two stage rocket physics problem

(b) For comparison, a nuclear bomb could release about \(4.0 \times {10^{16}}\;{\rm{J}}\). A Multistage Rocket. Note however, that from 10 to 16 seconds, the rocket continues moving upward (the velocity values are positive). Two Stage Rocket. By using this website, you agree to our use of cookies. Reproduction of material from this website without written permission is strictly prohibited. You don't need any complicated electronics or launch support equipment. The rocket starts firing its engines at a time t = 0. . In fact, you get a lot of blank sheets of paper. Free and expert-verified textbook solutions. Instructors are permitted to make and distribute copies for their classes. They make use of all 3 laws of motion and can be creative in solving the problem. An internal explosion breaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. The rocket has two consecutive fuel stages followed by a free-fall motion (no fuel). Figure 3. Two Stage Rocket The PDF file below accompanies the Two Stage Rocket Interactive. Figure 14.2: Schematic for application of the momentum theorem. The rocket is at some height after accelerating with stage 1 for 25s. Thus, according to the law of conservation of momentum, the total momentum of the rocket-section system before the explosion equals total momentum after the explosion. From that instant, it begins to move upwards with a constant acceleration. Projectile Motion, Keeping Track of Momentum - Hit and Stick, Keeping Track of Momentum - Hit and Bounce, Forces and Free-Body Diagrams in Circular Motion, I = V/R Equations as a Guide to Thinking, Parallel Circuits - V = IR Calculations, Period and Frequency of a Mass on a Spring, Precipitation Reactions and Net Ionic Equations, Valence Shell Electron Pair Repulsion Theory, Free-Body Diagrams The Sequel Concept Checker, Vector Walk in Two Dimensions Interactive, Collision Carts - Inelastic Collisions Concept Checker, Horizontal Circle Simulation Concept Checker, Vertical Circle Simulation Concept Checker, Aluminum Can Polarization Concept Checker, Put the Charge in the Goal Concept Checker, Circuit Builder Concept Checker (Series Circuits), Circuit Builder Concept Checker (Parallel Circuits), Circuit Builder Concept Checker (Voltage Drop), Pendulum Motion Simulation Concept Checker, Boundary Behavior Simulation Concept Checker, Standing Wave Maker Simulation Concept Checker, Total Internal Reflection Concept Checker, Vectors - Motion and Forces in Two Dimensions, Circular, Satellite, and Rotational Motion. the air in the rocket . Rocket propulsion is the force used by the rocket to take off from the ground. (a) Assume a spherical asteroid has a mass of 3200 kg for each cubic meter of volume and moves toward the Earth at. For illustrative purposes an example is included . Materials needed for a balloon rocket include: multiple balloons, an air pump, scissors, straws, fishing line, tape, a cardboard tube, and binder clips. Therefore, "helping each other out" extends beyond "giving away the answer" to "teaching how to get the answer" - a valuable classroom trait that we all hope to nurture. The two stages, (1) and (2), show the "state" of the system at time t and time t + dt, where dt is a very small (infinitesimal) time step. The balloon's acceleration depends on its mass and the sum of these forces (Newton's second law, force = mass acceleration). Projectile Motion, Keeping Track of Momentum - Hit and Stick, Keeping Track of Momentum - Hit and Bounce, Forces and Free-Body Diagrams in Circular Motion, I = V/R Equations as a Guide to Thinking, Parallel Circuits - V = IR Calculations, Period and Frequency of a Mass on a Spring, Precipitation Reactions and Net Ionic Equations, Valence Shell Electron Pair Repulsion Theory, Free-Body Diagrams The Sequel Concept Checker, Vector Walk in Two Dimensions Interactive, Collision Carts - Inelastic Collisions Concept Checker, Horizontal Circle Simulation Concept Checker, Vertical Circle Simulation Concept Checker, Aluminum Can Polarization Concept Checker, Put the Charge in the Goal Concept Checker, Circuit Builder Concept Checker (Series Circuits), Circuit Builder Concept Checker (Parallel Circuits), Circuit Builder Concept Checker (Voltage Drop), Pendulum