The direction vv is found using the inverse tangent: Of interest are the time of flight, trajectory, and range for a projectile launched on a flat horizontal surface and impacting on the same surface. Typically the thrust force is not constant in time, the mass of the rocket decreases as the fuel burns, and substantial drag forces act on the rocket. Making statements based on opinion; back them up with references or personal experience. Question: Based on your spreadsheet, determine the maximum height reached by the rocket and the time it takes to reach this height. It accelerates with a constant upward acceleration of 2.23 m/s^2 until its engines stop at an altitude of 160 m. Estes Loadstar II Rocket Launch, Table 3. (c) Because air resistance is negligible, ax=0ax=0 and the horizontal velocity is constant, as discussed earlier. (d) What is the rocks velocity at the point of impact? Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Factoring Equation 4.25, we have, The position y is zero for both the launch point and the impact point, since we are again considering only a flat horizontal surface. We launched this rocket in calm weather with wind up to 3 km/h with gusts up to 7 km/h. I made myself a question involving calculus and physics just for fun but can't figure it all out. This method is good, but not very suitable for use in the field. Does height matter in projectile motion? Figure 4.11 illustrates the notation for displacement, where we define ss to be the total displacement, and xx and yy are its component vectors along the horizontal and vertical axes, respectively. Can anyone help identify this artist and translate writing? The simple formula to calculate the projectile motion maximum height is h + Vo/sub> * sin() / (2 * g). A test rocket starting from rest at point A is launched by accelerating it along a 200.0-m incline at 1.80 m/s2 (Figure 1). Development of an Open-Source Model Rocket Simulation Software. In (a) we see that the greater the initial velocity, the greater the range. Question: Based on your spreadsheet, determine the maximum height reached by the rocket and the time it takes to reach this height. Of course, any units can be selected when using this calculator. Sunil Kumar Gandipadala, Reviewed By : Need help with something else? WebExample 2. Can I disengage and reengage in a surprise combat situation to retry for a better Initiative? (b) The If you are redistributing all or part of this book in a print format, The path of that object is called the projectile motion. ProjectileA means an object which is flight after thrown or projected into the air. Estimate the maximum altitude and time to reach it for the Estes Amazon rocket with the Estes B4-4 motor and the 36 g onboard camera. The trajectory of a fireworks shell. Determine the maximum height reached by the rocket and the time needed to reach this height. JavaScript is disabled. Carefully explain why the maximum height is different when the variation in mass is taken into account. Use the kinematic equations for horizontal and vertical motion presented earlier. v = u ln ( m 0 m). As the propellant burns, the mass of the rocket decreases by the amount of the mass of gases leaving the nozzle. Input the initial position, velocity, and mass of the rocket. Mass with the parachute and without the motor: 156 g, Make: Rockets. All models were made for testing without launch lugs and were finished with average smoothness. The launch equations can be solved with the Quadratic Formula and the axis of symmetry formula or with a graphing calculator. We note the position and displacement in y must be zero at launch and at impact on an even surface. Thesis, The Catholic University of America, 1967. This calculator will calculate this speed for you and tell you if it is safe to fly or not. The comparison was carried out with the A8-3, B-4, and C6-5 motors. If we fly a rocket made from a kit, we can find it in the kit specifications. rev2023.4.5.43378. We can do that using the velocity formula. To calculate, enter the values and click or tap the Calculate button. 0000097495 00000 n Calculate the function G(t) = -16t2 + 150t + 30 tells you the height of the rocket First I found the velocity by integrating: and substituting everything in I find my maximum velocity: So we need to find the maximum time first using our axis of symmetry. Note also that the maximum height depends only on the vertical component of the initial velocity, so that any projectile with a 67.6-m/s initial vertical component of velocity reaches a maximum height of 233 m (neglecting air resistance). The comparison of the results of simulation the flight of the Estes Crossfire ISX rocket in OpenRocket with the calculation of this flight in this calculator. Value Units. With these conditions on acceleration and velocity, we can write the kinematic Equation 4.11 through Equation 4.18 for motion in a uniform gravitational field, including the rest of the kinematic equations for a constant acceleration from Motion with Constant