# An Experiment to Determine the Coefficient of Static Friction

By desmondthebully
Jul 13, 2013
1097 Words

Name:

Rodney Francis a/l Xavier

ID:

1302969

Group members:

Yuan Li Hong, Desmond Wong

Practical Lecturer:

Mr Zoheir

Practical Group:

6

Part 1

Title:

To determine the coefficient of static friction between two surfaces.

Objectives:

1. To determine the relationship between the mass of load and the length of spring. 2. To determine the coefficient of static friction between two surface.

Apparatus and materials:

1. Retort stand

2. Spring

3. Slotted masses 200g with hanger

4. Meter rule

Setup:

[pic]

Theory:

If the wooden block is being displaced down the inclined plane, the block will return to its original position when released because the net force up the plane exceeds the limiting friction down the plane. The downward displacement is being reduced gradually until a stage where the block stays stationary when released. At this point, the force up the plane equalized the limiting friction down the plane.

If T is the tension of the spring, F is the limiting friction, and μ is the coefficient of static friction, then

T- mg sin θ = F

T- mg sin θ = μ mg cos θ

If T = m’g, where m’ = mass equivalent to tension T, then

m’g – mg sin θ = μ mg cos θ

m’ = m( μ cos θ + sin θ)

Procedure:

1. Hook one end of the spring on the retort stand.

2. Hang the hanger with a 20g slotted mass at the other end. 3. Measure the length l1 of the spring, record the mass m1 of the load. 4. Increase the mass m1, measure the corresponding length l1 of the spring. 5. Tabulate l1 and m1.

6. Plot a graph of l1 against m1.

Obervation/result:

Unextended spring length (initial) = 2.7cm

|Weight (g) |Spring extension (cm) | |20 |3.8 | |40 |4.2 | |60 |4.8 | |80 |5.2 | |100 |6.6 | |120 |7.2 | |140 |7.8 | |160 |8.4 | |180 |9.2 | |200 |9.6 |

[pic]

Part 2: The coefficient of friction between two surfaces

Apparatus and Materials:

1. A smooth plank as inclined plane

2. Retort stand

3. Wooden blocks

4. Electronic balance

5. Spring

6. Protractor

7. Pendulum bob

8. Thread

9. Plasticine

Setup:

[pic]

Procedure:

1. Weigh the mass of wooden block with a smooth surface. Record down the mass. 2. Adjust the retort stand, to adjust the angle of inclination of the plank, such that the wooden block can slide down the plane freely.

3. Measure and record the angle of inclination of the plank. 4. Set up the apparatus as shown in Figure 5-2.

5. Start with one wooden block attached to the lower end of the spring. 6. Displace the block downward and released, so that the block will be pulled up by the tension in the spring.

7. Repeat step [6] with a smaller displacement until a stage that the wooden block stays stationary upon released. Measure and record the length l2 of the spring. 8. From the graph of l1 against m1 in Part 1, obtain the corresponding mass, m’ for the length l2.

9. The mass of the wooden block could be increased by adding another wooden block on top of the first, weigh the new combined mass of the block. Repeat steps [6] to [8]. 10. Tabulate: m, l and m’.

11. Plot a graph of m’ against m.

12. Calculate the gradient of the graph of m’ against m.

13. Hence, determine the coefficient of static friction, μ . Observation/Results:

|Block |Mass (g) |

|A |141.96 |

|B |41.13 |

|C |25.74 |

|D |25.9 |

|E |22.93 |

|Weight applied |Spring extension (cm) | |ma |5.7 | |ma + mb |5.8 | |ma + mb + mc |6.4 | |ma + mb +mc +md |7.8 | |ma + mb +mc + md +me |8.4 |

Y = 0.0344x + 2.8933

X = (Y - 2.8933)/0.0344

m ̓ = (l-2.8933)/0.0344

1) l = 5.7cm

m ̓ = (5.7 - 2.8933)/0.0344

m ̓ = 81.6g

2) l = 5.8cm

m ̓ = (5.8 - 2.8933)/0.0344

m ̓ = 84.5g

3) l = 6.4cm

m ̓ = (6.4 - 2.8933)/0.0344

m ̓ = 101.9g

4) l = 7.8cm

m ̓ = (7.8 - 2.8933)/0.0344

m ̓ = 142.6g

5) l = 8.4cm

m ̓ = (8.4 - 2.8933)/0.0344

m ̓ = 160.1g

[pic]

