Basics of Rocket Propulsion Part 2 The Thrust Equation
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1) A rocket system can be modeled using Newton's Second Law of Motion. The thrust of a rocket is equal to the rate of change of momentum. 2) For a rocket of initial mass m drifting at velocity V0, the thrust is equal to the rate at which exhaust gases are ejected multiplied by the exhaust velocity. 3) The thrust equation relates the thrust of a rocket to the mass flow rate and exhaust velocity, where thrust equals the mass flow rate times exhaust velocity.
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For notes/articles, Visit my blog (link is given below).
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Rocket engines produce thrust by accelerating and ejecting stored propellants at high speeds through a nozzle. They obtain high thrust-to-weight ratios but have the lowest fuel efficiency of all jet engines. Key components include the combustion chamber, where propellants combust at high pressures and temperatures, and the supersonic nozzle, which converts the hot gas energy into kinetic energy of the exhaust jet for propulsion. Rocket performance is optimized by maximizing exhaust velocity and specific impulse through high combustion temperatures, low-mass propellants, and nozzle designs that adapt to changing ambient pressures.
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This document provides an overview of KAM Specialties' capabilities including engineering, manufacturing, and 3D printing services across several industries. Key points include:
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Momentum ppt physics grade 11
The document discusses momentum and Newton's second law of motion. It defines linear momentum as the product of an object's mass and velocity. Newton's second law is stated as the net external force equals the change in momentum divided by the change in time. The law of conservation of momentum states that the total momentum of an isolated system before and after an interaction, such as a collision, remains the same.
Study Unit Ill Engineerin M Part4 an1cs By And.docx
Study Unit
Ill Engineerin M
Part4
an1cs
By
Andrew Pytel, Ph.D.
Associate Professor, Engineering Mechanics
The Pennsylvania State University
When you complete this study unit, you'll be able to
• Calculate the mass moment of inertia
• Calculate the kinetic energy of a body
• Determine the linear impulse and momentum of a body
• Analyze the equations and conditions used to determine the forces involving rectilinear
translation
• Describe centripetal and centrifugal force
• Describe the forces that impact the rotation of a rigid body without translation
• Explain the motion of a wheel, and calculate the magnitude of the linear acceleration and
friction forces
• Analyze the work-energy method as it applies to the motion and action of a body
iii
PRELIMINARY EXPLANATIONS PERTAINING TO KINETICS .
FORCE-MASS-ACCELERATION METHOD .....
Translation of Rigid Body
Rotation of Rigid Body without Translation
General Plane Motion of Rigid Body
23
WORK-ENERGY METHOD . . . . . . . . . . . . . . . . . . . . . . . . . 53
Application of Method for Translation
Other Applications of Work-Energy Method
IMPULSE-MOMENTUM METHOD . . . . . . .
Rectilinear Translation of Single Body
Collision of Two Bodies
PRACTICE PROBLEMS ANSWERS
EXAMINATION . . . . . . . . . .
. ........... 77
93
95
Engineering Nlechanics, Part 4
PRELIMINARY EXPLANATIONS PERTAINING
TO KINETICS
Scope of This Text
1
1 • In the preceding texts on engineering mechanics, we have discussed
separately the relations of forces in a system and the conditions of mo-
tion of bodies. In this text, we shall consider the relation between the
motion of a body and the force or forces acting on the body to produce
the motion. The basis for the relationship between motion and force
is Newton's second law of motion. However, there are three different
methods of applying this law. These are commonly called the force-
mass acceleration method, the work-energy method, and the impulse-
momentum method. Each method is most useful for solving certain
types of problems.
Statement of Newton's Second Law of Motion
2 • In Engineering Mechanics, Part 1, Newton's second law of motion was
stated as follows:
If a resultant force acts upon a particle, the particle will be accelerated
in the direction of the force. Furthermore, the magnitude of the accel-
eration will be directly proportional to the magnitude of the resultant
force and inversely proportional to the mass of the particle.