Motion Simulation Concept Checker, Boundary Behavior Simulation Concept Checker, Standing Wave Maker Simulation Concept Checker, Total Internal Reflection Concept Checker, Vectors - Motion and Forces in Two Dimensions, Circular, Satellite, and Rotational Motion. Options vary with different browsers. a decreasing function of as more fuel is saved for the second stage. Right-clicking on the PDF above displays additional options. Sign up for free to discover our expert answers. It takes an enormous amount of energy (and therefore, fuel and money) to send a payload into space. Not finding what you wanted? Specific information is available there on the following topics: 1996-2022 The Physics Classroom, All rights reserved. In all such problems, the solution involves thought and good problem-solving strategies (draw a picture, list what you know, list pertinent equations, etc.). Acceleration of the rocket is given as: a = v e m m t g. Acceleration depends on the exhaust velocity, burning of the fuel . Consider the direction of motion of the rocket before the explosion to be the positive direction, i.e., direction away from the Earth to be positive. Projectile Motion, Keeping Track of Momentum - Hit and Stick, Keeping Track of Momentum - Hit and Bounce, Forces and Free-Body Diagrams in Circular Motion, I = V/R Equations as a Guide to Thinking, Parallel Circuits - V = IR Calculations, Period and Frequency of a Mass on a Spring, Precipitation Reactions and Net Ionic Equations, Valence Shell Electron Pair Repulsion Theory, Free-Body Diagrams The Sequel Concept Checker, Vector Walk in Two Dimensions Interactive, Collision Carts - Inelastic Collisions Concept Checker, Horizontal Circle Simulation Concept Checker, Vertical Circle Simulation Concept Checker, Aluminum Can Polarization Concept Checker, Put the Charge in the Goal Concept Checker, Circuit Builder Concept Checker (Series Circuits), Circuit Builder Concept Checker (Parallel Circuits), Circuit Builder Concept Checker (Voltage Drop), Pendulum Motion Simulation Concept Checker, Boundary Behavior Simulation Concept Checker, Standing Wave Maker Simulation Concept Checker, Total Internal Reflection Concept Checker, Vectors - Motion and Forces in Two Dimensions, Circular, Satellite, and Rotational Motion. A large fraction (typically 90%) of the mass of a rocket is propellant, thus it is important to consider the change in mass of the vehicle as it accelerates. According to Newton's third law of motion (for every action there is an equal and opposite reaction), this means the balloon is pushed forward along the string. In this rocket simulation, a model rocket is launched from the ground. Consider the direction of motion of the rocket before the explosion to be the positive direction, Astronomers estimate that a 2.0-km-diameter asteroid collides with the Earth once every million years. It is intermediate between a three-stage-to-orbit launcher and a hypothetical single-stage-to-orbit (SSTO) launcher.. At liftoff the first stage is responsible for accelerating the vehicle. Friction between the string and the straw acts opposite the direction of motion. Since the magnitude of both \({v_{\rm{A}}}\) and \({v_{\rm{B}}}\) is positive, the direction of both the fragments is away from the Earth. But will physics prevent a full-scale version from succeeding? Users are also granted the right to copy the . By using this website, you agree to our use of cookies. . Estimate the acceleration of a rocket at the moment when the spacecraft reaches the orbit. Consider an extremely simple toy model of a rocket. v is the difference between final and initial velocity. This saves energy because the depleted first stage is not carried all the way into orbit, allowing the second stage to travel farther with less fuel. The reason it works is explained by the physical make-up of the rocket motors. Then the first stage engine drops off revealing a second engine. Once it is out of fuel it continues upward, then falls back to earth, exploding on the . Net Force (and Acceleration) Ranking Tasks, Trajectory - Horizontally Launched Projectiles, Which One Doesn't Belong? This is why nearly all rockets into LEO have two stages. You can find this page online at: