other mass. The size of the pull depends on the masses of the objects. The experiment uses the force of gravity (weight) in order to find the maximum static friction force, Fs on an object before it turns into sliding friction force, Fk. This will help in the understanding of how the forces will either increase or decrease due to the mass of the object.

Figure 1

A small block was placed on the experiment surface as shown in Figure 1. When no force is applied to the block, the block remains at a stationary position. At this position, the normal force, Nf of block is equal to its own weight, W.

Figure 2

When a pulling force, Fp is applied to the block parallel to the horizontal surface, a friction force, Ff is acting in an opposite direction to the pulling force, Fp. If Fp is smaller than Ff, the block is not moving. If Fp is equal to Ff, the block is about to move[3]. If Fp is greater than Ff, the block is moving in the direction of Fp with acceleration.[2] The resultant force is given by the formula: Resultant force=F p −F f After that, we can calculate the coefficients of static and sliding friction (µs and µk) using the formulas: µ=

Ff Fp = Nf W

µ s=

Fs W

µk=

Fk w

To find the friction force, Ff we measure static friction force, Fs by noting the scale reading on spring balance just before the block slides. Static friction force, Fs has values from zero to its maximum value. When the block starts to move and static friction force, Fs has a maximum value. Once the block starts moving the friction is sliding friction force, Fk i.e. kinetic friction. We measure sliding friction force, Fk by continuing to pull the block at constant a speed. After getting the values of static and sliding friction forces (Fs and Fk), we can now compare with aspect to each factor to find out which factor causes the greatest effect on friction force, Ff. The equation below is used to calculate the percentage difference: Differenc e=Value1−Value2

Average =

Value 1+ Value2 2

(|

Percentage difference=

|)

Difference ×100 Average

Objectives 1.

2. 3.

To determine the static and sliding friction forces (Fs and Fk)as function of: a) Area b) Weight c) Material and then to compare the friction forces (Fs and Fk) for different areas, weights, and materials. To compare rolling and sliding friction forces (Fr and Fk) as a function of weight. To determine the friction coefficient of friction, µ in rolling case.

Apparatus 1. One set of four weights, 0.1kg, 0.2kg, 0.5kg and 1 kg with hook. 2. One set of six stand rods with length, 100mm and diameter, 12mm. 3. One set of three spring balances 1N, 5N and 10N. 4. One pair of wooden blocks with one of the sides covered with rubber.

Figure 3: 1kg, 0.5kg, 0.2kg and 0.1kg weights with hook

Figure 4: Stand rods

Figure 5: Spring balances 1N, 5N, 10N

Figure 6: Wooden blocks with one side covered with rubber

Procedure: Set 1: Static and sliding friction forces as a function of the area, the weight and the material (Refer to Fig.7) 1 2 3 4 5

The small block with its plastic (rubber) side down is placed on the experiment surface. The static and sliding friction force, Fs and Fk are measured. The wooden block is placed on the base surface with its wide wooden side and then narrow wooden side down. the measurement for Fs and Fk are repeated. The measurements are repeated with the large block for friction experiments. The results of FS and FK are plotted as a function of area, weight and material. The corresponding µs and µk are determined and the results are plotted as a function of area, weight, and material.

Figure 7: Measuring the static and sliding friction forces as a function of area, weight and material.

Set 2: Static and sliding forces as a function of the force of gravity (Refer to Fig.8) 1 2 3

The large block is placed on the experiment surface with its plastic side down. The static and sliding friction forces are measured. The weight of the block is incresed by adding in turn the weights of 0.1kg, 0.2kg, 0.5kg and 0.8kg. The measurements are repeated. The same measurements are carried out for the wooden side of the block as well. The results of Fs , Fk, µs and µk are plotted as a function of the force of gravity, i.e. weight, W.

Figure 8: Measuring the static and sliding friction force as a function of the force of gravity.

Set 3: Rolling and sliding friction as a function of the force of gravity (Refer to Fig.9) Procedure: 1 2 3 4 5

The stand rods are laid next to each other and the large block is placed on the rods with its plastic side down. The horizontal pulling force is measured by maintaining a uniform motion on the rolling rods as. This is the rolling friction force, Fr. The weight of the block is increased by adding in turn the weights 0.1kg, 0.2kg, 0.5kg and 1.0kg. The measurements are repeated. The block are aligned parallel to the rod axes. The sliding friction force, Fk is measured. The graph of sliding friction force and rolling friction force as a function of the force of gravity is plotted.

Figure 9: Measuring the rolling and sliding friction force as a function of the force of gravity.