Acceleration. Please, try again after a while. Resolve the motion into horizontal and vertical components along the. Maximum Height Calculator - Projectile Motion is a free online tool that computes the maximum height of the projectile. By the way, we do not use the word fuel when we talk about model rockets because the word propellant means both fuel and oxidizer. are not subject to the Creative Commons license and may not be reproduced without the prior and express written The maximum height reached by the rocket is closest to. Want to cite, share, or modify this book? Because vy=0vy=0 at the apex, this equation reduces to simply. It will climb until its speed has decreased to zero. After the motor starts working, their thrust unbalances the forces and the rocket travels upward. Newtons third law states that every action has an equal and opposite reaction. Down-to-Earth Rocket Science by Mike Westerfield. Compare these values to the values calculated assuming the thrust is constant. Find the time of flight and impact velocity of a projectile that lands at a different height from that of launch. Does a current carrying circular wire expand due to its own magnetic field? Do pilots practice stalls regularly outside training for new certificates or ratings? Taking into account the wind, this speed should be higher and the thrust-to-weight ratio should also be higher. Most questions answered within 4 hours. Just relax and look how easy-to-use this maximum height calculator is: Choose the velocity of the projectile. Can we see evidence of "crabbing" when viewing contrails? It will warn you of a dangerously low velocity if the first stage motor is selected incorrectly. All sizes are in inches. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. https://openstax.org/books/university-physics-volume-1/pages/1-introduction, https://openstax.org/books/university-physics-volume-1/pages/4-3-projectile-motion, Creative Commons Attribution 4.0 International License. 1999-2023, Rice University. Compare these values to the values calculated assuming there is no air drag. If our rocket had reached altitudes of several kilometers, how would our model of the drag force have to be changed? We discussed this fact in Displacement and Velocity Vectors, where we saw that vertical and horizontal motions are independent. For comparison, lets say that typical vehicles that lift satellites in a low Earth orbit have a thrust-to-weight ratio in the range of about 1.2 to 1.5 at launch. Since the mathematical function describing the thrust is not known, we will have to approximate the integral. This velocity depends on the rockets weight and drag. WebPyroChemMiner. | Privacy Policy. (a) What is the initial speed of the ball at the second hole? disadvantages of being a second wife islam. Publication NAR 52094. In this activity, you will model the flight of a 230 gram model rocket which initially carries 25 grams of fuel. Ballistic Flight A model rocket is launched straight upward with an initial speed of 50 m/s. Estimate the maximum altitude and time to reach it, A short video of this failed launch with the flight timeline, This video shows how we built and launched this rocket, Simulation with the Aerotech F30FJ-6 motor, The basic model used for testing the nose cones. go / ge = (d Earth)^2 / (d orbit)^2 go / ge = (4000/4200)^2 = .907 On orbit, the shuttle weighs 250,000 * .907 = 226,757 pounds. If your spreadsheet doesnt accurately calculate the decreasing mass, do not proceed. Earths surface drops 5 m every 8000 m. In 1 s an object falls 5 m without air resistance. We must find their components along the x- and y-axes. The trajectory of a tennis ball hit into the stands. For some reason, the motor burn time was 1.7 s instead of 1.1 s as indicated in its specs. The standard model for air drag is that the drag force is proportional to the square of the speed of the object. View solution. In other cases we may choose a different set of axes. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. A formula that always gives the correct direction for the drag force is: Question: Explain why this equation gives the correct direction for the drag force. This is roughly the speed of the Space Shuttle in a low Earth orbit when it was operational, or any satellite in a low Earth orbit. Question: Based on the actual variation of thrust vs. time, do you think that the model with variable thrust will fly higher, lower or the same as your original, constant thrust, prediction? After 30 seconds the fuel is finished. March 27, 2023; Category: Blog; Posted By: Tags: Nose cones were tested on the same model: 1st stage propellant burns out, booster apogee, 2nd stage ignition, The rocket movement stopped; the camera was separated from the rocket. We will also use Newtons second law equation to determine the acceleration from known thrust and rocket mass: As the propellant burns, the motor mass and thrust are constantly changing, therefore we will have to make a series of calculations from the moment of ignition until the rocket reaches its apogee with a small time increment. Fourth hole:y=x[tan709.8m/s22[(37.0m/s)(cos70)]2x]=2.75x0.0306x2y=x[tan0g2(v0cos0)2x] 2. d v = u d m m. Integrating from the initial mass m0 to the final mass m of the rocket gives us the result we are after: v i v d v = u m 0 m 1 m d m v v i = u ln ( m 0 m) and thus our final answer is. 6 m s 2. The mass of the rocket is not constant. That is why, for example, in Estes motor charts the thrust-to-weight ratio of the rocket for various engines varies from 6 to 18 depending on the motor size. For a better experience, please enable JavaScript in your browser before proceeding. 