Calculation:

m ̓ = m (µ cosӨ + sinӨ)

Gradient = m ( cosӨ + sinӨ)

Ө= 23 ̊

From the graph, gradient = 0.5652

0.5652= µ cos 23 ̊+ sin 23 ̊

µ = (0.5652 - sin 23 ̊) / cos 23 ̊

µ = 0.189

Discussion:

Static friction is a force found between two surface two surface in a moving object .When an object is moving towards the right the static friction is towards the left which is against the main direction .The coefficient of static friction is µ.

During the experiment it is found the most of results are found inaccurate.This is know as random error.Random error can be overcome by taking even the slightest value or mistake.During the experiment in diagram1.1 the spring used has been stretch until the initial length is inaccurate and the real initial is not found.This causes the initial length and final length of the spring to be inaccurate.Besides that during the experiment in diagram1.2 a rubber band is used to tie the woodwn blocks together also affected the reading.The friction between the rubber band and the wooden plane affects the length of the spring because the friction between the wooden board and rubber band does not let the wooden blocks to slide smoothly.Thus the final length of the spring is not accurately measured

Percaution should be taken during the experiment.For example when measuring the length of the final or initial length of spring a meter rule must be used.The eye is always perpendicular with the meter rule to avoid parallax error.When doing experiment in diagram1.2 the andle of inclination must be always same thoughout the whole experiment this is to avoid the angle Ɵ this will give an inaccurate result

In daily life there are a lot of sitiatin where static friction occurred.For example standing on a steep hill. The static friction keeps the feet from slipping. Next, a bolt holding the tire of the car, the static friction prevents the tire from coming out of the car.

Conclusion:

The static friction between two surface prevents both objects from moving away from each other when the static friction force is not exceeded by an external force.

Rodney Francis a/l Xavier

ID:

1302969

Group members:

Yuan Li Hong, Desmond Wong

Practical Lecturer:

Mr Zoheir

Practical Group:

6

Part 1

Title:

To determine the coefficient of static friction between two surfaces.

Objectives:

1. To determine the relationship between the mass of load and the length of spring. 2. To determine the coefficient of static friction between two surface.

Apparatus and materials:

1. Retort stand

2. Spring

3. Slotted masses 200g with hanger

4. Meter rule

Setup:

[pic]

Theory:

If the wooden block is being displaced down the inclined plane, the block will return to its original position when released because the net force up the plane exceeds the limiting friction down the plane. The downward displacement is being reduced gradually until a stage where the block stays stationary when released. At this point, the force up the plane equalized the limiting friction down the plane.

If T is the tension of the spring, F is the limiting friction, and μ is the coefficient of static friction, then

T- mg sin θ = F

T- mg sin θ = μ mg cos θ

If T = m’g, where m’ = mass equivalent to tension T, then

m’g – mg sin θ = μ mg cos θ

m’ = m( μ cos θ + sin θ)

Procedure:

1. Hook one end of the spring on the retort stand.

2. Hang the hanger with a 20g slotted mass at the other end. 3. Measure the length l1 of the spring, record the mass m1 of the load. 4. Increase the mass m1, measure the corresponding length l1 of the spring. 5. Tabulate l1 and m1.

6. Plot a graph of l1 against m1.

Obervation/result:

Unextended spring length (initial) = 2.7cm

|Weight (g) |Spring extension (cm) | |20 |3.8 | |40 |4.2 | |60 |4.8 | |80 |5.2 | |100 |6.6 | |120 |7.2 | |140 |7.8 | |160 |8.4 | |180 |9.2 | |200 |9.6 |

[pic]

Part 2: The coefficient of friction between two surfaces

Apparatus and Materials:

1. A smooth plank as inclined plane

2. Retort stand

3. Wooden blocks

4. Electronic balance

5. Spring

6. Protractor

7. Pendulum bob

8. Thread

9. Plasticine

Setup:

[pic]

Procedure:

1. Weigh the mass of wooden block with a smooth surface. Record down the mass. 2. Adjust the retort stand, to adjust the angle of inclination of the plank, such that the wooden block can slide down the plane freely.