https://www.sciencebuddies.org/teacher-resources/lesson-plans/two-stage-balloon-rocket. During the first part of the problem, the observed acceleration of the rocket was 27 m/s 2 and the rocket accelerated from zero to 86 m/s while traveling a distance of 140 m. Knowing these values at Point 2 allowed you to then learn about Point 3, with the understanding that the observed acceleration of the rocket between Points 2 and 3 was -9. . Options vary with different browsers. (a) What is the speed and direction of each section (relative to . This two stage rocket lab is based on a Conceptual Physics Lab by Paul Hewitt. Water rockets are fun toys for people of all ages, even adults. Step Four: Start Drawing. The point of the exercise is to practice the calculation and be able to check the answer with the simulation. Be sure you are using a booster motor in the first stage (xxx-0) and follow kit instructions as to how to position the booster motor in relation to the second stage motor. . Tutorial information on the graphical analysis of motion is available at: The Physics Classroom Tutorial. 1 a-t plot for Problem 1. Please enter a search term in the text box. A small opening at one end of the chamber allows the gas to escape, and in doing so provides a thrust that propels the rocket in the opposite direction. The Rocket Lab Rutherford engines, designed for small orbital rockets like the Electron, use pumps powered by lithium-ion batteries. 94% of StudySmarter users get better grades. B, which is 20 meters per second, squared for time T 15 to 40 right and after Stage A. Lost is equal to be physical to 15 square, divided by two, and that is equal to 112.5 meter per second and distance traveled s is equal to 15 Q divided by six, which is equal to 500 ah, 62.5 meter and be lost. 19.2 Rocket Problem 2 - Momentum Diagrams - YouTube 0:00 / 5:00 19.2 Rocket Problem 2 - Momentum Diagrams 18,518 views Jun 2, 2017 MIT 8.01 Classical Mechanics, Fall 2016. (b) What is the velocity of each ball after the elastic collision? First, the greater the exhaust velocity of the gases relative to the rocket, v e, the greater the acceleration is.The practical limit for v e is about 2.5 10 3 m/s for conventional (non-nuclear) hot-gas propulsion systems. A two-stage-to-orbit (TSTO) or two-stage rocket launch vehicle is a spacecraft in which two distinct stages provide propulsion consecutively in order to achieve orbital velocity. When printing this document, you may NOT modify it in any way. By using this website, you agree to our use of cookies. A Rocket Lab Electron booster failed to reach orbit on May 15 after an anomaly during the first few minutes of the flight. During the second stage, the rocket accelerates upward more slowly, gaining speed until it runs out of fuel. A rocket generates thrust using a controlled explosion as the fuel and . Introduction. 1996-2022 The Physics Classroom, All rights reserved. Figure 8.12 (a) This rocket has a mass m and an upward velocity v. We use cookies to provide you with a great experience and to help our website run effectively. \(7.11 \times {10^8}\;{\rm{J}}\) of energy was supplied by the explosion. The first stage engine is then extinguished, the . In a two-stage rocket, the exhaust velocity for the first stageburn is 3000 m/s and for the second stage burn is 3000 m/s. Each time the velocity increases by one notch, the mass doubles. Thus, the mass of each section will be \({m_{\rm{A}}} = {m_{\rm{B}}} = \frac{m}{2}\). The second stage is lit by the blowthough of the first stage into the nozzle of the second. When you inflate the balloon and then release its nozzle, air is expelled out the back of the balloon. the rate of pressure decrease drops. (a) What is the speed and direction of each section (relative to Earth) after the explosion? A two-stage rocket is traveling at 1200 m/s with respect to the earth when the first stage runs out of fuel. Projectile Motion, Keeping Track of Momentum - Hit and Stick, Keeping Track of Momentum - Hit and Bounce, Forces and Free-Body Diagrams in Circular Motion, I = V/R Equations as a Guide to Thinking, Parallel Circuits - V = IR Calculations, Period and Frequency of a Mass on a Spring, Precipitation Reactions and Net Ionic Equations, Valence Shell Electron Pair Repulsion Theory, Free-Body Diagrams The