Coefficient of Friction De La Salle University

Physics Department

LBYPHYX

Khalil, Ahmed I.

Abstract—

Friction is a force that can result from the simple

contact between two objects; it resists the motion of the object

either by slowing it down or by hindering its motion. It is

essential in keeping an object in a static position or in changing

an object’s direction or speed of movement. The experimental

values and the laws & equations allowed for the computation of

the value of the acceleration as 52.53 cm/s^2 and we were able to

compute for the angle of elevation from the equations.

I. INTRODUCTION

When an object is in contact with another such as a tissue or a piece of cloth on a table there is a force that is generated on the surface of contact, this force holds these two objects in place in relative to each other and hindering them from moving freely along. Another everyday experience is being accidentally rubbed against someone or something due to the lack of personal space, this happens mostly in crowded places, this rubbing slows the individuals down by dispensing heat as a result of the friction that occurred, it also occurs in machines where there are moving parts and oftentimes reduces the efficiency of these machines by wasting heat as a result of motion, but friction is also indispensable as it allows humans and machines to slow down, stop and start again. When a human is not moving for example there is static friction that result from simply standing or sitting, it is also felt when standing up in a stationary position as it is the one that prevents slipping while standing up or sitting, friction is also useful to produce heat from kinetic energy, an example of that would be the basis of work of a simple matchstick, different materials have different coefficient of friction as this paper will explain.

II. THEORETICAL BACKGROUND

Friction is a force that resists the motion of an object by way of dispersing the kinetic energy into thermal energy and thus reducing its velocity or hindering its motion. In theory any two objects touching each other produce friction, even at rest

there is static friction which is usually denoted by s . When

an object is in motion it has already overcame the force of static friction, and encounters kinetic friction which is denoted

by k . The standard equation for friction can be given as:

NF (1)

Where F is The Applied force, is the coefficient of friction and N is the normal force which is pushing the two objects together, in a case where an object is resting or moving on a flat surface N can be translated as its weight, but when the

object is on an incline, cosof the angle must be multiplied by

the weight in order to obtain the correct normal force using the following equation :

coswN (2)

Knowing The Forces applied it is now possible to calculate for the coefficient of friction using the following formula:

N

F (3)

III. METHODOLOGY

The following instruction will lead us towards achieving a successful experiment, the materials needed are: a Dynamic cart, a chronometer and a meter stick., it is important to set-up the Dynamic cart on a stable surface while slightly elevating one end of the cart

Procedure:

Take measures of the length of your dynamic cart’s rail.

Place the dynamic cart at one end of the rail and press the cart’s spring in.

Have a friend to help you time how long it takes the cart to get to a travel the specified distance at the defined angle of elevation.

Record them on a table; these will help in calculating the acceleration of the cart.

Pictures :

Fig. 1: Shows the materials needed to conduct the experiment

Fig. 2: Shows the timing procedure

Objectives:

The main objective of this experiment is to be able to determine the coefficient of friction and also to calculate the angle of inclination. Since the given equation for up slope acceleration is:

a gsinrg

Where a is acceleration of the object, is the angle of

inclination, r is the coefficient of friction and g is earth’s

gravitational acceleration. Knowing that the equation for down slope acceleration is:

a gsin-rg (5)

After obtaining the values for a experimentally it is possible to solve for acceleration using the following equation

2

2

t

da (6)

The numerical values that were obtained & filled the table are now experimental values that will help us determine the coefficient of friction and the angle of inclination.

IV. RESULTS AND DISCUSSIONS

During the experiment the following values have been obtained and calculated:

Table1. Experimental Values for distance in a direction

Trial First Direction

1 d(cm) t(sec) a(2s

cm )

2 61 2.38 21.53

3 61 2.55 18.76

4 61 2.52 19.21

5 61 2.80 15.56

6 61 2.56 18.61

Table2. Experimental Values for distance in another direction

Average acceleration = 70.09 2s

cm

Trial Second Direction

1 d(cm) t(sec) a(2s

cm )

2 61 2.31 71.09

3 61 1.30 72.19

4 61 1.30 72.19

5 61 1.36 65.96

6 61 1.35 66.94

Average 61 1.524 69.674

The table shows the time taken for the cart to get to cross the distance taken on the rail. And from these values and knowing that the acceleration is the change in velocity divided by the time interval, it was possible to calculate the cart’s acceleration

in centimeter/ 2second .

The initial releasing position is at 110 cm and the final position is at 18 cm, using simple arithmetic operations the result can be concluded as 92 cm which is the distance travelled. The following results were obtained from the experiment. From the experimental values obtained, acceleration can be calculated and then using the other

formulas, the angle coefficient of friction can also be calculated. The values show that the average acceleration is higher when the cart is moving at a lower angle.

We can calculate for the acceleration using equation 6.

2524.1

)61(2a = 52.53

And for

a = g sin (ignoring friction)

52.53= (9.8)sin

Therefore

Guide questions :

What would be another way of measuring friction?

Since friction is basically lost energy as heat, it is possible to

measure the heat that was generated and compute for the

friction that caused the release of thermal energy.

Would the force needed to overcome friction of the same

object on earth be more or less than the force needed on

the moon?

The force needed would be less on the moon since the

resisting friction relies on the weight of the object which

relies on the moon’s gravity which is 1/6th earth’s gravity.

Would the digits on the table be bigger or smaller if the

rail of the dynamics cart was inclined with a higher,

lower angle? The digits representing the time taken to travel a specific

distance would be smaller as the inclination gets lower or

approaches a horizontal position.

Does the surface area that is in contact between two

objects affect the friction?

No, since NF , surface area has no effect on friction.

V. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

The Experiment was conducted using a dynamics cart and a

chronometer, the time that it took the cart to get to a full stop was noted and by knowing the distance that it traveled, the experiment shows how to compute for the acceleration. We have concluded that the coefficient of friction and the acceleration which was calculated from the table’s experimental values are slightly off by a small percentage as they are not 100% accurate due to human error which is represented here as the differences in timing the cart’s travel time, it can also be added that other minor factors which might have slightly altered the results these might be air drag and external vibrations on the experimenting table. In order to minimize errors, it is recommended that the experiment should be conducted in a quiet environment, far from any major sources of noise or wind and student's body contact with the table should be minimal in order to avoid vibrations from the table. The experiment could have been more accurate if the students were using a more accurate method of timing, for example by using electronic relays which trigger the chronometer when the cart starts and sensors to stop the chronometer when the cart travels the designated distance.

REFERENCES

[1] - Johnson, Clifford V. "Friction." Microsoft® Student

2009 [DVD]. Redmond, WA: Microsoft Corporation, 2008.

[2] - De La Salle University -

http://www.dlsu.edu.ph/academics/colleges/cos/physics/

[3] – Cutnell & Johnson Physics – 5th ed.

Chapter 4 - forces and Newton’s laws of motion

[4] - Physics Exploring Life through Science 2nd edition

Silverio, Angelina