Newton's second law can be expressed mathematically by the following
equation:
F
a=k-
m
in which a = magnitude of the acceleration of a particle
k = a numerical factor
F = magnitude of the force acting upon the particle
m = mass of the particle
(1)
The mass of a particle is a measure of the exact amount of matter in
the particle. Any body is composed of a number of particles, and the
mass of a body is the sum of the masses of all the particles.
Lecture5. Hi conservation in law of momentum
This document discusses conservation of momentum and the center of mass concept. It defines momentum and explains that for a system of particles, the total momentum is conserved even with internal forces, as long as there are no external forces. It introduces the center of mass as a point where all the system's mass can be considered concentrated, allowing the system to be treated as a single particle. The center of mass moves as if affected only by external forces. Examples show how to calculate the center of mass and use it to solve problems by reducing them to a single-particle system.
Kinetics of particle
This document contains a presentation on Newton's second law of motion. The presentation topics include the relation between force, mass and acceleration, applications of Newton's second law, equations of motion, and an introduction to kinetics of particles. The document provides definitions and explanations of key concepts such as force, mass, acceleration, momentum, impulse, and kinetics. It also includes sample problems demonstrating applications of Newton's second law and equations of motion, along with step-by-step solutions. The presentation was made by Danyal Haider and Kamran Shah and covers fundamental principles of classical mechanics.
Momentum
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Science ace 2
Newton's 3 laws of motion are summarized as follows:
1) Newton's first law states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
2) Newton's second law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
3) Newton's third law states that for every action, there is an equal and opposite reaction.
Science ace 2
Newton's 3 laws of motion are summarized as follows:
1) Newton's first law states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
2) Newton's second law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
3) Newton's third law states that for every action, there is an equal and opposite reaction.
Science ace 2
Newton's 3 laws of motion are summarized as follows:
1) Newton's first law states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
2) Newton's second law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
3) Newton's third law states that for every action, there is an equal and opposite reaction.
Science ace 2
Newton's 3 laws of motion are summarized as follows:
1) Newton's first law states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
2) Newton's second law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
3) Newton's third law states that for every action, there is an equal and opposite reaction.
Science ace 2
Newton's 3 laws of motion are summarized as follows:
1) Newton's first law states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
2) Newton's second law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
3) Newton's third law states that for every action, there is an equal and opposite reaction.
Variable mass system
1) The document discusses center of mass and variable-mass systems. It provides examples of how basketball players and high jumpers manipulate their body positions to modify their center of mass during jumps.
2) Variable-mass systems are examined, using a rocket as an example. As the rocket ejects mass, it gains momentum from the thrust of the ejected gases.
3) An example calculation is shown for the Saturn V rocket, finding its initial acceleration upon lift-off to be 2.7m/s2.
Centro de masa y momento
The center of mass of a system of particles or solid object can be treated as a single point where all of the system's mass is concentrated. External forces on the system can be thought to act at this point. If the net external force on a system of particles is zero, the center of mass will travel with constant velocity. The linear momentum of a system of particles is equal to the total mass of the system multiplied by the velocity of its center of mass.
Unit 5: Impulse and momentum
Unit 5 of Physics in the Leveling course at Yachay Tech University (Urcuquí, Ecuador). Semester October 2014-March 2015
law of mechanics
This document provides an overview of engineering mechanics. It defines mechanics as the branch of physics dealing with rest and motion. Mechanics can be divided into classical mechanics, relativistic mechanics, and wave mechanics. Engineering mechanics is further divided into solid mechanics and fluid mechanics. Solid mechanics includes rigid body mechanics and deformable body mechanics. Rigid body mechanics contains statics and dynamics. Dynamics contains kinematics and kinetics. The document also outlines Newton's laws of motion, the law of universal gravitation, and other fundamental laws and concepts of mechanics. Finally, it discusses common units used in mechanics like the MKS, CGS, and FPS systems.
Lecture3.pdf
Here are the steps to solve this problem:
1) Draw the free body diagram and identify all forces acting on the mass m. There is a driving force F applied and gravity mg acting downwards.
