How Can Understanding Basic Physics Concepts Improve Everyday Problem Solving?

[AshUchiha]

Okay as suggested by one of the 'Staff:Mentor' , advised me to have a clear sense of "mass", "weight", "speed", "velocity", "force", and "acceleration" and the mathematical relationships between them. I know all of them, but it's not accurate/exact.

P.S.: Ofcourse, I can google search it, but there's a saying that "Your friends can teach you better than anyone else", and yes try simplifying your language meanwhile not letting down its scientific meaning

 

[rootone]

That is why math is the preferred language for science.
It makes the same sense whatever may be your cultural background.

 

[ellipsis]

Qualitative fundamentals of Newtonian mechanics

Mass is an intrinsic property all objects have - it is simply how much matter is encapsulated by the object you're talking about. It is a single number, by standard in units of kg, or kilograms. In this system, mass cannot be created nor destroyed.

Weight is different from mass. Indeed, an object on Earth weighs differently than that same object on the Moon does, even though it's still comprised of the same amount of matter. The weight of an object is simply the force exerted by gravity. Because it is a force, it has units of N, or Newtons.

Speed is the rate at which an object moves. It is a positive number, with zero being no movement, with increasingly higher numbers corresponding to increasingly faster speeds. It is in terms of the m/s unit, or "meters per second". This is easier to understand if you've studied calculus, which is the study of rates of change. Briefly, the meter is the standard unit of length, and the second is the standard unit of time

Velocity is similar to speed, but it is a vector, rather than a positive number, which is called a scalar. Vectors are one or more real numbers which specify a direction, as well as an 'amount', or magnitude. Vectors can either be coordinates, or speeds with an angle, depending on your model, and depending on how many spatial dimensions are involved. In terms of calculus, velocity is the first derivative of position.

Force is what pushes and pulls objects. Every force is exerted by some object. Furthermore, if object A exerts a force F on object B, then object B exerts that same force, but in the opposite direction, on A. Because of this fact, forces are described as being "equal, but opposite". This means that while the Earth exerts a gravitational force on you, pulling you down, you are exerting an equal gravitational force on the Earth, pulling it upward. As well as gravitational force, there is also tension, friction, and a variety of other different types.

Acceleration is the speed at which speed changes. When you accelerate a vehicle, you increase its speed (or velocity). When you decelerate, you decrease its speed. In this way, if you are speeding down a highway, but your speed is constant, then your acceleration is zero. This is in units of m/s^2, which is read as "meters per second squared". In terms of calculus, acceleration is the second derivative of position, and the first derivative of velocity.

Mathematical relationship of the above physical properties

The note above regarding the gravitational force you exert on the Earth seems very counter-intuitive. The fact is, the acceleration a force causes is dependent on the mass of the object, in the following way, where ##F_T## is total force exerted on an object, ##m## is mass, and ##a## is acceleration.

$$
F_T = ma
$$

You can use simple algebra to find that ## a = \frac{F}{m} ##. The gravitational acceleration you cause on the Earth is negligibly tiny, because the mass of the Earth is large, because of the inverse relationship I just described.

The gravitational force itself, when you are on the surface of Earth, obeys:

$$
F_g = mg
$$

where g is in this case approximately -9.81. Based on these two relationships, you can derive the fact that two objects with different mass on the surface of Earth accelerate downwards at the same rate: namely, ##g##.

More generally, the gravitational force between two objects follows the inverse-square law, where ##G## is the universal gravitational constant, ##M## is the mass of the other object, ##m## is the mass of the current object, and ##d## is the distance between those two objects.

$$
F_g = G\frac{Mm}{d^2}
$$

There's a bunch of other relationships, especially when it comes to the results of calculus, and the four "kinematic equations". Here's a few:

Speed is the absolute value of velocity:
$$
s = |v|
$$

When acceleration is constant, the final velocity is equal to the initial velocity plus the time elapsed multiplied by the acceleration.
$$
v_f = v_i+at
$$

What (I think) Newtonian mechanics is about

At the center of it, the kinematics side of Newtonian mechanics is just a mathematical tool to model and analyze certain physical situations under certain idealized rules. That is to say, the rules of Newtonian mechanics change based on what you're attempting to model.

