When an object is sitting on an incline plane there is a force that is holding it there. When an object is sliding down an incline plane there is a force that is opposing the motion. This force is static and kinetic friction. The force of static friction divided by the force normal can give you the coefficient of static friction. To find the coefficient of friction between a book and a board which is at an incline the book is place on the board the angle of the board is increased until the book starts to move. At this point measurements are made and then calculations are carried out. The coefficient of static friction can be found also using a Newton scale to get a more accurate answer. The coefficient of kinetic friction can be found by putting the book on the board and pulling it with a Newton scale at a constant velocity and then making calculations. Some errors can be made from rounding calculations and also pulling the book at an inconstant speed. These errors are minimized by performing the experiments multiply times.

Introduction:

Friction is a force that opposes motion. There are 2 kinds of friction. There is static friction and kinetic friction. The force of static friction is the force that keeps a object at rest. When something needs to be moved starting from rest the force of static friction must be overcome in order for the object to move. Once the object is in motion the friction is different because the object now wants to remain in motion the force that is now opposing this motion is called kinetic friction. Kinetic friction applies to objects that are already moving. Both of these forces are depend on the coefficients of friction between the two objects. Coefficient of friction is a number that indicates the ratio of the magnitude of friction between the objects and the force of normal between the objects. Coefficient of friction can be found by dividing the force of friction by the force of normal.

 

Purpose:

To find the coefficient of static and kinetic friction between a textbook and a wooden board on an incline.

Materials:

• Retort Stand
• Wooden Board
• Textbook
• Clamp
• Measuring Stick
• String
• Newton Scale

 

 

 

Procedure:

Part 1:

1.    The textbook was placed on the wooden board.

2.    The board was clamped on to the retort stand.

3.    The angle between the board and the ground was increased until the book moved.

4.    The height of the raised side and the length from on end of the board the other was measured.

 

Part 2:

1. The board was placed horizontally on the ground.
2. The textbook was placed on the board.
3. The Newton scale was attached to the book using a string.
4. The Newton scale was pulled on until the point the textbook moved.
5. The measurement on the Newton scale at that point was noted.

 

Part 3:

1. The board was placed horizontally on the ground.
2. The textbook was placed on top of the board.
3. The Newton scale was attached to the book using a string.
4. The Newton scale was pulled on so that the book was moving at a constant speed.
5. The measurement on the Newton scale while in constant motion was noted.

Observations:

Comparison Of Angles, Rises, Runs and Coefficients Of Friction

Try	Rise (cm)	Run (cm)	Θ (degree)	µs	Fn (N)
1	26	81	17.8	0.31	19.2
2	24.4	80	17.0	0.30	19.3
3	25	82	17.0	0.30	19.3
4	25.5	82.3	17.2	0.31	19.3
5	25.3	80.2	17.5	0.32	19.3
6	26.7	80.1	18.4	0.33	19.2

 

Force Measurements For Static Friction

Try	Force (N)
1	6.90
2	6.80
3	6.60
4	6.20
5	6.20
6	6.30

 

 

 

 

Force Measurements For Kinetic Friction

Try	Force (N)
1	6
2	6.6
3	6.5
4	6.1
5	6.2
6	6.4

 

Results:

Part 1:

To find the θ this formula was used:

Tan θ =  Height / Distance

Finding the θs:

Try 1:

Tan θ =  26 / 81

       θ = 17.8

Try 2:

Tan θ =  24.4 / 80

       θ = 17.0

Try 3:

Tan θ =  25 / 82

       θ = 17.0

Try 4:

Tan θ =  25.5 / 82.3

       θ = 17.2

Try 5:

Tan θ =  25.3 / 80.2

       θ = 17.5

Try 6:

Tan θ =  26.7 / 80.1

       θ =  18.4

The angle between the force of gravity and the line perpendicular to the board is equal to the angle made by the wooden board to the ground so we can make the summation:

∑Fy = Mass x Acceleration in y component = 0

     0 = Fn + (- mass x gravity x cosθ)          

   Fn = mass x gravity x cosθ

Then the summation of the x components:

∑Fy = 0

∑Fy = Fgx + Fsmax

     0 = (mass x gravity x sinθ) + (-µs x Fn) 

   µs = (mass x gravity x sinθ)/(Fn)

Fn = mass x gravity x cosθ  So…

µs = (mass x gravity x sinθ)/ (mass x gravity x cosθ) 

µs = sinθ / cosθ

Therefore the coefficient of static friction can be calculated using:

µs = sinθ / cosθ

Finding the coefficients of friction:

Try 1:

µs = sin17.8 / cos17.8

µs = 0.31

Try 2:

µs = sin17.0 / cos17.0

µs = 0.30

Try 3:

µs = sin17.0 / cos17.0

µs = 0.30

Try 4:

µs = sin17.2 / cos17.2

µs = 0.31

Try 5:

µs = sin17.5 / cos17.5

µs = 0.32

Try 6

µs = sin18.4 / cos18.4

µs = 0.33

Average µs = 0.31

Part 2:

The angle used for this part was 0 so the Fa equals the Ff.

µs = Ff / Fn

Fn = mass x acceleration

Fn = 2.0623 x 9.8

Fn = 20.2N

Try 1:

µs = 6.9 / 20.2

µs = 0.34

Try 2:

µs = 6.8 / 20.2

µs = 0.34

Try 3:

µs = 6.60 / 20.2

µs = 0.33

Try 4:

µs = 6.20 / 20.2

µs = 0.31

Try 5:

µs = 6.20 / 20.2

µs = 0.31

Try 6:

µs = 6.30 / 20.2

µs = 0.31

Average µs = 0.323

Part 3:

Finding the coefficient of kinetic friction:

µk = Ff / Fn

Fn = mass x gravity

Fn = 2.0623 x 9.8

Fn = 20.2N

Try 1:

µk = 6.0 / 20.2

µk = 0.30

Try 2:

µk = 6.6 / 20.2

µk = 0.33

Try 3:

µk = 6.5 / 20.2

µk = 0.32

Try 4:

µk = 6.1 / 20.2

µk = 0.30

Try 5:

µk = 6.2 / 20.2

µk = 0.31

Try 6:

µk = 6.4 / 20.2

µk = 0.32

Average µk = 0.31

Discussion:

The coefficient of friction in Part 1 which was without using a Newton scale was 0.31 and for with the scale was 0.323 the percent difference is calculated to be:

((0.323-0.31) / (0.323+0.31/2)) x 100 = Percent Difference

Percent Difference = 4.1%

This percent difference could have been because of the inaccuracy of the Newton scales or other factors such as wrong measurements, reading or rounding digits. The coefficient of kinetic friction is 0.31 which is less then the static friction. This makes sense because the object is moving and wants to remain in motion. Next time to eliminate some of the error better Newton scales can be used.