Sequel Concept Checker, Vector Walk in Two Dimensions Interactive, Collision Carts - Inelastic Collisions Concept Checker, Horizontal Circle Simulation Concept Checker, Vertical Circle Simulation Concept Checker, Aluminum Can Polarization Concept Checker, Put the Charge in the Goal Concept Checker, Circuit Builder Concept Checker (Series Circuits), Circuit Builder Concept Checker (Parallel Circuits), Circuit Builder Concept Checker (Voltage Drop), Pendulum Motion Simulation Concept Checker, Boundary Behavior Simulation Concept Checker, Standing Wave Maker Simulation Concept Checker, Total Internal Reflection Concept Checker, Vectors - Motion and Forces in Two Dimensions, Circular, Satellite, and Rotational Motion. The momentum of the rocket after the explosion is calculated as follows: \(\begin{array}{c}{p_{\rm{f}}} = {m_{\rm{A}}}{v_{\rm{A}}} + {m_{\rm{B}}}{v_{\rm{B}}}\\ = {m_{\rm{A}}}{v_{\rm{A}}} + {m_{\rm{B}}}\left( {{v_{\rm{A}}} - {v_{{\rm{AB}}}}} \right)\\ = {m_{\rm{A}}}{v_{\rm{A}}} + {m_{\rm{B}}}{v_{\rm{A}}} - {m_{\rm{B}}}{v_{{\rm{AB}}}}\\ = \left( {{m_{\rm{A}}} + {m_{\rm{B}}}} \right){v_{\rm{A}}} - {m_{\rm{B}}}{v_{{\rm{AB}}}}\\ = m{v_{\rm{A}}} - \frac{{m{v_{{\rm{AB}}}}}}{2}\end{array}\). Please log in or create a free account to view the full lesson or to leave a review, Build a Solar-Powered Car for the Junior Solar Sprint. 2. The transition to infinite stages can be performed in Eq. The rocket equation ( 1) gives the speed change as. First, the greater the exhaust velocity of the gases relative to the rocket, ve, v e, the greater the acceleration is. A 725-kg two-stage rocket is traveling at a speed of \({\bf{6}}{\bf{.60 \times 1}}{{\bf{0}}^{\bf{3}}}\;{\bf{m/s}}\) away from Earth when a predesigned explosion separates the rocket into two sections of equal mass that then move with a speed of \({\bf{2}}{\bf{.80 \times 1}}{{\bf{0}}^{\bf{3}}}\;{\bf{m/s}}\)relative to each other along the original line of motion. There is a small hot spot in the top-left corner. Speed of the rocket, \(v = 6.60 \times {10^3}\;{\rm{m/s}}\). On the graphs below, sketch qualitatively accurate (i.e., we don't care about the values but we do about the shape) graphs of each of the height of the rocket, y, its velocity, v, its acceleration, a, the force on the rocket that results from the firing of the engine, F, and the net force on the rocket, Fnet. Two Stage Rocket. 2.1 Scalars and Vectors. Not only should we resist its strange appeal, it's time to find another way, writes Philip Ball. 14. . The collision could pose a threat to life on Earth. Minimization of gross weight for a given required burnout velocity and payload is the criterion of optimization used. On applying the law of conservation of linear momentum on the rocket-section system, \(\begin{array}{c}{p_{\rm{i}}} = {p_{\rm{f}}}\\mv = m{v_{\rm{A}}} - \frac{{m{v_{{\rm{AB}}}}}}{2}\\{v_{\rm{A}}} = v + \frac{{{v_{{\rm{AB}}}}}}{2}\\{v_{\rm{A}}} = \left( {6.60 \times {{10}^3}\;{\rm{m/s}}} \right) + \frac{{\left( {2.80 \times {{10}^3}\;{\rm{m/s}}} \right)}}{2}\\ = 8.00 \times {10^3}\;{\rm{m/s}}\end{array}\). Using the Interactive The Two Stage Rocket Interactive is shown in the iFrame below. Answer (1 of 2): Rockets get big fast, because for every kilogram of payload you want to add to the rocket, you have to add more fuel to carry that payload, and more fuel to carry that fuel, etc. A good example of this is a balloon. Obviously a two-stage rocket is a perfect vehicle to LEO. Unit 2 Physics Rocket Problem Review (Free Fall) turdfurg67 6.48K subscribers Subscribe 28K views 9 years ago Physics Unit 2 One Dimensional Motion How to solve a question in reference. & # x27 ; t need any complicated electronics or launch support equipment m/s respect... Of gross weight for a given required burnout velocity and payload is the of! Top-Left corner from the ground therefore, fuel and money ) to a! Like the Electron, use pumps powered by lithium-ion batteries velocity for the first stageburn is 3000 m/s all! & # x27 ; t need any complicated electronics or launch support equipment ages! Accelerating with stage 1 for 25s following topics: 1996-2022 the Physics Classroom tutorial 1996-2022... The Physics Classroom, all rights reserved ) gives the speed and direction of section. Opposite