3. Measure and record the angle of inclination of the plank. 4. Set up the apparatus as shown in Figure 5-2.

5. Start with one wooden block attached to the lower end of the spring. 6. Displace the block downward and released, so that the block will be pulled up by the tension in the spring.

7. Repeat step [6] with a smaller displacement until a stage that the wooden block stays stationary upon released. Measure and record the length l2 of the spring. 8. From the graph of l1 against m1 in Part 1, obtain the corresponding mass, m’ for the length l2.

9. The mass of the wooden block could be increased by adding another wooden block on top of the first, weigh the new combined mass of the block. Repeat steps [6] to [8]. 10. Tabulate: m, l and m’.

11. Plot a graph of m’ against m.

12. Calculate the gradient of the graph of m’ against m.

13. Hence, determine the coefficient of static friction, μ . Observation/Results:

|Block |Mass (g) |

|A |141.96 |

|B |41.13 |

|C |25.74 |

|D |25.9 |

|E |22.93 |

|Weight applied |Spring extension (cm) | |ma |5.7 | |ma + mb |5.8 | |ma + mb + mc |6.4 | |ma + mb +mc +md |7.8 | |ma + mb +mc + md +me |8.4 |

Y = 0.0344x + 2.8933

X = (Y - 2.8933)/0.0344

m ̓ = (l-2.8933)/0.0344

1) l = 5.7cm

m ̓ = (5.7 - 2.8933)/0.0344

m ̓ = 81.6g

2) l = 5.8cm

m ̓ = (5.8 - 2.8933)/0.0344

m ̓ = 84.5g

3) l = 6.4cm

m ̓ = (6.4 - 2.8933)/0.0344

m ̓ = 101.9g

4) l = 7.8cm

m ̓ = (7.8 - 2.8933)/0.0344

m ̓ = 142.6g

5) l = 8.4cm

m ̓ = (8.4 - 2.8933)/0.0344

m ̓ = 160.1g

[pic]

Calculation:

m ̓ = m (µ cosӨ + sinӨ)

Gradient = m ( cosӨ + sinӨ)

Ө= 23 ̊

From the graph, gradient = 0.5652

0.5652= µ cos 23 ̊+ sin 23 ̊

µ = (0.5652 - sin 23 ̊) / cos 23 ̊

µ = 0.189

Discussion:

Static friction is a force found between two surface two surface in a moving object .When an object is moving towards the right the static friction is towards the left which is against the main direction .The coefficient of static friction is µ.

During the experiment it is found the most of results are found inaccurate.This is know as random error.Random error can be overcome by taking even the slightest value or mistake.During the experiment in diagram1.1 the spring used has been stretch until the initial length is inaccurate and the real initial is not found.This causes the initial length and final length of the spring to be inaccurate.Besides that during the experiment in diagram1.2 a rubber band is used to tie the woodwn blocks together also affected the reading.The friction between the rubber band and the wooden plane affects the length of the spring because the friction between the wooden board and rubber band does not let the wooden blocks to slide smoothly.Thus the final length of the spring is not accurately measured

Percaution should be taken during the experiment.For example when measuring the length of the final or initial length of spring a meter rule must be used.The eye is always perpendicular with the meter rule to avoid parallax error.When doing experiment in diagram1.2 the andle of inclination must be always same thoughout the whole experiment this is to avoid the angle Ɵ this will give an inaccurate result

In daily life there are a lot of sitiatin where static friction occurred.For example standing on a steep hill. The static friction keeps the feet from slipping. Next, a bolt holding the tire of the car, the static friction prevents the tire from coming out of the car.

Conclusion:

The static friction between two surface prevents both objects from moving away from each other when the static friction force is not exceeded by an external force.