Results and Observations: Constants: (i)

−2

Acceleration due ¿ gravity , g=9.81 m s

¿ 0.981 N

(ii) Weight of 0.1 kg mass=(0.1× 9.81) N (iii) Weight of 0.2 kg mass=(0.2× 9.81) N

¿ 1.962 N

(iv) Weight of 0.5 kg mass=(0.5 ×9.81) N

¿ 4.905 N

(v) Weight of 0.8 kg mass=(0.8 ×9.81) N

¿ 7.848 N

(vi) Weight of 1.0 kg mass=(1.0× 9.81) N

¿ 9.810 N

General Calculations: (i) Small Block: Mass=189.23 g

¿

189.23 kg 1000

Weight=( 0.18923 ×9.81 ) N

¿ 0.18923 kg

¿ 1.8563 N

Area of narrow wooden side= ( 0.119 ×0.0030 ) m 2 Area of wide wooden side=( 0.117 ×0.060 ) m 2 2

Area of rubber side=( 0.117× 0.060 ) m (ii) Large Block:

¿ 0.003570 m2

¿ 0.007020 m2

¿ 0.007020 m2

Mass=328.63 g

¿

328.63 kg 1000

Weight=( 0.32863 ×9.81 ) N

¿ 0.32863 kg

¿ 3.2239 N

Area of narro w wooden side=( 0.117 × 0.060 ) m2

Area of wide wooden side=( 0.117 ×0.060 ) m 2 Area of rubber side=( 0.117× 0.060 ) m2

2

¿ 0.007020 m

¿ 0.007020 m2

¿ 0.007020 m2

*Area of all three sides of the large block are the same.

Weight of block with 0.1 kg mass=( 3.2239+0.981 ) N

¿ 4.2049 N

Weight of block with0.2 kg mass=( 3.2239+1.962 ) N

¿ 5.1859 N

Weight of b lock with 0.5 kg mass=( 3.2239+ 4.905 ) N Weight of block with 0.8 kg mass= (3.2239+7.848 ) N

¿ 11.0719 N

Weight of block with 1.0 kg mass=( 3.2239+ 9.810 ) N Formula to calculate coefficient of friction, µ: µ=

F Pulling Force = p Weight of Object W

¿ 8.1289 N

¿ 13.0339 N

Set 1: Static and sliding friction forces as a function of the area, the weight and the material.

1 (i): Measuring Fs, Fk, µs and µk using the small block with its narrow wooden side down. Measurement, (N)

Coefficient of Friction, µ

I

II

III

IV

V

Average

Static Friction Force, Fs (N)

0.60

0.50

0.52

0.50

0.58

0.54

0.2909

Sliding Friction Force, Fk (N)

0.30

0.32

0.32

0.34

0.34

0.32

0.1724

Table 1

1 (ii): Measuring Fs, Fk, µs and µk using the small block with its wide wooden side down. Coefficient of Friction, µ

Measurement, (N)

Static Friction Force, Fs (N) Sliding Friction Force, Fk (N)

I

II

III

IV

V

0.5 0 0.5 0

0.7 0 0.5 0

0.6 0 0.4 0

0.7 0 0.5 0

0.7 0 0.5 0

Average 0.64

0.3448

0.48

0.2586

Table 2

1 (iii): Measuring Fs, Fk, µs and µk using the small block with its rubber side down. Measurement, (N) I

II

Coefficient of Friction, µ

III

IV

V

Average

Static Friction Force, Fs (N)

1.20 1.30

1.20

1.10

1.00

1.16

0.6249

Sliding Friction Force, Fk (N)

0.70 0.80

0.70

0.80

0.70

0.74

0.3986

Table 3

1 (iv): Measuring Fs, Fk, µs and µk using the large block with its wooden side down. Coefficient of Friction, µ

Measurement, (N) I

II

III

IV

V

Average

Static Friction Force, Fs (N)

0.90

1.10

0.90

1.10

1.00

1.00

0.3102

Sliding Friction Force, Fk (N)

0.60

0.70

0.70

0.80

0.70

0.70

0.2171

Table 4

1 (v): Measuring Fs, Fk, µs and µk using the large block with its rubber side down. Coefficient of Friction, µ

Measurement, (N) I

II

III

IV

V

Average

Static Friction Force, Fs (N)

2.40 2.30 2.00

2.20

2.20

2.22

0.6887

Sliding Friction Force, Fk (N)

1.70 1.80 1.60

1.80

1.90

1.76

0.5460

Table 5

1 (a) Friction Force and Coefficient of Friction as a function of Area a (i) Graph of Friction Force, F vs. Area * Constant variable: Material (Wood) and Weight (1.8563N/Small block)

Area, (m2)

Static Friction Force, Fs (N)

Sliding Friction Force, Fk (N)

0.003570

0.54

0.32

0.006903

0.64

0.48 Table 6

Graph of Friction Force, F vs. Area 0.70 0.65 0.60 0.55 F, (N)

0.50 0.45 0.40 0.35 0.30 0.003000 0.003500 0.004000 0.004500 0.005000 0.005500 0.006000 0.006500 0.007000 0.007500 Area, (m2)

Graph 1

a (ii) Graph of Coefficient of Friction, µ vs. Area * Constant variable: Material (Wood) and Weight (1.8563N/Small block)

Area, (m2)

