Why We Need Calculus for Mechatronics Studies

[Femme_physics]

Mechatronics course..someone asked me "why do we need to study calculus".how to reply

So we're mechatronics 1st year, we're about to start our second semester just having finished statics WITHOUT calculus. I presume this semester we're starting on Calculus. My classmate grudgingly asked me why do we even need to study calculus. Now, I know that Calculus is the math of change, but I'm not sure how to give him a proper reply as we haven't practiced the use of calculus and how it applies to machines or mechatronics. Can you guys give me a reply I can have for him?

 

[fss]

Because if you don't, your future classes will be much harder if not impossible.

 

[AlephZero]

The most obvious application of calculus in mechanics is what happens when things change with time. In other words, when things move. The general term for that study is dynamics, compared with statics. If you want to study anything that moves with varying speed, or which changes direction as it moves, you can't get very far without using calculus. In fact in Newton's law of motion which says "force equals rate of change of momentum", the words "rate of change" are a good indication that calculus is involved. (You may have met that law as "force = mass x acceleration", which is the special case where the mass of the object remains constant. Even then, acceleration is the rate of change of velocity over time)

Calculus is also useful for many problems in statics, when quantites vary not with time but with the position in the object. For example, a rod or a beam where the cross section tapers along its length, or the pressure load on an object in a fluid which depends on the depth, such as the force on the face of a dam, or the side of a ship.

 

[Studiot]

Mechatronics and calculus huh?

Well

Control Theory
Statistics for manufacturing and quality control
Hydraulics/pneumatics
Cam /tappet/tool theory
Your own self esteem when talking to engineers in other disciplines

go well

 

[Femme_physics]

The most obvious application of calculus in mechanics is what happens when things change with time. In other words, when things move. The general term for that study is dynamics, compared with statics. If you want to study anything that moves with varying speed, or which changes direction as it moves, you can't get very far without using calculus. In fact in Newton's law of motion which says "force equals rate of change of momentum", the words "rate of change" are a good indication that calculus is involved. (You may have met that law as "force = mass x acceleration", which is the special case where the mass of the object remains constant. Even then, acceleration is the rate of change of velocity over time)

Calculus is also useful for many problems in statics, when quantites vary not with time but with the position in the object. For example, a rod or a beam where the cross section tapers along its length, or the pressure load on an object in a fluid which depends on the depth, such as the force on the face of a dam, or the side of a ship.

Perfect answer :) thanks...I'll make sure he gets this. The idea in giving him a proper reply after all is not to make him feel lousy (I could've come up with fss's reply), but to make him understand the functional use of it. But thanks to the others.

 

[Femme_physics]

(You may have met that law as "force = mass x acceleration", which is the special case where the mass of the object remains constant. Even then, acceleration is the rate of change of velocity over time)

When an object mass in constant it's a special case?!? Isn't that the other way around?.. .I'm confused.

Calculus is also useful for many problems in statics, when quantites vary not with time but with the position in the object.

But objects don't move in statics

 

[batman394]

So..
I took ME 454/Mechatronics in college a few years ago.

When we were programming a rotating arm robot to land at a desired coordinate... everyone had trouble with it. Because the C++/microcontroller limited us to using linear equations only. And you were trying to compensate for friction, which is non-linear on the rotating arm, for where it would land.

Using calculus, you can dead on hit that spot, since you can calculate and adjust in real time.


That's a good example of why calculus is necessary.

Calculus allows us to get definite answers, not linear approximations.

And if the above fails, because I said so, and you have to pass my class.

 

[batman394]

When an object mass in constant it's a special case?!? Isn't that the other way around?.. .I'm confused.



But objects don't move in statics

No, think of airplanes. The mass is constantly changing as the engines burn fuel.

 

[Femme_physics]

Ah... I see. Thanks batman :)

 

[batman394]

Another good example, asteroid masses falling to Earth. As they go through the atmosphere, they burn up and get smaller.

And you never have to thank me.

 

[AlephZero]

When an object mass in constant it's a special case?!? Isn't that the other way around?.. .I'm confused.

You are confusing the differencce between the general case (the mass varies) and a special case (the mass is constant), with the most common case, which depends what area of engineering you are working in. For example if you are dealing with rocket launching, the mass of the rocket always changes, as it burns fuel.

But objects don't move in statics

Flexible objects do "move", or at least they change shape, under static loads. (Look carefully at your car tires and see if they are really "round" when they are supporting the weight of the car). In a first non-calculus course you may have only considered situations where you assume all the objects are rigid.

For example a cantilever beam bends into a curved shape when it is loaded. The amount of curvature at any point depends on the bending moment at that point (and also the shape of the cross section of the beam, the materal it is made from, etc). If there is a single force applied at the end of the beam, the bending moment changes along the length. The curvature is also related (by geometry) to the second derivative of the beam's displacement. So calculus comes into this sort of statics problem in several different ways.

 

[Studiot]

So calculus comes into this sort of statics problem in several different ways.

Very good point I missed from my list.

 

[Femme_physics]

You are confusing the differencce between the general case (the mass varies) and a special case (the mass is constant), with the most common case, which depends what area of engineering you are working in. For example if you are dealing with rocket launching, the mass of the rocket always changes, as it burns fuel. Flexible objects do "move", or at least they change shape, under static loads. (Look carefully at your car tires and see if they are really "round" when they are supporting the weight of the car). In a first non-calculus course you may have only considered situations where you assume all the objects are rigid.

For example a cantilever beam bends into a curved shape when it is loaded. The amount of curvature at any point depends on the bending moment at that point (and also the shape of the cross section of the beam, the materal it is made from, etc). If there is a single force applied at the end of the beam, the bending moment changes along the length. The curvature is also related (by geometry) to the second derivative of the beam's displacement. So calculus comes into this sort of statics problem in several different ways.

Oooh...great insight :) You're right, we've always assumed bodies are rigid. This is going to get more interesting, though :D

 

[TheAnswer]

hi I am new !

just curious wut U do you go to? I was trying to get into mechatronics but my school don't offer it so now I am just double major in ME and EE.and yea I would say Calculus is the algebra of continuous change, EG when you have a constant acceleration your speed is continuously changing right? what can you say about the change in displacement without knowing the idea of integral? as the matter of fact the kinematic equations are all derivation of the differential form of F=ma, which is F = dp/dt. you going to need it as you move on to higher level physics.

I took statics last quarter and now I am in dynamics, and I wonder if you guys cover moment of inertia or centroid in statics? I think that required calculus too didn't it?wish you luck in mechatronics!

 

[Femme_physics]

Thanks, TheAnswer! I was about to look at center of gravity as we'll be studying it this semester. Yes, it's covered in statics and I'm quite sure we'll learn it before dynamics.

 

[TheAnswer]

Thanks, TheAnswer! I was about to look at center of gravity as we'll be studying it this semester. Yes, it's covered in statics and I'm quite sure we'll learn it before dynamics.

no problem! so what's your math level? if you are learning cal next semester and this is your first year I think you are on track, there are only a couple left after cal and it's not that hard! don't be intimidated! study well my friend for your future!

 

[Femme_physics]

:) I am, I am giving my all and hold this course, physics, and math as the most important things in the world to me (sorry mom, dad, bf...).

My math level is good when it comes to algebraic manipulations, basics of logs, and trigonometry. We haven't touched matrices, complex numbers, or anything that we don't really need for statics and to solve for 3 unknowns..really basic stuff.

The problem that the math teacher told me that we're only studying the "basics" of calculus, so I don't really know how far we'd go. But, loving every little bit of math and physics I get, (and chemistry!) and devouring it!