Alex Davis. rocket project
Cover Letter
This year our whole 10th grade learned all about rockets, I had a lot of fun learning all of these steps in a fun interactive way by getting to build bottle rockets. Before we were even allowed to start building our rockets we had to learn all about them this included every calculation to figure out the rockets max highs, initial velocity, force of gravity, thrust, flight time, time of max height and decent velocity we went through many levels of trial and era after studying quadratics, trigonomic functions, derivatives and vectors in science with Julian. We learned all about how different variables affect the rocket's flight path and its arc.
To build our rockets we followed the engineering and design process. Ask, research, imagine, plan, create, test, and improve. Doing this process made us research countless designs to build our rocket and gather materials that will benefit us the most, and most importantly be able to refine our work by testing and improving our work. To build a rocket that met all the criteria we had to pay attention to all these steps closely. I think that the most important step to me during this project was being able to research we where able to find out how to make a nearly perfect rocket
A quadratic is an equation where the longest exponent above a variable is 2. There were three main components Position is represented by a point where it is the rocket's height/position given time. Velocity is the slope at each point on the graph where slope of the graph equals velocity. Acceleration is the change of slope throughout the launch which you can see on the graph as the curve itself. Another major factor is linear motion, linear motion involves the measurement of acceleration, which is referred to as G’s.
Three of the most important aspects of this project were Newton's laws of motion. Newton's first law of motion, An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an outside force. This highly involves inertia which is the property of matter by which it remains at the state of rest or in uniform motion in the same straight line unless acted upon by some external force. For an object to be in equilibrium, both the net force and the net torque on the object must be zero. Normal force is when the force a service gives to an object.
Newton's second law is the law of force and mass, force equals mass times acceleration. These are measured in a small measurement called a newton, this is a kilogram meter per second squared. Many things go into play with this law including drag and friction. Drag is the force pulling back on an object in motion, friction is the force that gives resistance from another surface when coming into contact with itself.
Mass and weight. These two measurements may seem the same but are completely different. Mass is the amount of matter in an object, and weight is the amount of force an object has pulled toward the ground due to gravity.
Newton's 3rd law, action and reaction. For every action there is an equal and opposite reaction. An example of this is me jumping, being me an object pushing off the ground into the air, but the ground is also pushing off me.
Calculation Max Height Using Soh Cah Toa
What we know:
CALCULATIONS
Max height
If we build a triangle it would look like. And we look at what the sides are corresponding to the angle we know
Step 1: The equation of best fit is tangent because we are using the opposite and the adjacent sides.
tan()=oppadj
Step 2: Fill out what we know
tan(54)=x60
Step 3: Get x by itself
60tan(54)=x
86.68=x
Step 4: Add the height of the angle measurer
Height above ground:
86.68 + 1.5 = 88.18
In order to find out our rocket's statistics, we had to calculate many separate parts throughout this unit. First off finding max height to do this we had to incorporate SOH CAH TOA. After applying this we applied TAN to our equation to find our final height. After finding out our max height we had to find our rocket's initial velocity. We had to label our variables which are
h(t) = height given time
G= gravity
Vo=initial velocity
Ho= starting height
Initial velocity
Because we were not given a video we had to take a longer route to figure out our answer. But after struggling through this whole process we were able to find our velocity.
Force of gravity
After finding the velocity of our rocket we went to find our rocket's force of gravity. To do this you need a little basic knowledge of gravity. All objects on (or near) Earth's surface accelerate at the same rate: 9.81 m/s. Because of this fact, we can calculate the force of gravity acting on objects of different mass by using the Force-Mass equation from Newton's second law of motion. While a rocket launches the rocket is being exposed to a few forces including gravity, air friction, and drag.
To this question we will have two answer one for our rocket with water and one without
With water our rocket weighed: 1.023 kg
With out water our rocket weighed: 0.176 kg
We had to plug these numbers into our equation to get our force of gravity
We had to solve this we had to multiply our weight by acceleration of gravity which is 9.81
1.023 x 9.81= 10.03 n
.176 x 9.81= 10.03 n
Full our rocket had a force of gravity of 10.03 n
Empty our rocket has a force of gravity of 7.45 n
Thrust
Our next step was to figure out our rocket's thrust. We took 3/30 to get .1 and plugged that into our equation to get
41.51/.1 this equals 415 this means our rocket had a thrust force of 415
Theoretical flight time
Now moving onto our theoretical flight time, we were given an equation where after we plugged into the A, B, and C places in the formula we were able to get your final answer where our rockets total flight time was 8.31 seconds.
Time of max height
Something that was also incorporated into this topic and graph was our time of mac height at 4.1 seconds into our launch right before our descent. Our rocket reached its max height because we did not have a video. This process was a little more difficult but we have found it was at 4.1 seconds.