Coefficient of Static Friction, µs

Coefficient of Sliding Friction, µk

0.003570

0.2909

0.1724

0.006903

0.3448

0.2586 Table 7

Graph of Coefficient of Friction, µ vs. Area 0.4000

0.3500

0.3000 µ 0.2500

0.2000

0.1500 0.003000 0.003500 0.004000 0.004500 0.005000 0.005500 0.006000 0.006500 0.007000 0.007500 Area, (m2)

Graph 2

1 (b) Friction Force and Coefficient of Friction as a function of Weight b (i) Graph of Friction Force, F vs. Weight, W * Constant variable: Material (Wood) and Area (0.007020m2)

Weight, W (N)

Static Friction Force, Fs (N)

Sliding Friction Force, Fk (N)

1.8563

0.64

0.48

3.2239

1.00

0.70 Table 8

Graph of Friction Force, F vs. Weight, W 1.1

1

0.9

0.8 F, (N) 0.7

0.6

0.5

0.4 1.6

1.8

2

2.2

2.4 W, (N)

Graph 3

2.6

2.8

3

3.2

3.4

b (ii) Graph of Coefficient of Force, µ vs. Weight, W * Constant variable: Material (Wood) and Area (0.007020m2)

Weight, W (N)

Coefficient of Static Friction, µs

Coefficient of Sliding Friction, µk

1.8563

0.3488

0.2586

3.2239

0.3102

0.2171 Table 9

Graph of Coefficient of Friction, µ vs. Weight, W 0.3600 0.3400 0.3200 0.3000 µ

0.2800 0.2600 0.2400 0.2200 0.2000 1.6

1.8

2

2.2

2.4 W, (N)

Graph 4

2.6

2.8

3

3.2

3.4

b (iii) Graph of Friction Force, F vs. Weight, W * Constant variable: Material (Rubber) and Area (0.007020m2)

Weight, W (N)

Static Friction Force, Fs (N)

Sliding Friction Force, Fk (N)

1.8563

1.16

0.74

3.2239

2.22

1.76 Table 10

Graph of Friction Force, F vs. Weight, W 2.5

2

1.5 F, (N) 1

0.5

0 1.6

1.8

2

2.2

2.4 W, (N)

Graph 5

2.6

2.8

3

3.2

3.4

b (iv) Graph of Coefficient of Force, µ vs. Weight, W * Constant variable: Material (Rubber) and Area (0.007020m2)

Weight, W (N)

Coefficient of Static Friction, µs

Coefficient of Sliding Friction, µk

1.8563

0.6249

0.3986

3.2239

0.6887

0.5460 Table 11

Graph of Coefficient of Friction, µ vs. Weight, W 0.7500 0.7000 0.6500 0.6000 0.5500 µ

0.5000 0.4500 0.4000 0.3500 0.3000 1.6000

1.8000

2.0000

2.2000

2.4000

2.6000

W, (N)

Graph 6

2.8000

3.0000

3.2000

3.4000

1 (c) Friction Force and Coefficient of Friction as a function of Material. c (i) Graph of Friction Force, F vs. Material * Constant variable: Area (0.007020m2) and Weight (1.8563N/Small block)

Material

Static Friction Force, Fs (N)

Sliding Friction Force, Fk (N)

Wood

0.64

0.48

Rubber

1.16

0.74 Table 12

Graph of Friction Force, Fs vs. Material 1.4

1.2

1

0.8 F, (N) 0.6

0.4

0.2

0 Material

Graph 7

c (ii) Graph of Coefficient of Friction, µ vs. Material * Constant variable: Area (0.007020m2) and Weight (1.8563N/Small block)

Material

Coefficient of Static Friction, µs

Coefficient of Sliding Friction, µk

Wood

0.3448

0.2586

Rubber

0.6249

0.3986 Table 13

Graph of Coefficient of Friction, µ vs. Material 0.7000

0.6000

0.5000

0.4000 µ 0.3000

0.2000

0.1000

0.0000 Material

Graph 8

c (iii) Graph of Friction Force, F vs. Material * Constant variable: Area (0.007020m2) and Weight (3.2239N/Large block)

Material

Static Friction Force, Fs (N)

Sliding Friction Force, Fk (N)

Wood

1.00

0.70

Rubber

2.22

1.76 Table 14

Graph of Friction Force, F vs. Material 2.50

2.00

1.50 F, (N) 1.00

0.50

0.00 Material

Graph 9

c (iv) Graph of Coefficient of Friction, µ vs. Material * Constant variable: Area (0.007020m2) and Weight (3.2239N/Large block)

Material

Coefficient of Static Friction, µs

Coefficient of Sliding Friction, µk

Wood

0.3102

0.2171

Rubber

0.6887

0.5460 Table 15

Graph of Coefficient of Friction, µ vs. Material 0.8000 0.7000 0.6000 0.5000 µ

0.4000 0.3000 0.2000 0.1000 0.0000 Material

Graph 10

The equation used to calculate the percentage difference: Difference=Value 1−Value 2

Average =

Value 1+ Value2 2

×100 |( Difference Average |)

Percentage difference=

1 (a) Coefficient of Friction as a function of Area (i) Coefficient of Friction, µ vs. Area * Constant variable: Material (Wood) and Weight (1.8563N/Small block)

