Mechanical: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=199
en-us2017 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 19 Sep 2017 22:31:48 GMTTue, 19 Sep 2017 22:31:48 GMTNew applications in the Mechanical categoryhttp://www.mapleprimes.com/images/mapleapps.gifMechanical: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=199
Vector space with projections and forces
https://www.maplesoft.com/applications/view.aspx?SID=154294&ref=Feed
With this application you will learn the beginning of the study of the vectors. Graphing it in a vector space from the plane to the space. You can calculate its fundamental characteristics as triangle laws, projections and strength. App made entirely in Maple for engineering students so they can develop their exercises and save time. It is recommended to first use the native syntax then the embedded components. In Spanish.<img src="/view.aspx?si=154294/vectors.PNG" alt="Vector space with projections and forces" align="left"/>With this application you will learn the beginning of the study of the vectors. Graphing it in a vector space from the plane to the space. You can calculate its fundamental characteristics as triangle laws, projections and strength. App made entirely in Maple for engineering students so they can develop their exercises and save time. It is recommended to first use the native syntax then the embedded components. In Spanish.154294Mon, 11 Sep 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloDisplacement and distance traveled with vectors
https://www.maplesoft.com/applications/view.aspx?SID=154293&ref=Feed
In this app you can use from the creation of curve, birth of the position vector and finally applied to the displacement and the distance traveled. All this application revolves around the creation of a path and the path of a particle over this generated by vectors. You will only have to insert the vector components and the times to evaluate. Designed for engineering students guided through Maple. In Spanish.<img src="/view.aspx?si=154293/desplvp.png" alt="Displacement and distance traveled with vectors" align="left"/>In this app you can use from the creation of curve, birth of the position vector and finally applied to the displacement and the distance traveled. All this application revolves around the creation of a path and the path of a particle over this generated by vectors. You will only have to insert the vector components and the times to evaluate. Designed for engineering students guided through Maple. In Spanish.154293Mon, 28 Aug 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloPlot of Position Vector
https://www.maplesoft.com/applications/view.aspx?SID=154290&ref=Feed
This app performs the trace of a given path r(t), then locates the position vector in a specific time. It also graphs the velocity vector, acceleration, tangential and normal unit vectors, along with the binormal. The numerical value of velocity, acceleration and curvature are also observed for a better analysis of the movement of particles in a curvilinear trajectory. Developed for our engineering students. In Spanish.<img src="/view.aspx?si=154290/bnrvp.png" alt="Plot of Position Vector" align="left"/>This app performs the trace of a given path r(t), then locates the position vector in a specific time. It also graphs the velocity vector, acceleration, tangential and normal unit vectors, along with the binormal. The numerical value of velocity, acceleration and curvature are also observed for a better analysis of the movement of particles in a curvilinear trajectory. Developed for our engineering students. In Spanish.154290Thu, 10 Aug 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloMomentum with two variable force
https://www.maplesoft.com/applications/view.aspx?SID=154273&ref=Feed
This app shows the calculation of the final velocity of a body after it made contact with a variable force taking as reference the initial velocity, mass and the graph of the variation of F as a function of time. Made with native maple syntax (use of promt) and embedded components.
In Spanish.<img src="/view.aspx?si=154273/cmimp.png" alt="Momentum with two variable force" align="left"/>This app shows the calculation of the final velocity of a body after it made contact with a variable force taking as reference the initial velocity, mass and the graph of the variation of F as a function of time. Made with native maple syntax (use of promt) and embedded components.
In Spanish.154273Tue, 04 Jul 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloKinematics using syntax
https://www.maplesoft.com/applications/view.aspx?SID=154271&ref=Feed
In this file you will be able to observe and analyze how the exercises and problems of Kinematics and Dynamics are solved using the commands and operators through a very well-structured syntax. Allowing me to save time and use it in interpretation. I hope you can share and spread to break the traditional and unnecessary myths. Only for Engineering and Science. Share if you like.
In Spanish.<img src="/view.aspx?si=154271/kinematicssint.png" alt="Kinematics using syntax" align="left"/>In this file you will be able to observe and analyze how the exercises and problems of Kinematics and Dynamics are solved using the commands and operators through a very well-structured syntax. Allowing me to save time and use it in interpretation. I hope you can share and spread to break the traditional and unnecessary myths. Only for Engineering and Science. Share if you like.