Decent velocity
For our descent velocity we are given our height of 86.68m we have to divide that my our decent speed which is 6m/s. After doing this calculation we found our decent velocity is 14.44 seconds till it reaches ground level.
86.68/6ms= 14.44
Blue print
DISCUSSION AND ANALYSIS
At every stage of the rocket's launch forces were applied to it. Even in its pre launch their were forces applied to it. While the rocket is at rest with no motion going on there were still force being applied that force is gravity. Every object even with no motion has this one force being applied regardless of movement or not.
Take off is the second stage of a rocket's flight path, During launch the rocket will be experiencing a lot of thrust going upward. Going down ward there will be drag at a small amount. And slightly larger that drag going down ward will be gravity because gravity is always at play if the object is within earth's atmosphere.
Rising Flight this is the third part of the rocket's flight path. During this segment of the rocket's flight path it will be experiencing only one force. Because all the water is out of the bottle there is no thrust being applied to the rocket. Even though it is still heading upward it does not have a force pushing it up. So the only force being applied is gravity heading down on the rocket.
In the second to last stage of a rocket's flight path is Controlled descent. Now that the rocket is moving downward it gains another force than the previous stages. Now that the rocket is moving down it is experiencing gravity and drag on itself.
All of these phases of launch incorporate Newton's laws of motion. For example before and right after the initial launch Newton's first law is playing heavily. There is no outside force before the launch making the rocket stand still but when the pressure is released (outside force) The rocket shoots up into the air. Another example is how the 3rd law of motion plays out in every action has an equal and opposite reaction, the action is the water pressure braking pushing off the ground and off the rocket cousin the rocket to fly.
Reflection
Throughout this unit I believe I have grown as a learner and collaborator. Being able to incorporate everybody's idea into our rocket so everyone is satisfied was an important aspect to me and my group. The end product I am extremely proud of, during our test launches our rocket did not do well, it was not functional and did not meet many of the requirements for our rocket. If I were to talk about my experience to next year's sophomores I would tell them that it is okay to change your design throughout the project. In the beginning I was pretty adamant about my design but after a few trials I realized I would have to change it. I think that the biggest challenge I faced was being able to agree on everything. For example while making a design for our fins no one in out group would agree, we all had different ideas about what shape and size they should be so we had to overcome this challenge to decide on our final designs fins Having three people in a group made it difficult to be able to make everything a mutual decision but we were able to make it work in the end.
Cover Letter
This year our whole 10th grade learned all about rockets, I had a lot of fun learning all of these steps in a fun interactive way by getting to build bottle rockets. Before we were even allowed to start building our rockets we had to learn all about them this included every calculation to figure out the rockets max highs, initial velocity, force of gravity, thrust, flight time, time of max height and decent velocity we went through many levels of trial and era after studying quadratics, trigonomic functions, derivatives and vectors in science with Julian. We learned all about how different variables affect the rocket's flight path and its arc.
To build our rockets we followed the engineering and design process. Ask, research, imagine, plan, create, test, and improve. Doing this process made us research countless designs to build our rocket and gather materials that will benefit us the most, and most importantly be able to refine our work by testing and improving our work. To build a rocket that met all the criteria we had to pay attention to all these steps closely. I think that the most important step to me during this project was being able to research we where able to find out how to make a nearly perfect rocket
A quadratic is an equation where the longest exponent above a variable is 2. There were three main components Position is represented by a point where it is the rocket's height/position given time. Velocity is the slope at each point on the graph where slope of the graph equals velocity. Acceleration is the change of slope throughout the launch which you can see on the graph as the curve itself. Another major factor is linear motion, linear motion involves the measurement of acceleration, which is referred to as G’s.
Three of the most important aspects of this project were Newton's laws of motion. Newton's first law of motion, An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an outside force. This highly involves inertia which is the property of matter by which it remains at the state of rest or in uniform motion in the same straight line unless acted upon by some external force. For an object to be in equilibrium, both the net force and the net torque on the object must be zero. Normal force is when the force a service gives to an object.
Newton's second law is the law of force and mass, force equals mass times acceleration. These are measured in a small measurement called a newton, this is a kilogram meter per second squared. Many things go into play with this law including drag and friction. Drag is the force pulling back on an object in motion, friction is the force that gives resistance from another surface when coming into contact with itself.
Mass and weight. These two measurements may seem the same but are completely different. Mass is the amount of matter in an object, and weight is the amount of force an object has pulled toward the ground due to gravity.
Newton's 3rd law, action and reaction. For every action there is an equal and opposite reaction. An example of this is me jumping, being me an object pushing off the ground into the air, but the ground is also pushing off me.
Calculation Max Height Using Soh Cah Toa
What we know:
- The angle measurer was taken 60 m back from the launcher.