Area, (m2)

Coefficient of Static Friction, µs

Coefficient of Sliding Friction, µk

0.003570

0.2909

0.1724

0.006903

0.3448

0.2586

(|

|)

(|

|)

Percentage di fference ( μS )=

Percentage difference ( μ K ) =

0.2909−0.3448 ×100 =17.0 (0.2909+ 0.3448)/2

0.1724−0.2586 × 100 =40.0 (0.1724+ 0.2586)/2

1 (b) Coefficient of Friction as a function of Weight (i) Graph of Coefficient of Force, µ vs. Weight, W * Constant variable: Material (Wood) and Area (0.007020m2)

Weight, W (N)

Coefficient of Static Friction, µs

Coefficient of Sliding Friction, µk

1.8563

0.3488

0.2586

3.2239

0.3102

0.2171

0.3488+0.3102 ¿ ¿ ¿ 0.3488−0.3102 ¿ ¿ ¿ Percentage di fference ( μs ) =¿

0.2586+0.2171 ¿ ¿ ¿ 0.2586−0.2171 ¿ ¿ ¿ Percentage difference ( μ K ) =¿

(ii) Graph of Coefficient of Force, µ vs. Weight, W * Constant variable: Material (Rubber) and Area (0.007020m2)

Weight, W (N)

Coefficient of Static Friction, µs

Coefficient of Sliding Friction, µk

1.8563

0.6249

0.3986

3.2239

0.6887

0.5460

0.6249+ 0.6887 ¿ ¿ ¿ 0.6249−0.6887 ¿ ¿ ¿ Percentage difference ( μ s )=¿

(|

Percentage difference ( μ K ) =

|)

0.3986−0.5460 ×100 =31.2 (0.3986+ 0.5460)/2

1 (c) Friction Force and Coefficient of Friction as a function of Material. (i) Graph of Coefficient of Friction, µ vs. Material * Constant variable: Area (0.007020m2) and Weight (1.8563N/Small block)

Material

Coefficient of Static Friction, µs

Coefficient of Sliding Friction, µk

Wood

0.3448

0.2586

Rubber

0.6249

0.3986

Percentage difference ( μ s )=

(|

|)

0.3448−0.6249 × 100 =57.8 (0.3448+ 0.6249)/2

(|

|)

0.2586−0.3986 × 100 =42.6 (0.2586+ 0.3986)/2

Percentage difference ( μ K ) =

(ii) Graph of Coefficient of Friction, µ vs. Material * Constant variable: Area (0.007020m2) and Weight (3.2239N/Large block)

Material

Coefficient of Static Friction, µs

Coefficient of Sliding Friction, µk

Wood

0.3102

0.2171

Rubber

0.6887

0.5460

Percentage difference ( μ s )=

(|

|)

0.3102−0.6887 × 100 =75.8 (0.3102+ 0.6887) /2

(|

Percentage difference ( μ K ) =

|)

0.2171−0.5460 ×100 =86.2 (0.2171+0.5460)/2

Set 2: Static and sliding forces as a function of the force of gravity.

2 (i): Measuring Fs, Fk, µs and µk using the large block with its rubber side down. Coefficient of Static Friction, µs

Additiona l Mass, (kg)

Weight of block, W (N)

I

II

III

IV

V

Average

0.00

3.2239

2.20

2.30

2.40

2.40

2.50

2.36

0.7320

0.10

4.2049

3.50

3.40

3.40

3.50

3.70

3.5

0.8324

0.20

5.1859

4.50

4.60

4.80

4.80

4.60

4.66

0.8986

0.50

8.1289

7.40

7.60

7.40

7.60

7.40

7.48

0.9202

Static Friction Force, Fs (N)

0.80

11.0719

9.10

9.30

9.40

9.10

9.60

9.30

0.8400

1.00

13.0339

11.00

11.10

11.00

11.20

10.60

10.98

0.8424

Table 16

Additiona l Mass, (kg)

Weight of block, W (N)

0.00

Coefficient of Sliding Friction, µk

Sliding Friction Force, Fk (N) I

II

III

IV

V

Average

3.2239

1.90

1.80

1.90

2.00

1.80

1.88

0.5831

0.10

4.2049

2.80

2.70

3.00

2.90

2.90

2.86

0.6802

0.20

5.1859

3.60

3.80

3.80

3.60

3.70

3.7

0.7135

0.50

8.1289

6.40

6.40

6.60

6.60

6.40

6.48

0.7972

0.80

11.0719

7.80

8.10

8.00

7.90

8.20

8.00

0.7225

1.00

13.0339

8.30

9.30

9.10

9.40

9.60

9.14

0.7012

Table 17

2 (ii): Measuring Fs, Fk, µs and µk using the large block with its wooden side down. Coefficient of Static Friction, µs

Additional Mass, (kg)

Weight of block, W (N)