In Spanish.154271Wed, 14 Jun 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloKinematics Curvilinear
https://www.maplesoft.com/applications/view.aspx?SID=154269&ref=Feed
With this application you can calculate the components of the acceleration. The scalar and vector components of the tangent and the normal. In addition to curvilinear kinetics in polar coordinates. It can be used in different engineers, especially mechanical, civil and more.
<BR><BR>
In Spanish.<img src="/view.aspx?si=154269/kc.png" alt="Kinematics Curvilinear" align="left"/>With this application you can calculate the components of the acceleration. The scalar and vector components of the tangent and the normal. In addition to curvilinear kinetics in polar coordinates. It can be used in different engineers, especially mechanical, civil and more.
<BR><BR>
In Spanish.154269Sat, 03 Jun 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloUniversal method of kinematic analysis of spatial and planar link mechanisms
https://www.maplesoft.com/applications/view.aspx?SID=154228&ref=Feed
The application of idea Draghilev method of solving systems of nonlinear equations for the kinematic analysis of link mechanisms with any number degrees of freedom.<img src="/view.aspx?si=154228/fig_2.jpg" alt="Universal method of kinematic analysis of spatial and planar link mechanisms" align="left"/>The application of idea Draghilev method of solving systems of nonlinear equations for the kinematic analysis of link mechanisms with any number degrees of freedom.154228Wed, 08 Mar 2017 05:00:00 ZAlexey IvanovAlexey IvanovStatically Indeterminate Structure
https://www.maplesoft.com/applications/view.aspx?SID=153940&ref=Feed
The application allows you to determine the constraint reactions, build diagrams of the normal forces N, shear forces Q and bending moments M for beams and frames with any number of sections and degree of static indefinability.
The application calculates the deformation (displacements) of the structure in millimeters and displays the displacements of nodes in the horizontal and vertical. It is also possible to calculate the displacement of any point of the structure.<img src="/view.aspx?si=153940/391e24e981ea8d11454375def604a185.gif" alt="Statically Indeterminate Structure" align="left"/>The application allows you to determine the constraint reactions, build diagrams of the normal forces N, shear forces Q and bending moments M for beams and frames with any number of sections and degree of static indefinability.
The application calculates the deformation (displacements) of the structure in millimeters and displays the displacements of nodes in the horizontal and vertical. It is also possible to calculate the displacement of any point of the structure.153940Wed, 09 Mar 2016 05:00:00 ZDr. Aleksey ShirkoDr. Aleksey ShirkoFuel Pod Design Optimization
https://www.maplesoft.com/applications/view.aspx?SID=153998&ref=Feed
A manufacturer has designed a fuel pod in NX. The fuel pod has a hemispherical and conical end, and a cylindrical midsection.
<BR><BR>
To minimize material costs, the manufacturer wants to minimize the surface area of the fuel pod while maintaining the existing volume.
<BR><BR>
This application:
<UL>
<LI>pulls the current dimensions of the fuel pod (radius of the hemispherical end, length of the cylindrical midsection, and height of the conical end) from the NX CAD model,
<LI>calculates the current volume of the fuel pod,
<LI>optimizes the dimensions to minimize the surface area while maintaining the existing volume,
<LI>and pushes the optimized dimensions back into the NX CAD model.
</UL><img src="/view.aspx?si=153998/fuel_pod.png" alt="Fuel Pod Design Optimization" align="left"/>A manufacturer has designed a fuel pod in NX. The fuel pod has a hemispherical and conical end, and a cylindrical midsection.
<BR><BR>
To minimize material costs, the manufacturer wants to minimize the surface area of the fuel pod while maintaining the existing volume.
<BR><BR>
This application:
<UL>
<LI>pulls the current dimensions of the fuel pod (radius of the hemispherical end, length of the cylindrical midsection, and height of the conical end) from the NX CAD model,
<LI>calculates the current volume of the fuel pod,
<LI>optimizes the dimensions to minimize the surface area while maintaining the existing volume,
<LI>and pushes the optimized dimensions back into the NX CAD model.
