Our Project
We used a frictional Ramp to represent georgia geography and weather conditions. Like for example, we used water from a hose to simulate rainy conditions. To test the materials grip.
Well, it's a common issue that affects many elderly/ younger children individuals, especially during rainy weather. Poorly designed sidewalks/playgrounds can lead to slips and falls, resulting in unnecessary injuries.
This is what our project is about. We tested various materials to make sidewalks safer for elderly individuals. The materials we used was to see which ones provided the best traction and durability.
We used a frictional Ramp to represent georgia geography and weather conditions. Like for example, we used water from a hose to simulate rainy conditions. To test the materials grip.
Wood(pine trees), and cardboard are the land materials we tested. To make the cardboard, they have to get raw softwood (like pine trees in Georgia), strip all the bark off, and chopped into small uniform pieces. Then they are dumped into a massive industrial boiler. They are cooked at very high temperatures with chemicals that are sodium hydroxide and sodium sulfide. Now they put chips after they were dumped in the solution, they are put in a chemical bath that dissolves the lignin. Which makes into Kraft pulp.
Then the Kraft pulp is rolled into long sheets. Now they steam blast the paper rolls in a machine called corrugator. Now they shape the Arches of the paper rolls into a permanent shape. Then to lock them in place, they use a hot cornstarch-based adhesive. To glue all the waves together. Then a machine instantly presses a flat sheet of linerboard onto of the waves, and another flat sheet to make there layers.
Then they combined the 3 layer board into the steam-heated baking plates to instantly cure the starch glue. Now finally they do a precise cut to give us the cardboard final size.
Plastic are the synthetic materials we tested. The plastic is made by using petroleum(oil) products which make it flexible, durable, and artificial.
To make the sidewalks safer for elderly individuals, we need to understand Gravitational Potential Energy (GPE) and Kinetic Energy (KE). Kinetic energy is the energy of motion, while gravitational potential energy is the energy an object has due to its position in a gravitational field.
So we had to calculate the KE and GPE to find the best materials for reducing friction. The formula for KE is KE = ½ of mass(KG) the object multiply by velocity squared(KE=1/2mv²), and the formula for GPE is mass(KG) of the object multiplied by the acceleration due to gravity(which is 9.8 meter per second) and the height in meters42 (GPE = mgh).
So to calculate loss energy do to friction we subtract the GPE from the top and KE at the bottom to get the loss of energy by friction. In our research, we can see how much energy is converted in to Kinetic Energy.
Friction is the force that resists the motion of objects or surfaces sliding against each other. It is a crucial factor in determining the safety and effectiveness of sidewalks, especially for elderly individuals. We can see how much energy is converted to thermal energy due to friction. By taking the maximum GPE subtract from maximum KE, we can determine the energy was converted thermal energy due to friction. The frictional force can be calculated using the formula: F = μN, where F is the frictional force, μ is the coefficient of friction, which can be calculeted for a ramp by
μ =
g sin θ - a
g cos θ
and N is the normal force. Which for a ramp is N=m x g x cos θ
In our research, we tested different materials to determine their coefficients of friction and how they affect the overall safety of sidewalks. By understanding the relationship between friction, energy loss, and material properties, we can make informed decisions about which materials are best suited for creating safer walking surfaces.
There are several mathematical concepts involved in our research to calculate the frictional forces and energy converts. To calculate the height, we used the formula: a2 + b2 = c2 . Which is the Pythagorean Theorem. We used this formula to determine the height of the ramp by making a right triangle with the ramp as the hypotenuse. After we made the triangle, by using the Pythagorean Theorem, we could calculate the height. We calculated the height using the using trigonometry. Since I know the hypotenuse and one of the other sides, I can use the sine function to find the height. Which is sine(sin) = opposite hypotenuse We used this trigonometry function, because I know the hypotenuse and the angle, but not the height (aka the opposite side of the angle).
So in order for us to make the Frictional Ramp, we need to understand the chemical processes to keep the stick in place. We used red Georgian clay, organic bone meal, and pine straws to create the necessary chemical bonds. The reason behind this is that these materials have the right chemical properties to form strong bonds and provide the necessary grip. The red clay soil has silicon Dioxide(SiO2 ) and Aluminum Oxide(Al2 O3 ) collided into the Calcium Oxide(CaO) and Phosphorus peroxide(P2 O5 ) from the bone meal, and the cellulose and lignin polymers to make this strong clay. The pine straws provided additional texture and grip when it was dried, but the CaO, P2o5, SiO2, and Al2O3 actually made the solution more strong.