I

II

III

IV

V

Average

0.00

3.2239

1.00

0.90

1.10

0.90

1.00

0.98

0.3040

0.10

4.2049

1.20

1.40

1.40

1.50

1.50

1.4

0.3329

0.20

5.1859

1.90

2.00

1.90

1.80

2.00

1.92

0.3702

0.50

8.1289

3.10

3.00

3.10

3.00

3.10

3.06

0.3764

0.80

11.0719

3.90

4.10

4.00

3.80

4.00

3.96

0.3577

1.00

13.0339

4.60

4.80

4.60

5.00

5.00

4.8

0.3683

Static Friction Force, Fs (N)

Table 18

Coefficient of Sliding Friction, µk

Additional Mass, (kg)

Weight of block, W (N)

I

II

III

IV

V

Average

0.00

3.2239

0.60

0.80

0.60

0.70

0.60

0.66

0.2047

0.10

4.2049

1.00

1.00

0.90

1.10

0.90

0.98

0.2331

0.20

5.1859

1.50

1.40

1.40

1.50

1.30

1.42

0.2738

0.50

8.1289

2.50

2.40

2.50

2.70

2.50

2.52

0.3100

0.80

11.0719

2.80

2.80

2.90

2.70

2.80

2.80

0.2529

1.00

13.0339

3.20

3.40

3.20

3.40

3.40

3.32

0.2547

Sliding Friction Force, Fk (N)

Table 19

2 (a) Friction Force and Coefficient of Friction as a function of Gravity a (i) Graph of Friction Force, F vs. Weight, W * Constant variable: Material (Rubber) and Area (0.007020m2)

Additional Mass, (kg)

Weight of block, W (N)

Static Friction Force, Fs (N)

Sliding Friction Force, Fk (N)

0.0

3.2239

2.36

1.88

0.1

4.2049

3.50

2.86

0.2

5.1859

4.66

3.70

0.5

8.1289

7.48

6.48

0.8

11.0719

9.30

8.00

1.0

13.0339

10.98

9.14

Table 20

Graph of Friction Force, F vs. Weight, W 12

10

8

F, (N)

6

4

2

0

2

4

6

8

10

12

14

W, (N)

Graph 11

a (ii) Graph of Coefficient of Friction, µ vs. Weight, W * Constant variable: Material (Rubber) and Area (0.007020m2)

Additional Mass, (kg)

Weight of block, W (N)

Coefficient of Static Friction, µs

Coefficient of Sliding Friction µk

0.0

3.2239

0.7320

0.5831

0.1

4.2049

0.8324

0.6802

0.2

5.1859

0.8986

0.7135

0.5

8.1289

0.9202

0.7972

0.8

11.0719

0.8400

0.7225

1.0

13.0339

0.8424

0.7012

Table 21

Graph of Coefficient of Friction, µ vs. Weight, W 0.9500 0.9000 0.8500 0.8000 0.7500 µ

0.7000 0.6500 0.6000 0.5500 0.5000

2

4

6

8

10

12

14

W, (N)

Graph 12

a (iii) Graph of Friction Force, F vs. Weight, W * Constant variable: Material (Wood) and Area (0.007020m2)

Additional Mass, (kg)

Weight of block, W (N)

Static Friction Force, Fs (N)

Sliding Friction Force, Fk (N)

0.0

3.2239

0.98

0.66

0.1

4.2049

1.40

0.98

0.2

5.1859

1.92

1.42

0.5

8.1289

3.06

2.52

0.8

11.0719

3.96

2.80

1.0

13.0339

4.80

3.32

Table 22

Graph of Friction Force, F vs. Weight, W 6.00

5.00

4.00

F, (N)

3.00

2.00

1.00

0.00

2

4

6

8 W, (N)

Graph 13

10

12

14

a (iv) Graph of Coefficient of Friction, µ vs. Weight, W * Constant variable: Material (Wood) and Area (0.007020m2)

Additional Mass, (kg)

Weight of block, W (N)

Coefficient of Static Friction, µs

Coefficient of Sliding Friction µk

0.0

3.2239

0.3040

0.2047

0.1

4.2049

0.3329

0.2331

0.2

5.1859

0.3702

0.2738

0.5

8.1289

0.3764

0.3100

0.8

11.0719

0.3577

0.2529

1.0

13.0339

0.3683

0.2547

Table 23

Graph of Coefficient of Friction, µ vs. Weight, W 0.4000

0.3500

0.3000 µ 0.2500

0.2000

0.1500

2

4

6

8 W, (N)

Graph 14

10

12

14

Set 3: Rolling and sliding friction as a function of the force of gravity.