I wrote this more for me, not for you, I'm happy to say. Best way to learn something is to teach it. Good luck.

 

[AshUchiha]

Can you add "distance" in your definition's too ??

P.S. And yes, more for yourself.

 

[PWiz]

Can you add "distance" in your definition's too ??

Distance is the actual path taken by an object. It is different from displacement, which is the shortest path between two points.

Acceleration is the speed at which speed changes.

This is slightly incorrect because of your terminological usage - acceleration is the rate at which velocity changes, and is a vector quantity itself.

I think it's very important to stress on the importance of the Galilean principle of relativity here. Newtonian mechanics has its roots over there (Newton's laws hold in all inertial frames of reference - in other words, non-accelerating points of view). It would then help to read about Newton's three laws of motion (the first goes hand in hand with the Galilean principle, and the second one defines what is "force" - more on that later), and understand what it all means qualitatively. I trust that you're well aware of the 7 fundamental quantities? ellipsis has explained a good deal on one of them, and you would benefit from reading more about conservation laws and the other 6 fundamental quantities on the Internet to clear up some of your confusion (the post would become too long if I explain them here).

Newtonian mechanics can be classified into kinematics and dynamics. Kinematics is the study of motion - angular velocity, acceleration, etc. Dynamics is the study of forces and energy. Both of them are linked together beautifully using Maths, or more specifically, calculus. All the non-fundamental quantities can be derived from the fundamental ones using calculus. A small bit of info on mass (just adding on ellipsis' comprehensive explanation): there are two kinds of mass. One is called inertial mass which is given by ##\frac{F}{a}## (Newton's second law), and the second is gravitational mass, responsible for producing gravitational effects. Coincidentally, the two of them are equal to each other, and mass can be left alone until one tackles Einstein's theory of relativity.

Another point - ##F=ma## is a simplified version of Newton' 2nd law. To understand it, you need to understand momentum. Again, one can write books on each one of these concepts, so I'll leave the figuring up to you. All that can be said is that force is the rate at which momentum changes.

It is also worthwhile to mention that most of the quantities described by ellipsis have linear and rotational "versions." Here's a link which explains it well - http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html

Finally, you should understand that the vector quantities that you mentioned in the OP (force, velocity, weight and acceleration) can be expressed geometrically in Euclidean space, and all these concepts carry over very smoothly over there as well.

The problem here is that the question is too broad - most introductory Physics textbooks spend at least 100-150 pages trying to explain these concepts. You can always ask more directed questions as separate threads on the forums, and I'm sure many will be there to help you out ;)

 

[ellipsis]

This is slightly incorrect because of your terminological usage - acceleration is the rate at which velocity changes, and is a vector quantity itself.

I know that, pedant.

Einstein's theory of relativity.

Has nothing to do with Newtonian mechanics. Normal relativity (the fact that velocity and position are invariant) does, sure. But they're different.

You also mention "seven fundamental quantities", which was actually new to me. I looked it up, and found that some say they're not so fundamental after all, considering the Planck units.

Finally, what are the odds that we're all Naruto fans? I'm currently reading https://www.fanfiction.net/s/4203131/1/Reload

 

[PWiz]

Has nothing to do with Newtonian mechanics.

Which is why I didn't explore it in my post. Btw, the question isn't specifically about Newtonian mechanics, so I only thought it would be fair to provide some up-to-date references...

You also mention "seven fundamental quantities", which was actually new to me.

That's weird. My HS Physics textbook has them listed on the first page (Length, rest mass, time, amount of matter, electric current, luminosity and thermodynamic temperature)! Planck units are simply units of measurement which are based on fundamental constants. I can't see what they have to do with fundamental quantities

I know that, pedant.

Hahaha, physics does that to you, it really does

 

[ellipsis]

Which is why I didn't explore it in my post. Btw, the question isn't specifically about Newtonian mechanics, so I only thought it would be fair to provide some up-to-date references...

That's weird. My HS Physics textbook has them listed on the first page (Length, rest mass, time, amount of matter, electric current, luminosity and thermodynamic temperature)! Planck units are simply units of measurement which are based on fundamental constants. I can't see what they have to do with fundamental quantities

Hahaha, physics does that to you, it really does

Bah, you didn't reply to the most interesting part of my response.