</UL>153998Wed, 02 Mar 2016 05:00:00 ZSamir KhanSamir KhanGas Orifice Flow Meter Calculator
https://www.maplesoft.com/applications/view.aspx?SID=153999&ref=Feed
This application calculates the flowrate through a large-diameter orifice using the approach outlined in ISO 5167 2:2003.
<BR><BR>
Orifice meters use the pressure loss across a constriction (that is, the orifice plate) in a pipe to determine the flowrate.
<BR><BR>
The formulas are valid for:
<UL>
<LI>pipes diameters between 50mm and 1000 mm,
<LI>and pressure ratios greater than 0.75.
</UL><img src="/view.aspx?si=153999/gas_orifice.png" alt="Gas Orifice Flow Meter Calculator" align="left"/>This application calculates the flowrate through a large-diameter orifice using the approach outlined in ISO 5167 2:2003.
<BR><BR>
Orifice meters use the pressure loss across a constriction (that is, the orifice plate) in a pipe to determine the flowrate.
<BR><BR>
The formulas are valid for:
<UL>
<LI>pipes diameters between 50mm and 1000 mm,
<LI>and pressure ratios greater than 0.75.
</UL>153999Wed, 02 Mar 2016 05:00:00 ZSamir KhanSamir KhanOptimizing the Design of a Helical Spring
https://www.maplesoft.com/applications/view.aspx?SID=154000&ref=Feed
The design optimization of helical springs is of considerable engineering interest, and demands strong solvers. While the number of constraints is small, the coil and wire diameters are raised to higher powers; this makes the optimization difficult for gradient-based solvers working in standard floating-point precision; a larger number of working digits is needed.
<BR><BR>
Maple lets you increase the number of digits used in calculations; hence numerically difficult problems, like this, can be solved.
<BR><BR>
This application minimizes the mass of a helical spring. The constraints include the minimum deflection, the minimum surge wave frequency, the maximum stress, and a loading condition.
<BR><BR>
The design variables are the diameter of the wire, the outside diameter of the spring, and the number of coils.<img src="/view.aspx?si=154000/helical_spring.png" alt="Optimizing the Design of a Helical Spring" align="left"/>The design optimization of helical springs is of considerable engineering interest, and demands strong solvers. While the number of constraints is small, the coil and wire diameters are raised to higher powers; this makes the optimization difficult for gradient-based solvers working in standard floating-point precision; a larger number of working digits is needed.
<BR><BR>
Maple lets you increase the number of digits used in calculations; hence numerically difficult problems, like this, can be solved.
<BR><BR>
This application minimizes the mass of a helical spring. The constraints include the minimum deflection, the minimum surge wave frequency, the maximum stress, and a loading condition.
<BR><BR>
The design variables are the diameter of the wire, the outside diameter of the spring, and the number of coils.154000Wed, 02 Mar 2016 05:00:00 ZSamir KhanSamir KhanTuned Mass Spring Damper
https://www.maplesoft.com/applications/view.aspx?SID=154001&ref=Feed
A mass-spring-damper is disturbed by a force that resonates at the natural frequency of the system.
<BR><BR>
This application calculates the optimum spring and damping constant of a parasitic tuned-mass damper that minimizes the vibration of the system.
<BR><BR>
The vibration of system with and without the tuned mass-spring-damper is viewed as a frequency response, time-domain simulation and power spectrum.<img src="/view.aspx?si=154001/mass_spring_damper.png" alt="Tuned Mass Spring Damper" align="left"/>A mass-spring-damper is disturbed by a force that resonates at the natural frequency of the system.
<BR><BR>
This application calculates the optimum spring and damping constant of a parasitic tuned-mass damper that minimizes the vibration of the system.
<BR><BR>
The vibration of system with and without the tuned mass-spring-damper is viewed as a frequency response, time-domain simulation and power spectrum.154001Wed, 02 Mar 2016 05:00:00 ZSamir KhanSamir KhanWelded Beam Design Optimization
https://www.maplesoft.com/applications/view.aspx?SID=154002&ref=Feed
The total cost of production is equal to the labor costs (a function of the weld dimensions) plus the cost of the weld and beam material.