3 (i): Measuring Fr, Fk, µr and µk using the large block with its rubber side down. Additional Mass, (kg)

Weight of block, W (N)

Coefficient of Rolling Friction, µr

I

II

III

IV

V

Average

0.00

3.2239

0.08

0.10

0.08

0.09

0.10

0.09

0.0279

0.10

4.2049

0.18

0.16

0.14

0.18

0.20

0.17

0.0404

0.20

5.1859

0.20

0.22

0.22

0.20

0.20

0.21

0.0405

0.50

8.1289

0.32

0.32

0.34

0.38

0.36

0.34

0.0418

1.00

13.0339

0.56

0.54

0.60

0.50

0.50

0.54

0.0414

Rolling Frictional Force, Fr (N)

Table 24

Additional Mass, (kg)

Weight of block, W (N)

Coefficient of Sliding Friction, µk

I

II

III

IV

V

Average

0.00

3.2239

1.60

1.70

1.70

1.50

1.80

1.66

0.5149

0.10

4.2049

2.50

2.50

2.40

2.40

2.40

2.44

0.5803

0.20

5.1859

3.10

3.20

3.30

3.30

3.20

3.22

0.6209

0.50

8.1289

4.20

4.00

4.00

4.00

4.20

4.08

0.5019

1.00

13.0339

8.20

8.80

8.40

8.20

8.60

8.44

0.6475

Sliding Frictional Force Fk (N)

Table 25

3 (a): Friction Force as a function of Gravity a (i): Graph of Friction Force, F vs. Weight, W * Constant variable: Material (Rubber) and Area (0.007020m2)

Additional Mass, (kg)

Weight of block, W (N)

Sliding Friction Force, Fk (N)

Rolling Friction Force, Fr (N)

0.00

3.2239

1.66

0.09

0.10

4.2049

2.44

0.17

0.20

5.1859

3.22

0.21

0.50

8.1289

4.08

0.34

1.00

13.0339

8.44

0.54

Table 26

Graph of Friction Force, F vs. Weight, W 9 8 7 6 5 F , (N)

4 3 2 1 0

2

4

6

8 W (N)

Graph 15

10

12

14

a (ii): Graph of Coefficient of friction, µ vs. Weight, W * Constant variable: Material (Rubber) and Area (0.007020m2)

Additional Mass, (kg)

Weight of block, W (N)

Coefficient of Sliding Friction, µk

Coefficient of Rolling Friction, µr

0.0

3.2239

0.5149

0.0279

0.1

4.2049

0.5803

0.0404

0.2

5.1859

0.6209

0.0405

0.5

8.1289

0.5019

0.0418

1.0

13.0339

0.6475

0.0414

Table 27

Graph of Coefficient of Friction, µ vs. Weight, W 0.7

0.6

0.5

0.4 µ 0.3

0.2

0.1

0

2

4

6

8 Weight, W (N)

Graph 16

10

12

14

Discussion:

Figure 10

1.

When an object is subjected to a an external force, pulling force, Fp, it experiences friction force, Ff in the opposite direction. When friction force, Ff is of the same magnitude as the pulling force, Fp, the object is moving at constant velocity. Hence, F f =F p At the same time, the object also experiences force from its weight, weight, W and a resultant force due to its weight, normal force, Nf. These two forces are always equal in magnitude but acts in opposing directions. Thus, it can be said that N f =W The general formula used to obtain the coefficient of friction, µ is µ=

Frictional Force F f = Normal Force Nf

Applying the first two formulas, we get µ=

2.

Pulling Force F p = Weight W

Frictional force, Ff can be divided into a three types, static friction force Fs, sliding friction force Fk and rolling friction force Fr . Static friction force, Fs is the friction that exists between a stationary object and the surface in which it is resting. Sliding friction force, Fk is the friction that occurs when two objects are moving relative to each other while they are in contact. Rolling friction force, Fr is the friction resisting the motion of the

body when it rolls on a surface.

Coefficient of friction, µ is also divided into three types, coefficient of static friction µs coefficient of sliding friction µk, and coefficient of rolling friction µr 3.

As a general assumption, F s> F k F k> F r µ s >µ k µ k > µr Static friction force, Fs is greater than sliding friction force, Fk due to the object’s inertia. To move a stationary object, the pulling force, Fp must be great enough to overcome the inertia of the object. Sliding friction force, Fk is greater than rolling friction force, Fr because of the greater friction experience when an object rubs against a surface. The rolling motion of the object greatly reduces the friction between the two bodies. The relation between static friction force, Fs and sliding friction force, Fk is shown in the graph below.

Figure 11

Set 1: Static and sliding friction forces as a function of the area, the weight and the material. 1.

To determine the static and sliding friction forces (Fs and Fk) as a function of the area, the weight and the material, we repeated the experiment and its procedures with different values of area, weight, and material. The small block and large block allowed us to experiment with different value of weight (eg. 1.8563N for the small block and 3.2239N for the large block). Their dimensions provided us with different values of area (eg. 0.003570m2 and 0.007020m2). It should be noted that the large block had the same area for its narrow and wide side. This limited our findings in ways that will be discussed later in this section. Both blocks also had a side made of rubber. This made it possible for us to compare the effects of different materials.

2.

In section 1(a) of the results, we compared the static friction force, Fs and sliding friction force, Fk as a function of area. To do this, we had to keep the weight and the material in contact with the surface constant. As the large block had the same area for its wide and narrow surface, we were not able to use the measurements using the large block in this part. To keep the weight constant, we only compared measurements made with the small block and to keep the material constant, we compared measurements made when the wooden side of the block was placed on the bottom.

3.