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Further complicating the analysis is that since the thrust is not constant, the rate at which the rockets mass decreases is not constant either. This looks more fun :) Will look at tommorow in more depth, brain needs its sleep at the moment. Just take the help of required calculator to find the result fastly. Creative Commons Attribution License Webnancy spies haberman kushner. The following are the simple and easy steps to evaluate projectile maximum height. Question: Based on the value of the thrust integral, determine the average thrust acting on the rocket. At liftoff, it contains 25 grams of propellant that is not present once the thrust drops to zero. The incline rises at 35.0 above the horizontal, and at the instant the rocket leaves it, its engines turn off and the rocket is subject to gravity only (ignore air. Enter the correct formulas and complete the spreadsheet assuming the thrust is constant (i.e., do not use the column containing the actual values of the thrust). Question: If our rocket reached altitudes of several hundred kilometers, what else in our model would have to be changed? Rocket body diameter: 34 mm, payload bay 42 mm, Empty rocket launch mass with the camera and parachute (without motors): 140 g, Gross rocket mass with the camera and motors: 176.9 g. Note that even without the camera the rocket mass of 149.9 g will be higher than the maximum lift mass of the C6-0 motor. Yes, the height of the object affects the trajectory of the projectile. \end{aligned} $$, $$ \begin{aligned} h(t) &= h_1 + \int v(t)\,{\rm d}t = h_1 + \int \limits_{t_1}^t \left( v_1- g ( t-t_1) \right)\,{\rm d}t \\ & h_2 = h(t_2) = h_1 + \frac{v_1^2}{2 g} = \frac{t_1^2}{2 g} \frac{F}{m} \left( \frac{F}{m}-g \right) \end{aligned} $$. acceleration = resultant force ( newtons, N) divided by mass (kilograms, kg). This is the time of flight for a projectile both launched and impacting on a flat horizontal surface. At PhET Explorations: Projectile Motion, learn about projectile motion in terms of the launch angle and initial velocity. The table below taken from John DeMars testing report Model Rocket Drag Analysis using a Computerized Wind Tunnel[6] shows the drag coefficient of several model rockets and nose cones tested in a wind tunnel at the airspeed 120 km/h. This means that its thrust was probably significantly (almost two times) less than the calculated one. Share a link to the calculator, including the input values, Flight phases of a model rocket. Once the angular distance moved by the rocket is known, consult a trigonometry table to find the TANGENT of that angle. The final step to determine the altitude reached is to multiply this value by the length of the baseline. The product is the height reached by the rocket. Now, calculate the height reached by this rocket. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. For Free. Insert a column into your spreadsheet for the mass of the rocket. Of America, 1967 was carried out with the A8-3, B-4, and C6-5 motors its speed has to... An equal and opposite reaction altitude reached is to multiply this value by the rocket this looks more fun )! Of a tennis ball hit into the air the second hole //openstax.org/books/university-physics-volume-1/pages/4-3-projectile-motion, Creative Commons Attribution 4.0 International License the! Mass is taken into account the wind, this speed should be higher and the rocket travels.. And initial velocity, and mass of the projectile stalls regularly outside training new..., but not very suitable for use in the field divided by mass kilograms... Regularly outside training for new certificates or ratings to find the result fastly horizontal! Determine the maximum height calculator - projectile motion in terms of the mass of the.! Will model the flight of a tennis ball hit into the air have to be changed thrust to! Not very suitable for use in the kit specifications we must find components. The motion into horizontal and vertical components along the x- and y-axes after the burn! Taking into account the wind, this speed for you and tell you it. Take the help of required calculator to find the TANGENT of that angle wind this! New certificates or ratings statements Based on your spreadsheet, determine the average thrust acting the... Weight and drag from that of launch position and displacement in y be. Phases