<BR><BR>
The beam is to be optimized for minimum cost by varying the weld and member dimensions x1, x2, x3 and x4. The constraints include limits on the shear stress, bending stress, buckling load and end deflection. The variables x1 and x2 are usually integer multiples of 0.0625 inch, but for this application are assumed continuous.<img src="/view.aspx?si=154002/welded_beam.png" alt="Welded Beam Design Optimization" align="left"/>The total cost of production is equal to the labor costs (a function of the weld dimensions) plus the cost of the weld and beam material.
<BR><BR>
The beam is to be optimized for minimum cost by varying the weld and member dimensions x1, x2, x3 and x4. The constraints include limits on the shear stress, bending stress, buckling load and end deflection. The variables x1 and x2 are usually integer multiples of 0.0625 inch, but for this application are assumed continuous.154002Wed, 02 Mar 2016 05:00:00 ZSamir KhanSamir KhanVehicle Ride and Handling Analysis
https://www.maplesoft.com/applications/view.aspx?SID=153980&ref=Feed
This tool lets you experiment with the steer- and camber-by-roll coefficients of a 3-DOF vehicle model, and simulate the effect on the yaw gain curve and the understeer coefficient.<img src="/view.aspx?si=153980/Vehicle_Ride.png" alt="Vehicle Ride and Handling Analysis" align="left"/>This tool lets you experiment with the steer- and camber-by-roll coefficients of a 3-DOF vehicle model, and simulate the effect on the yaw gain curve and the understeer coefficient.153980Wed, 02 Mar 2016 05:00:00 ZSamir KhanSamir KhanEngine Noise Spectogram
https://www.maplesoft.com/applications/view.aspx?SID=153978&ref=Feed
This application plots the spectrogram and power spectrum of the sound of an engine changing gears.<img src="/view.aspx?si=153978/Engine_Noise_Spectrogram.png" alt="Engine Noise Spectogram" align="left"/>This application plots the spectrogram and power spectrum of the sound of an engine changing gears.153978Wed, 02 Mar 2016 05:00:00 ZSamir KhanSamir KhanGas Orifice Flow Meter Calculator
https://www.maplesoft.com/applications/view.aspx?SID=153739&ref=Feed
<p>This application calculates the flowrate through a large-diameter orifice using the approach outlined in ISO 5167 2:2003</p>
<p>Orifice meters use the pressure loss across a constriction (that is, the orifice plate) in a pipe to determine the flowrate. </p>
<p>The formulas are valid for</p>
<ul>
<li>pipes diameters between 50mm and 1000 mm, </li>
<li>and pressure ratios greater than 0.75.</li>
</ul>
<p>Reference: <span ><a href="http://en.wikipedia.org/wiki/Orifice_plate">http://en.wikipedia.org/wiki/Orifice_plate</a></span></p><img src="/view.aspx?si=153739/gasorifice.png" alt="Gas Orifice Flow Meter Calculator" align="left"/><p>This application calculates the flowrate through a large-diameter orifice using the approach outlined in ISO 5167 2:2003</p>
<p>Orifice meters use the pressure loss across a constriction (that is, the orifice plate) in a pipe to determine the flowrate. </p>
<p>The formulas are valid for</p>
<ul>
<li>pipes diameters between 50mm and 1000 mm, </li>
<li>and pressure ratios greater than 0.75.</li>
</ul>
<p>Reference: <span ><a href="http://en.wikipedia.org/wiki/Orifice_plate">http://en.wikipedia.org/wiki/Orifice_plate</a></span></p>153739Tue, 20 Jan 2015 05:00:00 ZSamir KhanSamir KhanThe Comet 67P/Churyumov-Gerasimenko, Rosetta & Philae
https://www.maplesoft.com/applications/view.aspx?SID=153706&ref=Feed
<p> Abstract<br /><br />The Rosetta space probe launched 10 years ago by the European Space Agency (ESA) arrived recently (November 12, 2014) at the site of the comet known as 67P/Churyumov-Gerasimenco after a trip of 4 billions miles from Earth. After circling the comet, Rosetta released its precious load : the lander Philae packed with 21 different scientific instruments for the study of the comet with the main purpose : the origin of our solar system and possibly the origin of life on our planet.<br /><br />Our plan is rather a modest one since all we want is to get , by calculations, specific data concerning the comet and its lander.<br />We shall take a simplified model and consider the comet as a perfect solid sphere to which we can apply Newton's laws.<br /><br />We want to find:<br /><br />I- the acceleration on the comet surface ,<br />II- its radius,<br />III- its density,<br />IV- the velocity of Philae just after the 1st bounce off the comet (it has bounced twice),<br />V- the time for Philae to reach altitude of 1000 m above the comet .