From Table 6 and Graph 1, it can be seen that both static friction force, Fs and sliding friction force, Fk increases slightly with increasing area. The same is shown in Table 7 and Graph 2 for the respective coefficients of friction, µ. However, theoretically, friction will not increase with area. This is assumption is based on the formulas: F f =µ N f Pressure=

Force Area

If we increase the contact area of the small block, we also decrease the pressure acting on the contact surface as well. This decrease in pressure and increase in surface area cancels out each other in the end. Therefore, there is only a slight difference in the friction forces when the area is increased. The same applies to the coefficients of friction, µ. 4.

In section 1(b), we compared static friction force, Fs and sliding friction force, Fk as a function of weight. In this section, we kept the area and material in contact with the surface constant. As the wooden surface of the large block had the same area as the wide wooden side of the small block we were able to compare these two measurements. This also applies to the rubber side of both blocks. Thus we were able to compare the friction force with the weight in two different ways, with the wooden side and rubber side on the bottom.

5.

Table 8, Table 10, Graph 3 and Graph 5 shows that static friction force, Fs and sliding friction force, Fk increases significantly with increasing weight. This is because friction is directly proportional to the normal force. A greater value for weight will produce a greater value of normal force. More pulling force is needed to overcome the higher frictional force. Based on Table 9, Table 11 , Graph 4 and Graph 6, we see that there is little difference between the coefficients of friction, µ when the weight increases. This is based on the formula: µ=

Pulling Force F p = Weight W

As weight increases, the frictional force also increases. This produces a constant value for the coefficient of friction, µ. The fluctuation from a constant value might be due to inconsistent pulling force or parallax error that occurred when taking the measurements. 6.

In section 1(c) we compare static friction force, Fs and sliding friction force, Fk as a function of material. For accurate results, we compared measurements that we obtained when using the same weight and area. To achieve this, we compared measurements made when using the small block with its wide wooden side down with measurements made when using the small block with its rubber side down. For the large block, we used measurements obtained when using its wooden side and rubber side.

7.

Table 12, Table 14, Graph 7 and Graph 9 shows that static friction force, Fs and sliding friction force, Fk increases with greatly when changing the material from wood to rubber. This happens because the properties of rubber make it softer. The irregularities on the rubber surface get interlocked easier with the microscopic bumps on the table. Hence, it has a better grip on the surface of the table compared to wood. This results in more friction between the rubber and the table compared to wood. The static and sliding friction forces (Fs and Fk) of the large block is greater than the small block due to the difference in weight, as discussed previously in 5. Table 13, Table 15, Graph 8 and Graph 10 all show that the coefficients of friction, µ experience a significant increase when changing from wood to rubber. This occurs because of the increase in their relative frictional forces. 8. To calculate the percentage difference, we used the formula:

(|

Percentage difference=

|)

Difference ×100 Average

1.

Based on the calculation, we found out that the change in material, from wood to rubber made the most difference. With all percentages reaching above 40%. The effect from the change in material was most prominent when using the large block. On the other hand, changes in weight made the least difference, with the lowest percentage of less then 10% Set 2: Static and sliding forces as a function of the force of gravity. To determine the static and sliding friction forces (Fs and Fk) as a function of the force of gravity (weight), we repeated the experiment with different values of weight and material using the large block. To provide a range of different weights, we use the weights provided to increase the weight of the block. We repeated the experiment twice, once using the wooden side of the block and the second time using the rubber side of the block. The area was kept constant at 0.007020m2.

2.

In section 2(a)(i) and 2(a)(ii) of the results, we compared the static friction force, Fs and sliding friction force, Fk as a function of weight and coefficient of static friction, µs and coefficient of sliding friction, µk as a function of weight respectively. We kept the area constant and used the rubber side for this set of measurements.

3.

From Table 20 and Graph 11 we understand that as the weight increases, both the static friction force, Fs and sliding friction force, Fk increases steadily with it. The line of best fit shows us that the measurement taken did not stray and followed a pattern. As discussed before, the static friction force, Fs is greater than the sliding friction force, Fk due to the effects of inertia when the block is stationary.

4.

From Table 21 and Graph 12, it is shown that both coefficients of friction, µ do not experience significant change in their value. They also do not follow a general pattern. Increasing as little at first then experiencing a decrease in their final values. In an ideal situation, the coefficient of static friction, µs and coefficient of sliding friction, µk are constant for any weight of the block, as long as the characteristics of the two interacting surfaces do not change. The coefficients of friction, µ fluctuate around a certain constant value. This fluctuations may have been caused by inconsistent force when pulling the block. The microscopic bumps and irregular surface may also cause the changing values. Any increased force could cause deformation of the surface in such a way that the value of the coefficients will change. This causes the ranges of values. The properties of the rubber surface contribute to this.

5.

In section 2(a)(iii) and 2(a)(iv), we compared the static friction force, Fs and sliding friction force, Fk as a function of weight and coefficient of static friction, µs and coefficient of sliding friction, µk friction as a function of weight respectively. We kept the area constant as in 2(a)(i) and 2(a)(ii) but instead of the rubber side, we used the wooden side for this set of measurements.