- The angle was 54 degrees
- The Altitude of the angle measurer above ground is 1.5m
CALCULATIONS
Max height
If we build a triangle it would look like. And we look at what the sides are corresponding to the angle we know
Step 1: The equation of best fit is tangent because we are using the opposite and the adjacent sides.
tan()=oppadj
Step 2: Fill out what we know
tan(54)=x60
Step 3: Get x by itself
60tan(54)=x
86.68=x
Step 4: Add the height of the angle measurer
Height above ground:
86.68 + 1.5 = 88.18
In order to find out our rocket's statistics, we had to calculate many separate parts throughout this unit. First off finding max height to do this we had to incorporate SOH CAH TOA. After applying this we applied TAN to our equation to find our final height. After finding out our max height we had to find our rocket's initial velocity. We had to label our variables which are
h(t) = height given time
G= gravity
Vo=initial velocity
Ho= starting height
Initial velocity
Because we were not given a video we had to take a longer route to figure out our answer. But after struggling through this whole process we were able to find our velocity.
Force of gravity
After finding the velocity of our rocket we went to find our rocket's force of gravity. To do this you need a little basic knowledge of gravity. All objects on (or near) Earth's surface accelerate at the same rate: 9.81 m/s. Because of this fact, we can calculate the force of gravity acting on objects of different mass by using the Force-Mass equation from Newton's second law of motion. While a rocket launches the rocket is being exposed to a few forces including gravity, air friction, and drag.
To this question we will have two answer one for our rocket with water and one without
With water our rocket weighed: 1.023 kg
With out water our rocket weighed: 0.176 kg
We had to plug these numbers into our equation to get our force of gravity
We had to solve this we had to multiply our weight by acceleration of gravity which is 9.81
1.023 x 9.81= 10.03 n
.176 x 9.81= 10.03 n
Full our rocket had a force of gravity of 10.03 n
Empty our rocket has a force of gravity of 7.45 n
Thrust
Our next step was to figure out our rocket's thrust. We took 3/30 to get .1 and plugged that into our equation to get
41.51/.1 this equals 415 this means our rocket had a thrust force of 415
Theoretical flight time
Now moving onto our theoretical flight time, we were given an equation where after we plugged into the A, B, and C places in the formula we were able to get your final answer where our rockets total flight time was 8.31 seconds.
Time of max height
Something that was also incorporated into this topic and graph was our time of mac height at 4.1 seconds into our launch right before our descent. Our rocket reached its max height because we did not have a video. This process was a little more difficult but we have found it was at 4.1 seconds.
Decent velocity
For our descent velocity we are given our height of 86.68m we have to divide that my our decent speed which is 6m/s. After doing this calculation we found our decent velocity is 14.44 seconds till it reaches ground level.
86.68/6ms= 14.44
Blue print
DISCUSSION AND ANALYSIS
At every stage of the rocket's launch forces were applied to it. Even in its pre launch their were forces applied to it. While the rocket is at rest with no motion going on there were still force being applied that force is gravity. Every object even with no motion has this one force being applied regardless of movement or not.
Take off is the second stage of a rocket's flight path, During launch the rocket will be experiencing a lot of thrust going upward. Going down ward there will be drag at a small amount. And slightly larger that drag going down ward will be gravity because gravity is always at play if the object is within earth's atmosphere.
Rising Flight this is the third part of the rocket's flight path. During this segment of the rocket's flight path it will be experiencing only one force. Because all the water is out of the bottle there is no thrust being applied to the rocket. Even though it is still heading upward it does not have a force pushing it up. So the only force being applied is gravity heading down on the rocket.
In the second to last stage of a rocket's flight path is Controlled descent. Now that the rocket is moving downward it gains another force than the previous stages. Now that the rocket is moving down it is experiencing gravity and drag on itself.
All of these phases of launch incorporate Newton's laws of motion. For example before and right after the initial launch Newton's first law is playing heavily. There is no outside force before the launch making the rocket stand still but when the pressure is released (outside force) The rocket shoots up into the air. Another example is how the 3rd law of motion plays out in every action has an equal and opposite reaction, the action is the water pressure braking pushing off the ground and off the rocket cousin the rocket to fly.
Reflection
Throughout this unit I believe I have grown as a learner and collaborator. Being able to incorporate everybody's idea into our rocket so everyone is satisfied was an important aspect to me and my group. The end product I am extremely proud of, during our test launches our rocket did not do well, it was not functional and did not meet many of the requirements for our rocket. If I were to talk about my experience to next year's sophomores I would tell them that it is okay to change your design throughout the project. In the beginning I was pretty adamant about my design but after a few trials I realized I would have to change it. I think that the biggest challenge I faced was being able to agree on everything. For example while making a design for our fins no one in out group would agree, we all had different ideas about what shape and size they should be so we had to overcome this challenge to decide on our final designs fins Having three people in a group made it difficult to be able to make everything a mutual decision but we were able to make it work in the end.