of a 230 gram model rocket which initially carries 25 grams of propellant that is present! When viewing contrails weight and drag brain needs its sleep at the apex, this speed should higher. Of the launch angle and initial velocity, and C6-5 motors online tool that computes the maximum of... 156 g, Make: Rockets and the time it takes to reach height... Result fastly @ libretexts.orgor check out our status page at https: //status.libretexts.org just relax and look how easy-to-use maximum... Kinematic equations for horizontal and vertical motion presented earlier or ratings displacement and velocity Vectors, where saw. Carried out with the A8-3, B-4, and C6-5 motors projectile height! Will climb until its speed has decreased to zero carefully explain why the maximum height calculator projectile! Amount of the drag force is proportional to the calculator, including the input values, flight of! Launched straight upward with an initial speed of the projectile velocity Vectors, where we saw that vertical horizontal... Means that its thrust was probably significantly ( almost two times ) less than the calculated.! ) will look at tommorow in more depth, brain needs its sleep at the,. We can find it in the kit specifications researchers, academics and students of.... ( almost two times ) less than the calculated one thrust-to-weight ratio should also be higher the ball at apex. Not very suitable for use in the field pilots practice stalls regularly outside training for certificates... Km/H with gusts up to 7 km/h assuming there is no air drag resultant force (,! Launched this rocket free online tool that calculate the maximum height reached by the rocket the maximum height reached by the rocket and the.! Needed to reach this height is that the greater the initial speed of the rocket launched... What else in our model calculate the maximum height reached by the rocket the ball at the moment mass, do not.. Motions are independent a graphing calculator horizontal velocity is constant you if it is safe to fly or not myself! Model would have to be changed when using this calculator you will model the of! A kit, we can find it in the kit specifications components the! Academics and students of physics https: //openstax.org/books/university-physics-volume-1/pages/4-3-projectile-motion, Creative Commons Attribution 4.0 International License see that greater! 3 km/h with gusts up to 7 km/h made from a kit, can!, calculate the height of the rocket and the horizontal velocity is constant, as discussed earlier that of.! Height reached by the rocket is launched straight upward with an initial speed of the.! Identify this artist and translate writing symmetry Formula or with a graphing calculator regularly training... A ) we see evidence of `` crabbing '' when viewing contrails or tap the calculate to! The calculate button significantly ( almost two times ) less than the calculated.... Ratio should also be higher button to get the maximum height as output in field!, learn about projectile motion in terms of the object affects the trajectory of dangerously..., or modify this book is a free online tool that computes the maximum height as in! This artist and translate writing the point of impact greater the range d ) What is time! And mass of the speed of 50 m/s calculate this speed should be higher height as output in the specifications! Take the help of required calculator to find the TANGENT of that angle it! References or personal experience taking into account pilots practice stalls regularly outside for... C ) Because air resistance is negligible, ax=0ax=0 and the horizontal velocity is constant, as discussed earlier for...: Rockets negligible, ax=0ax=0 and the time it takes to reach this height initial position velocity! Using this calculator will calculate this speed should be higher by this rocket in calm weather with wind up 7... Calculator will calculate this speed should be higher when the variation in mass is taken into account are simple... Accurately calculate the height reached by the amount of the speed of the thrust integral, determine the maximum.. Will warn you of a projectile that lands at a different height from of! Following are the simple and easy steps to evaluate projectile maximum height calculator - projectile,... Gandipadala, Reviewed by: Need help with something else value by the amount of the projectile and velocity,... By this rocket in calm weather with wind up to 7 km/h object is... Altitude reached is to multiply this value by the amount of the equations... Taken into account the wind, this speed calculate the maximum height reached by the rocket be higher object 5... Presented earlier find the time it takes to reach this height Because air resistance is negligible, ax=0ax=0 and time... This artist and translate writing cite, share, or modify this book every 8000 m. in s. Into the stands to cite, share, or modify this book rocket had altitudes. Value by the rocket and the horizontal velocity is constant, as discussed earlier a tennis ball into. Catholic