16 March 2015. Modeling Friction Forces.

Purpose
to model friction forces, and basically finding the static and kinetic coefficient of friction forces in different certain conditions as assigned.

Apparatus:

1. Blocks. These blocks with different masses are going to be used as the objects of experiment.
2. Sledges. As the path for blocks, and object of experiment (to determine their static and kinetic frcition).
3. Masses of different varieties.
4. Pulley.
5. Tape and string.

Procedure and Data analysis

for this lab blog only, the procedure and data analysis will be described individually under one part section. Since there are five parts of this experiment.

Part 1 (static friction)

Procedure

1. We set up the sledge, the blocks (first mass), and the cup of water (second mass) as shown in the picture below.
2. Then, we add the second mass (water) inside the cup, to make the block in the position just as it about to move. This will enable us to calculate the static friction
3. Then we add more of the first mass (more blocks) and more of the second mass (water, or if it is not enough put some weigh inside the cup)
4. Then, we repeat the step to drop the water inside the cup until the block is in the position just as it about to move.
5. Always record each masses (first and second).

First we only use one blocks (left). Then we add more blocks one by one until it reaches four blocks (right).

Data Analysis

• We set up the sledge, the blocks (first mass), and the cup of water (second mass) as shown in the picture above. Then, these are the only force acting. Just as it about to move means we are calculating the static friction which is defined as fstaticmax divided by normal force. This is the explanation of the picture.

• Now, that we understand how the system works, lets input the data that we got.

• Now, we input it to logger pro and do a linear fit, and the slope of the mass of the blocks versus the masses of the cup of water will give us the static friction as explained above.

μ_{s = 0.2567}

Part 2 (kinetic friction)

Procedure

1. Calibrate the force sensor by "weighing" any mass, and see the result of the data from the application logger pro. If you get around that mass times 9.8 (gravity), the device is working properly. We weigh a 500 g mass and get around 4.9 N.
2. We set up the block and the force sensor as shown in the picture.
3. Then we pull it with constant force, and we produce constant speed, which means the acceleration is equal zero.
4. Then, we add more mass (add one block at a time until it reaches), and pull it again with constant force.

Data Analysis

• We set up the the whole thing to calculate the kinetic friction which is defined as fkinetic divided by normal force. This is the explanation of the body diagram.

• Now, that we understand how the system works, lets input the data that we got.

• We calculate the average (mean) Forces that we generate using Logger Pro.

• Now, we input it to logger pro and do a linear fit, and the slope of the mass of the blocks versus the Forces generate will give us the static friction as explained above.

μ_{k = 0.2451}

Part 3 (static friction from a sloped surface)

Procedure

1. Place a block on an horizontal surface.
2. Slowly raise one end of the surface, tilting it until the block starts to slip.
3. Use the angle which slipping just begins to determine the coefficient of static friction between the block and the surface.

Data Analysis

• We got the angle to be = 16 degrees +/- 2 degrees
• Calculation shown below.

Part 4 (kinetic friction from sliding a block down and incline)

Procedure

1. Set the motion detector, the sledge, the block, and some masses as the picture shown. For the masses, choose it adequately heavy enough that the block will move.
2. Let go of the block, and record the motion of movement (acceleration).
3. Then we can determine the coefficient of kinetic friction by considering the angle of incline, the force acting, mass of the block, etc.

Data Analysis

• From the motion detector and logger pro, we got the graph of velocity vs time, and the slope of this graph is the acceleration.

a = 1.194 m/s

• With the known value of acceleration and mass of both object, we now can calculate the coefficient of friction as shown below.

Part 5 (predicting the acceleration of a two-mass system)

Procedure

1. Set the motion detector, the sledge, the block, the pulley, and some masses as the picture shown.
2. For the mass number 2 (cup and water), choose it adequately heavy enough that the block will move.
3. Record all data.

Data Analysis

• From the motion detector and logger pro, we got the graph of velocity vs time, and the slope of this graph is the acceleration (experimental value of acceleration).

• Then, from the value of coefficient of kinetic friction found from part 4, we can predict the acceleration ("true" value of acceleration).

• From both value of acceleration, we now can find the percentage error as shown below

Conclusions

• The result of the coefficient that we got is pretty good, considering there are a lot of other factors that we did not consider such as the fact that the coefficient may not be the same all way through the sledge, but we treat it as constant.
• We manage to model friction and through that predict acceleration.

11 March 2015. Modelling the fall of an object falling with air resistance.

Purpose

Part 1
to determine the relationship between air resistance force and speed.
Part 2
to model the fall on an object including the air resistance

Apparatus:

1. Brown coffee filter. This is going to be used as the object of the free fall that are going to be modeled  with the force of air resistance.
2. Meter stick. This will be used as the comparison to the real life measurement in the video that are going to be recorded.
3. Digital balance. to record the mass of the coffee filter.

Meter stick

Procedure:

Part 1

1. We will go to the Design Technology Building to drop the brown coffee filter from an "adequate" height to find the relationship between the filter's speed falling down, and the air resistance force.

2. As you can see in the picture, we are going to used the meter stick as a comparison measurement in the video that are recorded.
3. From this height, we are going to drop one coffee filter, then two coffee filter combined, then three, until five combination of coffee filter.

4. We are going to record these free falls in the laptop; these data later are going to be analyzed.
5. Weigh the masses of the coffee filter.

Part 2: The procedure for part 2 are combined in the Data Analysis section, since it needs data from part 1 to model the free fall object.