 

[AshUchiha]

Distance is the actual path taken by an object.

What exactly do you mean by "actual path" . And you used the word "taken" , seems a bit...uneasy for me to digest {That's an idiom}. Would it be right to rearrange your definition to "The total path traveled by an object"

 

[PWiz]

What exactly do you mean by "actual path" . And you used the word "taken" , seems a bit...uneasy for me to digest {That's an idiom}. Would it be right to rearrange your definition to "The total path traveled by an object"

It means the same thing, since "taken" and "traveled" are synonymous here. What's important is that the reference to causality should not be lost in the definition.

 

[AshUchiha]

But "traveled" would again be wrong I guess, because if path traveled comes under distance, then what does distance traveled means? Is it just an adjective?

 

[PWiz]

Everyday language is framed very loosely. Talking in specific terms, distance is the numerical quantity which signifies the "length" of a path. A path is the trace of the actual motion of an object. They are two different things. When you travel along a path, you cover distance. There really isn't much more to this.

 

[AshUchiha]

Ellipsis, loved the way you explained. But I wanted definitions, of course your explanation is awesome. But you know I wanted definition in a simple way meanwhile not dishonoring it's scientific meaning. But still learned a lot from you sir. Anyway, I've always been confused that, every action has equal and opposite reaction.

Let's say take an example of badminton.

QUESTION 1

Ball comes and hits the bat.
Mass of the ball=m
Mass of the bat=M
Force exerted by ball= ƒ
Force exerted by the bat=F

Every action as equal and opposite reaction (---1---) . P.S. {here action word is used instead of the word "force" , its more than what meets the eye}.

ƒ=F right? (Since, ---1--- is correct).
But if that's so, the ball should stay there only. How does it move when we hit it?

QUESTION 2

Also, Our Earth and us. Earth applies force on us , so we are applying equal and opposite force to it. If that's so, then why are we attracted towards it? Why don't we just fly in the air because we apply equal force on it always.

QUESTION 3

If we are on Earth, we will experience other planet's gravitation too right? So if we are on space, aren't we supposed to be attracted towards sun and fall for it?

QUESTION 4

{Okay this question is bit out of the topic} , Our Earth moves very fast, but why don't we experience such a fast motion??

 

[rootone]

1. Some of the kinetic energy of the bat is transferred as kinetic energy of the ball.
2. Gravity is exerting a pull on you and the ground is pushing back with equal force, so you stay where you are.
3. Gravity of distant objects is tiny compared to that of the Earth which you are standing on.
4. Because you are not in motion relative to the Earth, only in relation to some external reference frame, and you can't be existing in a reference frame external to to yourself.

 

[PWiz]

A1 and A2: Action and reaction are equal and opposite forces, but they act on different objects and so do not cancel each other out.
A3: Of course you do. You're even experiencing the incredibly tiny amount of gravitational force pulling you towards a black hole thousands of light years away, but the effect at such distances is so small that it is negligible. The attractive force between two objects is not only dependent on their masses, but on the separation between them as well, so the net force on you will clearly be affected by the dominant factor in your local vicinity. If you are in space, you will move wherever the net force takes you (the small distance between you and some nearby planet may outweigh the difference in mass of the Sun and the planet and pull you to its surface and not towards the Sun).

Constant velocity in itself can't be "felt" - only acceleration/force can. The rotational motion of the Earth generates something known as the Coriolis force (constant angular velocity does not mean that the linear velocity is constant). The Earth does not have an angular velocity high enough to produce a noticeable "dragging" force on us. It's interesting to note that if for some reason the Earth was made to spin faster, you would "weigh" less, and a you would be weightless at one particular angular velocity. Anything more than this and you'd be flung away from the Earth.

 

[Cruz Martinez]

Qualitative fundamentals of Newtonian mechanics

Mass is an intrinsic property all objects have - it is simply how much matter is encapsulated by the object you're talking about. It is a single number, by standard in units of kg, or kilograms. In this system, mass cannot be created nor destroyed.

This definition of mass is too simple. It is true that mass is an intrinsic property of an object. But to define it appropriately you need to look at the law of inertia.
The law of inertia is the basis for a correct and quantitatively unambiguous definition of the concept of mass.