6.

7.

From Table 22 and Graph 13, we can see the static friction force, Fs and sliding friction force, Fk increase as the weight increases. They follow the same pattern and reasoning as the results from 2(a)(i). Table 23 and Graph 14 shows a similar pattern as the results from Table 21 and Graph 12 but with more consistency and with generally lower values. The same idea applies for this set of results. However, the more consistent values may be caused by the material used for this part of the experiment, which was the wooden side of the block. It was easier to maintain a constant and steady pulling for the wood as its properties allowed it to rest and slide on the surface of the table easier than the rubber side. Nevertheless, The grain of the wood, for example, could cause the value of the coefficients of friction, µ to vary as the objects slide over each other. The lower values of the coefficients of friction, µ is due to the properties of the wooden surface.

Set 3: Rolling and sliding friction as a function of the force of gravity. 1.

To determine the rolling and sliding friction forces (Fr and Fk) as a function of gravity (weight), we did the experiment with different values of weight using the large block. As in Set 2, we added weight to the block to vary its weight. The area was kept constant at 0.007020m2 and only the rubber side was used on the metal rods. The experiment was not conducted on the table’s surface even when measuring the sliding friction force, Fk as to keep the two surfaces constant. Thus, we cannot compare the measurements of the sliding friction force, Fk from Set 2 with Set 3. Due to the properties of the metal surface which is much smoother than the table, the measurements when taken with the metal surface will always be lower.

2.

In section 3(a)(i), we compared the sliding friction force, Fk and rolling friction force, Fr as a function of weight. We kept the area and material constant when taking the measurements.

3.

From Table 26 and Graph 15, we see that as weight increases, both sliding friction force, Fk and rolling friction force, Fr increases with it. As the weight of the block increases, the value for normal force acting on the block also increases. This puts more pressure on the block with the surface of the metal rods, increasing the friction between these two surfaces. These results are consistent with what was discussed previously. However, the line of best fit for the sliding friction force, Fk has a significantly higher value for its gradient than the line of best fit of rolling friction force, Fr. This occurs because rolling friction is the resistance to motion experienced by a body when it rolls upon another. It is much less than sliding friction for same pair of bodies. When one body rolls upon another, there is theoretically, no sliding or slip between them. This results in the rolling friction force, Fr being much less than sliding friction and experiencing less change than the sliding friction force, Fk with increasing the increasing weight of the block.

4.

In section 3(a)(i), we compared the coefficient of sliding friction, µk and coefficient of rolling friction, µr as a function of weight.

5.

From Table 27 and Graph 16, it is apparent that both coefficient of sliding friction, µk and coefficient of rolling friction, µr, do not increase with the mass. Instead they fluctuate around an average value. This has been discussed in Set 2.

6.

The average value of coefficient of rolling friction, µr is taken as its theretical value. Therefore we conclude that the coefficient of rolling friction, µr is 0.0384

Conclusion: 1.

Static friction force, Fs and sliding friction force, Fk does not increase with increasing area.

2.

Coefficient of static friction, µs and coefficient of sliding friction, µk does not increase with increasing area.

3.

Static friction force, Fs and sliding friction force, Fk increases with the increasing weight of the object.

4.

Coefficient of static friction, µs and coefficient of sliding friction, µk does not increase with the increasing weight of the object.

5.

Static friction force, Fs and sliding friction force, Fk increases with the increasing roughness of the surface in contact.

6.

Coefficient of static friction, µs and coefficient of sliding friction, µk increases with the increasing roughness of the surface in contact.

7.

Static friction force, Fs is always greater than sliding friction force, Fk when comparing surfaces of the same area and material with a constant weight for the object.

8.

The coefficient of static friction, µs is always greater than the coefficient of sliding friction, µk when comparing surfaces of the same area and material with a constant weight for the object.

9.

Sliding friction force, Fk and rolling friction force, Fr increases with the increasing weight of the object.

10.

Sliding friction force, Fk is always greater than rolling friction force, Fr when comparing surfaces of the same area and material with a constant weight for the object.

11.

The coefficient of sliding friction, µk is always greater than the coefficient of rolling friction, µr when comparing surfaces of the same area and material with a constant weight for the object.

12.

The coefficient of rolling friction, µr is 0.0384.

References: [1] Victor Jeung, Cathy Liu, Jason Feng, Terry Tong (2011, October 14). Friction Forces Lab: Finding an object’s μS and μK through the use of tension force (1st ed). [online]. Available: http://niha0.weebly.com/uploads/9/0/4/7/9047334/friction_lab_report.pdf [July. 25, 2015] [2]

John Elfick. (2010) “Friction”. [online] Available : http://www.uq.edu.au/_School_Science_Lessons/UNPh17, July. 25, 2015 [July. 25, 2015]

[3] Hibbeler, R.C., “Friction” in Engineering Mechanics: Statics and Dynamics, 6th edition, New York, USA, MacMillan Publishing Co., 1992, pp 389-392