<br /><br />We shall compare our findings with the already known data to see how close our simplified mathematical model findings are to the duck-shaped comet already known results.<br />It turned out that our calculations for a sphere shaped comet are very close to the already known data.<br /><br />Conclusion<br /><br />Even with a shape that defies the application of any mechanical laws we can always get very close to reality by adopting a simplified mathematical model in any preliminary study of a complicated problem.<br /><br /></p><img src="/applications/images/app_image_blank_lg.jpg" alt="The Comet 67P/Churyumov-Gerasimenko, Rosetta & Philae" align="left"/><p> Abstract<br /><br />The Rosetta space probe launched 10 years ago by the European Space Agency (ESA) arrived recently (November 12, 2014) at the site of the comet known as 67P/Churyumov-Gerasimenco after a trip of 4 billions miles from Earth. After circling the comet, Rosetta released its precious load : the lander Philae packed with 21 different scientific instruments for the study of the comet with the main purpose : the origin of our solar system and possibly the origin of life on our planet.<br /><br />Our plan is rather a modest one since all we want is to get , by calculations, specific data concerning the comet and its lander.<br />We shall take a simplified model and consider the comet as a perfect solid sphere to which we can apply Newton's laws.<br /><br />We want to find:<br /><br />I- the acceleration on the comet surface ,<br />II- its radius,<br />III- its density,<br />IV- the velocity of Philae just after the 1st bounce off the comet (it has bounced twice),<br />V- the time for Philae to reach altitude of 1000 m above the comet .<br /><br />We shall compare our findings with the already known data to see how close our simplified mathematical model findings are to the duck-shaped comet already known results.<br />It turned out that our calculations for a sphere shaped comet are very close to the already known data.<br /><br />Conclusion<br /><br />Even with a shape that defies the application of any mechanical laws we can always get very close to reality by adopting a simplified mathematical model in any preliminary study of a complicated problem.<br /><br /></p>153706Mon, 17 Nov 2014 05:00:00 ZDr. Ahmed BaroudyDr. Ahmed BaroudyOptimizing the Design of a Coil Spring
https://www.maplesoft.com/applications/view.aspx?SID=153608&ref=Feed
<p>The design optimization of helical springs is of considerable engineering interest, and demands strong solvers. While the number of constraints is small, the coil and wire diameters are raised to higher powers; this makes the optimization difficult for gradient-based solvers working in standard floating-point precision; a larger number of working digits is needed.</p>
<p>Maple lets you increase the number of digits used in calculations; hence numerically difficult problems, like this, can be solved.</p>
<p>This application minimizes the mass of a helical spring. The constraints include the minimum deflection, the minimum surge wave frequency and the maximum stress, and a loading condition.</p>
<ul>
<li>the minimum deflection, </li>
<li>the minimum surge wave frequency, </li>
<li>the maximum stress, </li>
<li>and a loading condition.</li>
</ul>
<p>The design variables are the</p>
<ul>
<li>diameter of the wire, </li>
<li>the outside diameter of the spring,</li>
<li>and the number of coils</li>
</ul>
<p> Reference: "Introduction to Optimum Design", Jasbir S. Arora, 3<sup>rd</sup> Edition 2012.</p><img src="/view.aspx?si=153608/695d991fff8fb4975d1e1dcd90bb771d.gif" alt="Optimizing the Design of a Coil Spring" align="left"/><p>The design optimization of helical springs is of considerable engineering interest, and demands strong solvers. While the number of constraints is small, the coil and wire diameters are raised to higher powers; this makes the optimization difficult for gradient-based solvers working in standard floating-point precision; a larger number of working digits is needed.</p>
<p>Maple lets you increase the number of digits used in calculations; hence numerically difficult problems, like this, can be solved.</p>
<p>This application minimizes the mass of a helical spring. The constraints include the minimum deflection, the minimum surge wave frequency and the maximum stress, and a loading condition.</p>
<ul>
<li>the minimum deflection, </li>
<li>the minimum surge wave frequency, </li>