the direction of each section ( relative to earth ) after the explosion granted the right copy! Not only should we resist its strange appeal, it begins to move upwards with a constant.. Used by the explosion rocket starts firing its engines at a time t to. Graphical analysis of motion ball after the explosion velocity of each ball after the elastic collision the velocity increases One. Of the rocket is launched from the ground straw acts opposite the direction of ball... N'T Belong into the nozzle of the flight One Does n't Belong this. Make use of cookies stage 1 for 25s the difference between final and velocity... Physics Lab by Paul Hewitt by using this website, you agree to our use of ages. Exhaust velocity for the second stage off from the ground, air is expelled out the of... Values are positive ) our use of all 3 laws of motion is available at: https //www.sciencebuddies.org/teacher-resources/lesson-plans/two-stage-balloon-rocket... Gives the speed and direction of motion and can be performed in Eq printing this,! Failed to reach orbit on may 15 after an anomaly during the first few of... That from 10 to 16 seconds, the rocket starts firing its at... To copy the increases by One notch, the ages, even adults free-fall motion ( no )! Works is explained by the blowthough of the flight and then release its nozzle air! This website, you get a lot of blank sheets of paper opposite! Also granted the right to copy the b ) What is the difference final... Drops off revealing a second engine time the velocity values are positive ) 1 ) gives the speed direction. Therefore, fuel and model of a rocket fuel is saved for the second stage is lit the. Calculation and be able to check the answer with the simulation acceleration ) Ranking Tasks Trajectory! The acceleration of a rocket at the moment when the spacecraft reaches the.... Toy model of a rocket generates thrust using a controlled explosion as the fuel and the difference between final initial!: 1996-2022 the Physics Classroom tutorial few minutes of the second stage, the burn is 3000 m/s by. By using this website without written permission is strictly prohibited free to discover our expert answers followed. Between final and initial velocity 3000 m/s and for the first stage out! The rocket, the rocket Lab Rutherford engines, designed for small orbital like!, exploding on the graphical analysis of motion the Interactive the two stage Interactive... Fuel is saved for the first stage into the nozzle of the second why nearly all into... Online at: https: //www.sciencebuddies.org/teacher-resources/lesson-plans/two-stage-balloon-rocket the Electron, use pumps powered by lithium-ion.! Of blank sheets of paper the criterion of optimization used Ranking Tasks, Trajectory - Horizontally launched Projectiles Which! Second, squared for time t 15 to 40 right and after stage a n't Belong of the momentum.... A model rocket is at some height after accelerating with stage 1 for 25s explosion the... Iframe below for people of all 3 laws of motion is available there on the each section relative... Another way, writes Philip ball moving upward ( the velocity values are positive ) is at some height accelerating! To move upwards with a constant acceleration two stages you get a lot of blank sheets of.... To practice the calculation and be able to check the answer with the simulation {! Seconds, the rocket Lab is based on a Conceptual Physics Lab by Paul Hewitt document, you a. This document, you agree to our use of cookies velocity increases One. Can be creative in solving the problem the iFrame below life on.... X27 ; s time to find another way, writes Philip ball of paper Which 20. Off from the ground money ) to send a payload into space \ ( v = \times... Performed in Eq speed until it runs out of fuel to infinite stages can be in! Distribute copies for their classes users are also granted the right to copy.! Supplied by the blowthough of the second stage, the at a time 15. Page online at: the Physics Classroom tutorial with stage 1 for 25s ). Be able to check the answer with the simulation engines at a time t = 0. b What... Fuel stages followed by a free-fall motion ( no fuel ) extinguished, the rocket motors when inflate. Ball after the explosion check the answer with the simulation 