2) Write the equation of motion in the y-direction: F - mg = ma
3) Integrate twice to find expressions for velocity and position as a function of time:
v(t) = gt + (F/m)t
y(t) = (1/2)gt^2 + (F/m)t
4) Substitute the desired times into the expressions for velocity and position to find the answers.
So in summary, use Newton's Second Law
Analyzing motion of system of particles
This document discusses analyzing the motion of particle systems using Newton's laws of motion. It defines a particle as a point mass with no orientation or rotational inertia, and discusses describing particle position, velocity, and acceleration using Cartesian components of position, velocity, and acceleration vectors. It presents Newton's three laws of motion and provides everyday examples. It also discusses calculating forces required to cause prescribed particle motions using free body diagrams and Newton's second law, and deriving and solving equations of motion for particle systems.
Center of Mass and Momentum.pdf
1) The center of mass of a system of particles or solid body represents the point where all the mass can be considered to be concentrated and external forces are applied.
2) Newton's second law can be applied to the center of mass of a system, where the net external force equals the mass times the acceleration of the center of mass.
3) For a closed, isolated system where no external forces act, the total linear momentum of the system remains constant over time.
Unit 6, Lesson 5 - Newton's Laws of Motion
Unit 6, Lesson 5 - Newton's Laws of Motion
Lesson Outline:
1. Law of Inertia
2. Law of Acceleration
3. Law of Interaction
4. Momentum and Impulse: An Overview
Physics newton's laws
The document describes an experiment using an Atwood machine to study and apply Newton's second law of motion. The experiment involves:
1) Setting up an Atwood machine with a pulley, light string, and slotted weights of 100g each on both sides, with an extra 13-20g added to one side.
2) Timing how long it takes the heavier mass to fall a distance d and calculating its acceleration using kinematic equations.
3) Considering the forces on each mass to calculate acceleration using Newton's second law and comparing the results.
4) Repeating trials adding more mass to vary the net force to improve accuracy.
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3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
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Estimation of Magnisium sulphate
Calcium gluconate
Complexometric Titration/ chelatometry titration/chelating titration, introduction, Types-
1.Direct Titration
2.Back Titration
3.Replacement Titration
4.Indirect Titration
Masking agent, Demasking agents
formation of complex
comparition between masking and demasking agents,
Indicators/Metal ion indicators/ Metallochromic indicators/pM indicators,
Visual Technique,PM indicators (metallochromic), Indicators of pH, Redox Indicators
Instrumental Techniques-Photometry
Potentiometry
Miscellaneous methods.
Complex titration with EDTA.
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Basics of Rocket Propulsion Part 2 The Thrust Equation
- 1. Basics of Rocket Propulsion Part 2 The Thrust Equation
- 2. Newton’s Second Law of Motion • The rate of change of linear momentum of a body is directly proportional to the external force applied on the body, and this change takes place in the direction of the applied force.
- 3. 1.Constant Mass System An external force will cause the body to accelerate at a rate that is proportional to the force, We know that:- F = ma For a force F, applied for a time dt, :- This law can also be expressed as F = dP/dt i.e rate of change of Momentum.
- 4. 2. Rocket System Consider a rocket of mass m, drifting at velocity Vo. The Initial Momentum Po, would be INITIAL MOMENTUM at Time = 0
- 5. Rocket System FINAL MOMENTUM at Time = t When a rocket is fired, it releases gases weighing mass dm, the rocket it self now weighs m-dm. The final velocity become Vo + dV. The gases leave the exhaust at a velocity u. Momentum at time t, Pt would be:
- 6. Rocket System • The Term dVdm is very small and can be ignored. (Very small number multiplied by a very small number)
- 7. Rocket System Change in Momentum • The change in Momentum therefore would be: Since it’s a closed system, the net force is zero, giving:-
- 8. Thrust Equation Dividing both sides per unit time t, we get: This is the thrust Equation
- 9. Thrust Equation The thrust of a rocket is given by the exhaust velocity multiplied by the Rate of mass ejection.