ANALYSIS

Besides the topics that we have already talked about, specifically the

resolution of forces, kinematics, projectile motion, and newton’s second law of

motion, there is also friction. Any object that movies in any direction experiences

an opposing force from air or from another body in contact. That force tends to

either slow down or completely stop the motion of that object. That force which

opposes the motion of the object is called as friction. Friction can manifest in either

as a static or kinetic friction. Static friction or frictional resistance is greater to the

point where the body is about to start its motion. Once the body is in motion, a

lesser amount of resistance, this resistance is called the kinetic friction. Usually

when there are friction between two objects, the surface generates sounds, lights,

and heat energy. It can also be referred as the retarding force of even drag force in

the form of air resistance.

Frictional Force is found to be directly proportional to the normal force

which is represented by N which can be mathematically represented as:

f ∝ N

f =kN

The coefficient of friction or µ takes the place of k which is the constant of

proportionality which will result to:

f =µN

If the body slides down the incline due to its own weight, the angle between

the horizontal and the incline is called the angle of repose.

If it is along the y-axis it can be represented as: Σ F y=0 , N=W cosθ

If it is along the x-axis it can be represented as: Σ F x=0 , f =W sin θ

It will then result to:

µ= fN

= WsinθWcosθ

, µ=tanθ

Thus, the coefficient of friction is equal to the tangent of the angle of repose.

For our experiment 105 entitled Friction. We will need 1.5m string, a meter

stick, a pan, a wooden block, a platform balance, an inclined plane with pulley, and

one set of weights.

We are also asked to clean the surface of the wooden block and plane by

wiping them with a piece of scratch paper or tissue to remove dust and other

particles. We also made sure not to touch the surface we will use in this experiment

so that we can avoid contamination.

The first part of the experiment is the determination of the coefficient of

friction. What we did was to first position the wooden plane horizontally. The next

thing is we recorded the weight of the block and the pan which was written on it.

The next thing we did was to tie one end of the string to the block’s hook and the

other end to the pan passing over the pulley of the plane. We then made necessary

adjustments on the string so that the block will have a room for displacement along

the track. We then planed the narrow side of the block on top of the track. We then

slowly added weights on the plan until we can observe a uniform sliding motion or

constant motion of the block along the track. We then recorded that. We then

repeated this for four more time to get 5 trials. We then calculated the µ for each

trial and determine its average value after wards. The following is a photograph of

the set-up, the table, and the graph:

Determination if the Coefficient Friction

TRIAL (Wblock + Weightadded)

Wb

(Wpan + Weightadded)

Wp

Coefficient Friction

µ

1 130.8 g 30 g 0.23

2 170.8 g 35 g 0.20

3 130.8 g 30 g 0.23

4 250.8 g 55 g 0.22

5 290.8 g 60 g 0.21

Coefficient Friction, µ

Average

0.22

With a slope of: 0.196969697

The second part of our experiment is the determination of the angle of

repose. What we did first was to remove the string that is tied to the block then

25 30 35 40 45 50 55 60 650

50

100

150

200

250

300

350

130.8

170.8

130.8

250.8

290.8

Determination of the Coefficient of Friction

Weightblock + Weightadded

Wei

ghtp

an +

Wei

ghta

dded

place the block, facing its wider side, to the center of the plane’s surface. We then

gradually increased the inclination of the plane until such time that we can observe

the same type of motion the block had, in the first part of the procedure. We then

measured the corresponding vertical height and horizontal distance then recorded

them. We then repeated this until we got to 5 trials. We then computed the

coefficient of friction by getting the tangent of then angle. The result and a

photograph of our set up is as follows:

Determination of the Angle Repose

TRIALVertical Height

h

Horizontal Distance

b tan𝜽 𝜽1 28 cm 109 cm 0.257 14.41o

2 34 cm 123 cm 0.276 15.45o

3 26 cm 96 cm 0.271 15.15o

4 30 cm 112 cm 0.268 15o

5 32 cm 122.5 cm 0.261 14.64o

Based on the gathered data in the experiment, increasing the vertical height

and the horizontal distance will make the coefficient friction a little constant just

like in the first part of the experiment.

For the third part of our experiment

which is the determination of maximum

force that causes uniform motion, we first

set up the track at an angle of 20o. The next think we did was to add weights on the

pan until there is constant upward acceleration of the block. We then recorded the

weights then using Newton’s first law of motion, determined the theoretical value

of the Wp that will cause the block to slide up at a constant speed,

By summing up forces along x and y-

axes, and equating the forces to zero, the

theoretical value of Wp is:

Σ F x=0

W p=f +W b sinθ ; f =μN

Σ F x=0

N=W b cosθ

Therefore,

W p=μW h cosθ+W b sinθ

We then calculated the Wp using the formula above. It will serve as our AV

or calculated value. We then used the average coefficient from part 1and observed

the value. The picture of the set-up and the table for our graph are as our follows:

Table 3. Determination of the Angle Repose

TRIAL 𝜽 Wp (calculated) Wp

(experimental)

Percent Difference

1 13 o 57.46 g 60 g 4.42%

2 15o 71.08 g 70 g 1.52%

3 17o 85.87 g 85 g 1.01%

4 19o 101 g 100 g 1%

5 21o 118.84 g 115 g 3.23%

CONCLUSION

To determine the coefficient of friction which is represented by μ between

the contact surfaces as one body moves with uniform motion. We did the first part

of the experiment. The result of our experiment was 0.23, 0.20, 0.23, and 0.21.

What we did was to set the track horizontally. We then tied the string to the hook

of the block and the other end to the pulley. We then added weights to the pan

which is at 30, 35, 55, and 60 grams. We gave a little push to the block in order to

remove static friction. After that we divided the weight of the pan and the added

weights to the weight of the block and its added weight. And the results are what is

writing above. We also found that if we used the small or the bigger part of the

block, there will still be constant motion. We also found that the weight of the pan

and its added weight is directly proportional to the weight of the block and its

added weight. By getting the average the results of our experiment, we then

conclude that the coefficient of friction between the contact surfaces as one body is

equal to 0.22.

To establish the relationship between the angle of repose and coefficient of

friction. All the forces that are involved are being translated with relation to the

surface’s inclination. We know that there is a normal force that pushes down the

object. And if we set the angle of repose as θ, it will result to two components the

x-axis and the y-axis which will contribute to the object sliding. For the y-axis it is

the Wcosθ for the x-axis it is the Wsinθ. The Wsinθ is parallel to the surface and

Wcosθ is perpendicular to the surface. Since the system will be in equilibrium,

Wsinθ is also equal to the frictional force and the Wcosθ is also equal to the

normal force. If we determine the coefficient of friction, it will result to

FN

= WsinθWcosθ

=tanθ. We can see now that we can relate coefficient to the tangent ofθ.

Graph:

Slope: 0.196969697

25 30 35 40 45 50 55 60 650

50

100

150

200

250

300

350

130.8

170.8

130.8

250.8

290.8

Determination of the Coefficient of Friction

Weightblock + Weightadded

Wei

ghtp

an +

Wei

ghta

dded

Interpretation: The Weight of the pan and its added weight is directly proportional

to the weight of the block and its added weight.