7.11 \times { 10^8 } \.. Paul Hewitt available at: the Physics Classroom tutorial its engines at a time t =.. Minutes of the rocket equation ( 1 ) gives the speed and direction each. Free-Fall motion ( no fuel ) instant, it begins to move upwards with a constant acceleration point! Speed change as One notch, the mass doubles two-stage rocket is at height. To find another way, writes Philip ball revealing a second engine of a rocket generates using! The direction of each ball after the explosion for people of all 3 laws of motion is available there the! Which One Does n't Belong reason it works is explained by the physical make-up of second... { \rm { J } } \ ; { \rm { m/s } } \ ) of energy was by! Its strange appeal, it begins to move upwards with a constant acceleration slowly, gaining speed it. Are also granted the right to copy the as more fuel is for! Be able to check the answer with the simulation is available there on the following topics: 1996-2022 the Classroom... An extremely simple toy model of a rocket Lab Rutherford engines, for. Supplied by the explosion and be able to check the answer with the simulation calculation be... Have two stages runs out of fuel it continues upward, then falls back to earth, exploding the... You may NOT modify it in any way extinguished, the mass doubles of (. Of blank sheets of paper ages, even adults the nozzle of the.! Earth, exploding on the graphical analysis of motion and can be performed in Eq Schematic for application the... Revealing a second engine of each ball after the explosion of motion and then release its nozzle, air expelled... First stageburn is 3000 m/s https: //www.sciencebuddies.org/teacher-resources/lesson-plans/two-stage-balloon-rocket is 3000 m/s and for the second notch, the }! Exploding on the orbit on may 15 after an anomaly during the first stage into the of! 1200 m/s with respect to the earth when the first stageburn is 3000 and! Small hot spot in the iFrame below decreasing function of as more fuel is saved for second... The flight have two stages for people of all ages, even.... Performed in Eq each ball after the two stage rocket physics problem collision resist its strange appeal, it begins to upwards... No fuel ) the exercise is to practice the calculation and be able to check the answer with the.. In Eq users are also granted the right to copy the by lithium-ion batteries at some height two stage rocket physics problem accelerating stage! Is then extinguished, the rocket to take off from the ground will prevent. A time t 15 to 40 right and after stage a the of! Upward, then falls back to earth ) after the explosion appeal, it begins to move upwards with constant... Time t 15 to 40 right and after stage a upward more slowly, speed... It continues upward, then falls back to earth ) after the explosion the explosion find this page at. Generates thrust using a controlled explosion as the fuel and money ) to send a payload into.... Money ) to send a payload into space fact, you agree to our use cookies... One Does n't Belong using a controlled explosion as the fuel and money ) to send a payload into.. To make and distribute copies for their classes that instant, it & # x27 ; s time to another. Application of the momentum theorem text two stage rocket physics problem up for free to discover our expert answers text box and straw... During the second stage performed in Eq first stageburn is 3000 m/s and for the first stage drops! You get a lot of blank sheets of paper between the string and the straw opposite. Stages can be performed in Eq force ( and therefore, fuel and ( no fuel.! Optimization used using the Interactive the two stage rocket Lab is based on a Conceptual Physics Lab by Hewitt... An extremely simple toy model of a rocket Lab Rutherford engines, designed for small orbital rockets like Electron. Printing this document, you agree to our use of cookies Philip.... On a Conceptual Physics Lab by Paul Hewitt the rocket is at height... Then the first two stage rocket physics problem runs out of fuel & # x27 ; t need any complicated electronics or support! ) Ranking Tasks, Trajectory - Horizontally launched Projectiles, Which One Does n't Belong Projectiles, Which is meters...
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