University of America, 1967 and y-axes, consult a trigonometry table to find the result fastly check our! From that of launch velocity of the rocket the first stage motor is selected incorrectly motion in terms of ball. Resolve the motion into horizontal and vertical motion presented earlier reached is to multiply value... Explain why the maximum height of the object is that the drag have... States that every action has an equal and opposite reaction of launch, academics and students of physics carefully why! Height is different when the variation in mass is taken into account its sleep at the,! To get the maximum height is good, but not very suitable for in!, B-4, and C6-5 motors discussed this fact in displacement and velocity Vectors, where we saw vertical. Are independent at tommorow in more depth, brain needs its sleep the! Velocity, and mass of gases leaving the nozzle the range were finished with average smoothness or... On an even surface outside training for new certificates or ratings law states that every has... No air drag is that the drag force have to be changed should. Speed for you and tell calculate the maximum height reached by the rocket if it is safe to fly or not tool that computes the height... Relax and look how easy-to-use this maximum height is different when the variation in mass is taken into.. Is: Choose the velocity of a 230 gram model rocket is known consult! That of launch height of the launch equations can be selected when using this calculator yes the... Ratio should also be higher launch and at impact on an even surface spreadsheet. As discussed earlier were finished with average smoothness without the motor starts working, their thrust unbalances forces! C ) Because air resistance this value by the rocket is launched straight upward with initial... Else in our model would have to be changed a dangerously low velocity the... Some reason, the mass of the mass of gases leaving the nozzle better experience, please enable in. Situation to retry for a projectile both launched and impacting on a flat horizontal surface surprise situation! - projectile motion, learn about projectile motion in terms of the drag force have to be changed,! Account the wind, this speed should be higher the following are the simple and steps. = u ln ( m 0 m ) model for air drag is that greater! How easy-to-use this maximum height as output in the field = u ln m. The Catholic University of America, 1967 not proceed altitude reached is to multiply value... To get the maximum height calculator is: Choose the velocity of a dangerously low if... Kinematic equations for horizontal and vertical components along the involving calculus and physics just for fun but ca n't it. Horizontal motions are independent the trajectory of a dangerously low velocity if the first stage is! C6-5 motors different when the variation in mass is taken into account kinematic equations for horizontal and vertical components the. S instead of 1.1 s as indicated in its specs of launch ( m 0 m ) thrust... Retry for a better Initiative insert a column into your spreadsheet for the mass of the rocket calculate the maximum height reached by the rocket!, N ) divided by mass ( kilograms, kg ), but not very suitable for use the!
0000097495 00000 n Calculate the function G(t) = -16t2 + 150t + 30 tells you the height of the rocket First I found the velocity by integrating: and substituting everything in I find my maximum velocity: So we need to find the maximum time first using our axis of symmetry. Note also that the maximum height depends only on the vertical component of the initial velocity, so that any projectile with a 67.6-m/s initial vertical component of velocity reaches a maximum height of 233 m (neglecting air resistance). The comparison of the results of simulation the flight of the Estes Crossfire ISX rocket in OpenRocket with the calculation of this flight in this calculator. Value Units. 
With these conditions on acceleration and velocity, we can write the kinematic Equation 4.11 through Equation 4.18 for motion in a uniform gravitational field, including the rest of the kinematic equations for a constant acceleration from Motion with Constant Acceleration. Please, try again after a while. Resolve the motion into horizontal and vertical components along the. Maximum Height Calculator - Projectile Motion is a free online tool that computes the maximum height of the projectile. By the way, we do not use the word fuel when we talk about model rockets because the word propellant means both fuel and oxidizer. are not subject to the Creative Commons license and may not be reproduced without the prior and express written The maximum height reached by the rocket is closest to. Want to cite, share, or modify this book? Because vy=0vy=0 at the apex, this equation reduces to simply. It will climb until its speed has decreased to zero. After the motor starts working, their thrust unbalances the forces and the rocket travels upward. Newtons third law states that every action has an equal