The calculations for trigonometric functions and energy conversions are essential in determining the safety and effectiveness of our frictional ramp design. This how we got the height of the ramp. We don't know the opposite side, so we called it x. The hypotenuse is 3.7, and the angle is 32.86 degrees
sin(32.86) =
x
3.7
Now we can solve for x. First, we multiply both sides by 3.7,
3.7 * sin(32.86) = x. Then, we multiply sin(32.86) by 3.7, and the value of x ~
The height of the ramp is ~ 2.01m.
Now we need to calculate the Gravitational Potential Energy (GPE). The formual is GPE = mgh, the g is the acceleration due to gravity which is 9.8m/s² and the mass is 2.5kg. So the GPE is ~
. This is the graph
Now we got the GPE, so now we need get the KE. The formula for KE is KE = 1/2mv2
m is mass which is in kilos, the v is the velocity, which is
velocity =
distance
time
For KE there is multiple numbers, because the speed changes each materials wet or dry.
For the dry wood the velocity is
, so 2.5 x 5.61 squared equal
, That is the KE for the dry wood. For wet wood the velocity is ~
, so 2.5 x 3.33 is ~
so that the KE for the wet wood. For dry cardboard the velocity is ~
, so 2.5 x 2.98 is ~
, That is the KE for the dry cardboard. For wet cardboard the velocity is ~
, so 2.5 x 2.42 is ~
that is the KE for the wet cardboard. For the dry plastic the velocity is ~
, so 2.5 x 4.57 is ~
, that is the KE for the dry plastic. For wet plastic the velocity is ~
, so 2.5 x 3.78 is ~
, that is the KE for the wet plastic.
This is the graph for the KE of the friction ramp. These color are the same for all graphs. Red is the dry wood, violet is the wet wood, green is the dry cardboard, blue is the wet cardboard, orange is the dry plastic, and black is the wet plastic.
How we can compare the velocity of the other materials, we can see that the dry wood has the highest velocity, and the wet cardboard has the lowest velocity. The dry wood has the highest KE, and the wet cardboard has the lowest KE.
Now we can calculate the loss of energy due to friction. We can do this by subtracting the GPE from the KE. For dry wood, the conversion of energy to heat is ~
.
For the wet wood, the conversion of energy to heat is ~
.
For the dry cardboard, the conversion of energy to heat is ~
.
For the wet cardboard, the conversion of energy to heat is ~
.
For the dry plastic, the conversion of energy to heat is ~
. For the wet plastic, the conversion of energy to heat is ~
.
Now we have to calculate friction. First we need to calculate the normal force. To calculate normal force, we need to multiply 2.5kg, 9.8m/s², and cos 32.86, because this is a ramp. Which is ~
. Now we can calculate friction. To find friction, we use the formula F = μN, where F is the frictional force, μ is the coefficient of friction, and N is the normal force. We can find the coefficient of friction by using μ =
g sin θ - a
g cos θ
. For dry wood, the coefficient of friction is μ =
9.8 sin 31.57 - a
9.8 cos 31.57;
which a is acceleraion 2.08. The answer is ~
. For wet wood, the coefficient of friction is
g sin 31.57 - a
g cos 31.57
which a is 2.35. The answer is ~
. For dry cardboard, the coefficient of friction is ~
g sin 31.57; - a
g cos 31.57
. which a is 1.89. The answer is ~
. For wet cardboard, the coefficient of friction is ~
g sin 31.57 - a
g cos 31.57
. which a is 1.27. The answer is ~
. For dry plastic, the coefficient of friction is ~
g sin 31.57 - a
g cos 31.57
. which a is 4.42. The answer is ~
. For wet plastic, the coefficient of friction is ~
g sin 31.57 - a
g cos 31.57
. which a is 3.02. The answer is ~
Now we got the coefficient of friction(μ), we can calculate the frictional force. For dry wood, the frictional force is 24.50 x 1.73, which is ~ .
For wet wood, the frictional force is 24.50 x 0.61, which is ~
.
For dry cardboard, the frictional force is 24.5 x 0.49, which is ~
.
For wet cardboard, the frictional force is 24.5 x 0.33, which is ~
.
For dry plastic, the frictional force is 24.5 x 1.15, which is
~ .
For wet plastic, the frictional force is 24.5 x 0.79, which is
~ .
So which all the calculations we did, the results is that cardboard is the best material, both wet and dry, that we tested. Obviously cardboard is not a strong material. A similar material that is better is Hot-Rolled mild Steel(A36/S235) and Weathering Steel(Corten/A588). So Hot-Rolled mild, or Weathering Steel is the best materials to use for building.