<li>the maximum stress, </li>
<li>and a loading condition.</li>
</ul>
<p>The design variables are the</p>
<ul>
<li>diameter of the wire, </li>
<li>the outside diameter of the spring,</li>
<li>and the number of coils</li>
</ul>
<p> Reference: "Introduction to Optimum Design", Jasbir S. Arora, 3<sup>rd</sup> Edition 2012.</p>153608Tue, 17 Jun 2014 04:00:00 ZSamir KhanSamir KhanTuned Mass-Spring-Damper Design
https://www.maplesoft.com/applications/view.aspx?SID=153572&ref=Feed
<p>A mass-spring-damper is disturbed by a force that resonates at the natural frequency of the system.</p>
<p>This application calculates the optimum spring and damping constant of a parasitic tuned-mass damper that the minimizes the vibration of the system.</p>
<p>The vibration of system with and without the tuned mass-spring-damper is viewed as a frequency response, time-domain simulation and power spectrum.</p><img src="/view.aspx?si=153572/cdf00085048c6b59e75db56bb6c0210b.gif" alt="Tuned Mass-Spring-Damper Design" align="left"/><p>A mass-spring-damper is disturbed by a force that resonates at the natural frequency of the system.</p>
<p>This application calculates the optimum spring and damping constant of a parasitic tuned-mass damper that the minimizes the vibration of the system.</p>
<p>The vibration of system with and without the tuned mass-spring-damper is viewed as a frequency response, time-domain simulation and power spectrum.</p>153572Wed, 07 May 2014 04:00:00 ZSamir KhanSamir KhanDescartes & Mme La Marquise du Chatelet And The Elastic Collision of Two Bodies
https://www.maplesoft.com/applications/view.aspx?SID=153515&ref=Feed
<p><strong><em> ABSTRACT<br /> <br /> The Marquise</em></strong> <strong><em>du Chatelet in her book " Les Institutions Physiques" published in 1740, stated on page 36, that Descartes, when formulating his laws of motion in an elastic collision of two bodies B & C (B being more massive than C) <span >having the same speed v</span>, said that t<span >he smaller one C will reverse its course </span>while <span >the more massive body B will continue its course in the same direction as before</span> and <span >both will have again the same speed v.<br /> <br /> </span>Mme du Chatelet, basing her judgment on theoretical considerations using <span >the principle of continuity</span> , declared that Descartes was <span >wrong</span> in his statement. For Mme du Chatelet the larger mass B should reverse its course and move in the opposite direction. She mentioned nothing about both bodies B & C as <span >having the same velocity after collision as Descartes did</span>.<br /> <br /> At the time of Descartes, some 300 years ago, the concept of kinetic energy & momentum as we know today was not yet well defined, let alone considered in any physical problem.<br /> <br /> Actually both Descartes & Mme du Chatelet may have been right in some special cases but not in general as the discussion that follows will show.</em></strong></p><img src="/applications/images/app_image_blank_lg.jpg" alt="Descartes & Mme La Marquise du Chatelet And The Elastic Collision of Two Bodies" align="left"/><p><strong><em> ABSTRACT<br /> <br /> The Marquise</em></strong> <strong><em>du Chatelet in her book " Les Institutions Physiques" published in 1740, stated on page 36, that Descartes, when formulating his laws of motion in an elastic collision of two bodies B & C (B being more massive than C) <span >having the same speed v</span>, said that t<span >he smaller one C will reverse its course </span>while <span >the more massive body B will continue its course in the same direction as before</span> and <span >both will have again the same speed v.<br /> <br /> </span>Mme du Chatelet, basing her judgment on theoretical considerations using <span >the principle of continuity</span> , declared that Descartes was <span >wrong</span> in his statement. For Mme du Chatelet the larger mass B should reverse its course and move in the opposite direction. She mentioned nothing about both bodies B & C as <span >having the same velocity after collision as Descartes did</span>.<br /> <br /> At the time of Descartes, some 300 years ago, the concept of kinetic energy & momentum as we know today was not yet well defined, let alone considered in any physical problem.<br /> <br /> Actually both Descartes & Mme du Chatelet may have been right in some special cases but not in general as the discussion that follows will show.</em></strong></p>153515Fri, 07 Mar 2014 05:00:00 ZDr. Ahmed BaroudyDr. Ahmed Baroudy