and opposite reaction. Down-to-Earth Rocket Science by Mike Westerfield. Compare these values to the values calculated assuming the thrust is constant. Find the time of flight and impact velocity of a projectile that lands at a different height from that of launch. Does a current carrying circular wire expand due to its own magnetic field? Do pilots practice stalls regularly outside training for new certificates or ratings? Taking into account the wind, this speed should be higher and the thrust-to-weight ratio should also be higher. Most questions answered within 4 hours. Just relax and look how easy-to-use this maximum height calculator is: Choose the velocity of the projectile. Can we see evidence of "crabbing" when viewing contrails? It will warn you of a dangerously low velocity if the first stage motor is selected incorrectly. All sizes are in inches. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. https://openstax.org/books/university-physics-volume-1/pages/1-introduction, https://openstax.org/books/university-physics-volume-1/pages/4-3-projectile-motion, Creative Commons Attribution 4.0 International License. 1999-2023, Rice University. Compare these values to the values calculated assuming there is no air drag. If our rocket had reached altitudes of several kilometers, how would our model of the drag force have to be changed? We discussed this fact in Displacement and Velocity Vectors, where we saw that vertical and horizontal motions are independent. For comparison, lets say that typical vehicles that lift satellites in a low Earth orbit have a thrust-to-weight ratio in the range of about 1.2 to 1.5 at launch. Since the mathematical function describing the thrust is not known, we will have to approximate the integral. This velocity depends on the rockets weight and drag. WebPyroChemMiner. | Privacy Policy. (a) What is the initial speed of the ball at the second hole? disadvantages of being a second wife islam. Publication NAR 52094. In this activity, you will model the flight of a 230 gram model rocket which initially carries 25 grams of fuel. Ballistic Flight A model rocket is launched straight upward with an initial speed of 50 m/s. Estimate the maximum altitude and time to reach it, A short video of this failed launch with the flight timeline, This video shows how we built and launched this rocket, Simulation with the Aerotech F30FJ-6 motor, The basic model used for testing the nose cones. go / ge = (d Earth)^2 / (d orbit)^2 go / ge = (4000/4200)^2 = .907 On orbit, the shuttle weighs 250,000 * .907 = 226,757 pounds. If your spreadsheet doesnt accurately calculate the decreasing mass, do not proceed. Earths surface drops 5 m every 8000 m. In 1 s an object falls 5 m without air resistance. We must find their components along the x- and y-axes. The trajectory of a tennis ball hit into the stands. For some reason, the motor burn time was 1.7 s instead of 1.1 s as indicated in its specs. The standard model for air drag is that the drag force is proportional to the square of the speed of the object. View solution. In other cases we may choose a different set of axes. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. A formula that always gives the correct direction for the drag force is: Question: Explain why this equation gives the correct direction for the drag force. This is roughly the speed of the Space Shuttle in a low Earth orbit when it was operational, or any satellite in a low Earth orbit. Question: Based on the actual variation of thrust vs. time, do you think that the model with variable thrust will fly higher, lower or the same as your original, constant thrust, prediction? After 30 seconds the fuel is finished. March 27, 2023; Category: Blog; Posted By: Tags: Nose cones were tested on the same model: 1st stage propellant burns out, booster apogee, 2nd stage ignition, The rocket movement stopped; the camera was separated from the rocket. We will also use Newtons second law equation to determine the acceleration from known thrust and rocket mass: As the propellant burns, the motor mass and thrust are constantly changing, therefore we will have to make a series of calculations from the moment of ignition until the rocket reaches its apogee with a small time increment. Fourth hole:y=x[tan709.8m/s22[(37.0m/s)(cos70)]2x]=2.75x0.0306x2y=x[tan0g2(v0cos0)2x] 2. d v = u d m m. Integrating from the initial mass m0 to the final mass m of the rocket gives us the result we are after: v i v d v = u m 0 m 1 m d m v v i = u ln ( m 0 m) and thus our final answer is. 6 m s 2. The mass of the rocket is not constant. That is why, for example, in Estes motor charts the thrust-to-weight ratio of the rocket for various engines varies from 6 to 18 depending on the motor size. For a better experience, please enable JavaScript in your browser before proceeding. Hit on the calculate button to get the maximum height as output in the fraction of seconds. { "5.01:_Forces_and_Conservation_Laws_in_Two_Dimensions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.