 

[ellipsis]

First of all, these are all wonderful questions. And, I guarantee, we all asked these questions too.

QUESTION 1

Ball comes and hits the bat.
Mass of the ball=m
Mass of the bat=M
Force exerted by ball= ƒ
Force exerted by the bat=F

Every action as equal and opposite reaction (---1---) . P.S. {here action word is used instead of the word "force" , its more than what meets the eye}.

ƒ=F right? (Since, ---1--- is correct).
But if that's so, the ball should stay there only. How does it move when we hit it?

What actually moves the ball is acceleration, not force. Let's say the bat's mass is 5kg, and the ball's mass is .25kg, and the force induced from the bat to the ball is 25N.
$$
F_{bat->ball} = 25N
$$
$$
F_{ball->bat} = -25N
$$

By Newton's second law, ##F=ma## :
$$
F_{ball} = m_{ball}a_{ball}
$$
$$
F_{bat} = m_{bat}a_{bat}
$$

We solve this for the acceleration of the ball and bat:
$$
a_{ball} = \frac{F_{ball}}{m_{ball}}
$$
$$
a_{bat} = \frac{F_{bat}}{m_{bat}}
$$

We know the forces involved, and we know the masses, so we can find the acceleration:
$$
a_{ball} = \frac{25}{.25} = 100 \frac{m}{s^2}\
$$
$$
a_{bat} = \frac{-25}{5} = -5 \frac{m}{s^2}
$$

So, you see, the motion of each object is different, even though the force is the same, because they have different masses.

QUESTION 2

Also, Our Earth and us. Earth applies force on us , so we are applying equal and opposite force to it. If that's so, then why are we attracted towards it? Why don't we just fly in the air because we apply equal force on it always.

This is the same question as question 1.

My mass is 59kg. To find the force of gravity between me and the Earth, we use the equation I used above:
$$
F_g = -mg
$$
$$
F_g = -(59)(9.81) = -578.79 N
$$

Now, because of Newton's third law, we know that the force I exert on the Earth is 578.79N... Note the missing negative sign: The force is equal, but opposite.

Now, using Newton's second law, we can calculate the gravitational acceleration me and the Earth end up getting.

$$
a_{me} = \frac{-578.79}{59} = -9.81 \frac{m}{s^2}\
$$
$$
a_{Earth} = \frac{578.79}{5972198600000000000000000} = .00000000000000000000009691 \frac{m}{s^2}
$$
That's small.

QUESTION 3

If we are on Earth, we will experience other planet's gravitation too right? So if we are on space, aren't we supposed to be attracted towards sun and fall for it?

The International Space Station is 407120 meters above the surface of the Earth. The Earth's radius is 6367444 meters. The distance the ISS has from the center of the Earth is the sum of these two values, which is 6774564 meters.

The mass of the Earth is of course 5972198600000000000000000 kg.

The universal gravitational constant, G, is .0000000000667.

We can use these numbers with Newton's law of universal gravitation, which I defined earlier:
$$
F_g = G\frac{M_{ISS}M_{Earth}}{d^2}
$$
Since we only care about the ISS's acceleration of gravity, we can factor out the mass of the ISS itself.
$$
a_g = -G\frac{M_{Earth}}{d^2} = -(.0000000000667)\frac{5972198600000000000000000}{6774564^2} = -8.68 \frac{m}{s^2}
$$

That's not anywhere close to zero. In fact, it seems the astronauts are still quite affected by Earth's gravity. It seems paradoxical. For an intuitive understanding, I invite you to play Kerbal Space Program. =^)

QUESTION 4

{Okay this question is bit out of the topic} , Our Earth moves very fast, but why don't we experience such a fast motion??

You're also going very fast on an airplane, or on a highway, and you don't experience that fast motion, do you? It's Newton's first law: Whatever is in motion, stays in motion. Inertia.

We can only "experience" acceleration, in the way you describe. Indeed, when you speed up in a car, or lift off in an airplane, you're pushed to the back of you seat.

And of course, we do "experience" the gravitational and rotational acceleration of the Earth in the form of the tides and the precession of the Foucault pendulum.

 

[Cruz Martinez]

(the fact that velocity and position are invariant)

Velocity and position are not invariant quantities in Einsteinian relativity nor in Galilean relativity.