Data Analysis:

Part 1

• From the calculated "guessing" shown in the picture below, we now expect that air resistance force on a particular object can be modeled as F(resistance) = k.V^n.

• The V that are going to be used here is the terminal velocity, because thinking logically, the coffee filter can not add more speed (it reaches terminal velocity) because the force of air resistance is finally equal its maximum speed.
• We found each velocity of the coffee filters at a fixed height per time (s) by using logger pro as shown below.

• We acquire the terminal velocity by fitting the linear portion (indicating that the V is constant) of the position vs. time graph of each combination of coffee filters (5 combination) as shown below.

One Coffee Filter. Vt = 0.8155 m/s

Two Coffee Filter. Vt = 1.251 m/s

Three Coffee Filter. Vt = 1.385 m/s

Four Coffee Filter. Vt = 1.673 m/s

Five Coffee Filter. Vt = 1.918 m/s

• From these graphs, we can now see the slope, which is actually the value of the terminal velocity of each combination of coffee filters.
• Now, we need to find our forces acting in the coffee filters when it reaches terminal velocity, which is only influenced by gravity, which equals the weight of the coffee filters. (explanation and calculation shown below). Noted that we weighed 50 brown coffee filters = 46.3 g.

• Then, we modeled all of our forces data and velocity data into a curve fit as shown below.

• We get our equation! (pic)

Part 2: to find the model of air resistance (to find the terminal velocity), and compare it to the experimental value.

• From the data that we get, we are going to compute all of them to excel, with header of each row shown below.

• Remember, the smaller the ∆t is we are more precise in calculating the a, V, x, at any time t when we compute this to excel (explanation found in other lab post).
• Formula for each header are shown below (and how to get them).

• We use ∆t = 0.001s because we find out that when we smaller the ∆t, the results does not change much anymore, so this is already "quite good".
• We know that the coffee filter reaches terminal velocity, when a is zero, which means it does not add more speed or speed is constant.
• Below is several screen shot from excel, with varying mass of the coffee filter.

One Coffee Filter. Vt = 0.8107365 m/s

Two Coffee Filter. Vt = 1.1708268 m/s

Three Coffee Filter. Vt = 1.4516444 m/s

Four Coffee Filter. Vt = 1.6908520 m/s

Five Coffee Filter. Vt = 1.9032222 m/s

• The percent error of our experimental value of terminal velocity is shown below.

• With average percent error =

  0.2921%

  the model actually work pretty well, and the error can actually be caused by the wind from other direction blowing up the coffee filter, the uncertainties of the mass of the coffee filter, small mistakes in plotting the direction of free fall, and other external factors that we did not calculate.

Conclusions:

• Using this model that we found, we can calculate any objects with variety of mass and find it terminal velocity.
• Our model work pretty well with percent error of 0.2921%.
• Force of air resistance in the Building Design and Technology can be modeled as:

4 March 2015. Propagated Uncertainty in Measurements.

Purpose
to calculate uncertainties in a measurements from the calculation of measuring the Density of Metal Cylinders and determination of an Unknown Mass.

Apparatus:

Part 1

1. Vernier Caliper: A vernier caliper is a measuring instrument which can make inside, outside, or depth measurements (tresnainstrument.com). This device basically use two kinds of separate "ruler". The big one measure the "normal" cm ruler with no decimal places, and the second smaller ruler on the below measures the first decimal places, therefore the precision is until the tenth (+- 0.01 cm).
2. Digital balance: A digital scale is a measurement device used to measure the weight or mass of an object or substances (wisegeek.com). The one that we use in this experiment is precise until the ones.

Part 2

1. Spring Scales: a spring fixed at one end with a hook to attach an object at the other. It works by Hooke's Law, which states that the force needed to extend a spring is proportional to the distance that spring is extended from its rest position.
2. Angle measurement apparatus:  a device that is used to measure angle (shown below)

Spring Scales

Angle Measurement

Procedure:

Part 1

1. Measure all width (diameter), weight, and length of all three cylinders given (steel, cooper, and aluminium) using a caliper and digital balance.

STEEL

COOPER

ALUMINIUM

2. Record all data.
3. Calculate the propagated error in each density measurements.

Part 2

1. You will find in the back of the class, three set up as shown in the picture below.

2. Choose two of the set ups, and write down the number marked on the unknown mass, and record the values found on the spring scales.
3. Measure the angle as appointed in the picture.

unknown mass 1

unknown mass 7

Data Analysis:

Part 1

• Below is the collection of data we got with the device precision included.

• Now, we calculated the density propagated error as show below

• Below is the real density of each cylinder.

Materials	Steel	Cooper	Aluminum
Density	7.75 g/cm3	8.96 g/cm3	2.70 g/cm3

• In comparison the percent error we got is:

•  The value is still within the range of our calculated density, therefore our calculation is "quite accurate".

Part 2

• Below is the data we got from the set up.

Unknown 1	Spring Scales
	F1 = 5.3 N +/- 0.50N	F1 = 7.2 N +/- 0.50N
	Angle
	Θ1 = 28° +/- 0.01π	Θ2 = 42° +/- 0.01π
Unknown 7	Spring Scales
	F1 = 8.0 N +/- 0.50N	F1 = 5.3 N +/- 0.50N
	Angle
	Θ1 = 38° +/- 0.01π	Θ2 = 24° +/- 0.0

• Now, we calculate the mass as shown below.

Conclusions:

• From calculating the propagated error of each measurements, we are most likely to find the "true" value in the bigger range, but as a risk, we are getting more "calculated error".
• The more uncertainties we agreed upon a device, the more calculated error we will make toward the end of calculation.