B Understanding Weight and Inertia: A Comparison of Mars and Earth

[rudransh verma]

https://www.feynmanlectures.caltech.edu/I_09.html
“Weight and inertia are proportional, and on the earth’s surface are often taken to be numerically equal, which causes a certain confusion to the student. On Mars, weights would be different but the amount of force needed to overcome inertia would be the same.”

What does it mean?
The statement seems confusing!

If we try to throw a ball up on Mars then it would require less force than on Earth because the resisting force of gravity is less. Weight is less!

 

[Doc Al]

Weight is a measure of the gravitational force on an object. Sure, a ball on Mars would weigh less than on Earth.

But does that change the amount of force needed to produce a given acceleration? What does Newton's 2nd law say about that?

 

[rudransh verma]

Weight is a measure of the gravitational force on an object. Sure, a ball on Mars would weigh less than on Earth.

But does that change the amount of force needed to produce a given acceleration? What does Newton's 2nd law say about that?

If a ball is at rest on Earth and one on mars, there will be less force needed to overcome inertia of rest on mars.

 

[phinds]

If a ball is at rest on Earth and one on mars, there will be less force needed to overcome inertia of rest.

How on Earth (or Mars) do you come to such a nonsensical conclusion? Have you really THOUGHT about this. Do you have ANY sense, physically, of what inertia IS?

 

[Doc Al]

If a ball is at rest on Earth and one on mars, there will be less force needed to overcome inertia of rest on mars.

Oh really? How about calculating the force needed to give a 1 kg ball an acceleration of 1 m/s^2. Do it for both Mars and for Earth.

 

[berkeman]

Oh really? How about calculating the force needed to give a 1 kg ball an acceleration of 1 m/s^2. Do it for both Mars and for Earth.

Specifically a horizontal acceleration...

 

[Doc Al]

Specifically a horizontal acceleration...

That would perhaps eliminate some confusion, but the net force required will be the same regardless of direction.

 

[rudransh verma]

Specifically a horizontal acceleration...

No not horizontal but vertical. Horizontal will be same.

That would perhaps eliminate some confusion, but the net force required will be the same regardless of direction.

The force required to lift a 1kg mass on Earth is 9.8N but on Mars it’s only 3.7 N. So weight as well as the force required to break the state of inertia will vary from planet to planet specially for vertical lifts.

 

[Doc Al]

So weight as well as the force required to break the state of inertia will vary from planet to planet specially for vertical lifts.

The net force required to accelerate a mass will be the same on any planet. Of course, the amount of force you have to provide to produce a given vertical acceleration will vary.

The (net) force required to accelerate a mass ("overcome inertia") is the same everywhere. That's Feynman's point.

 

[rudransh verma]

The (net) force required to accelerate a mass ("overcome inertia") is the same everywhere. That's Feynman's point.

Ok! But it’s quite fascinating that a person throwing a ball up can throw it even further on planets with less gravity like on mars. Astronauts can jump even higher on moon.
But what if he races against time. Will he beat his record on moon? Will he run faster or slower than on earth?

 

[phinds]

No not horizontal but vertical. Horizontal will be same.

Continuing to spout the same nonsense will not make it true. You would be better off listening to what people are saying to you rather than ignoring it.

 

[rudransh verma]

planet to planet specially for vertical lifts.

I will correct myself here.

 

[Vanadium 50]

This thread is turning into another dumpster fire.

@rudransh verma , it's very clear you are ttempting more advanced physics than you are ready for. You will make more progress by backing up and getting a solid foundation.

 

[ergospherical]

But what if he races against time. Will he beat his record on moon? Will he run faster or slower than on earth?

This would be quite an interesting question! I don't think there's any simple answer, because there's so many factors at play. The most obvious one is the drag-reduction because of the lack of atmosphere. The athlete also doesn't need to work as hard to overcome his weight (vertically), but since he/she spends longer in the air it's probably also harder to put a lot of power down (just look at the stride rate of professional sprinters!).

 

[rudransh verma]

The most obvious one is the drag-reduction because of the lack of atmosphere.

Let’s take atmosphere out of the question. Then I think if a person jumps on moon with some force making an angle of 45 with horizontal then he will surely go higher on moon but the horizontal distance covered will be same. In other words he cannot run faster on moon but surely he can run longer. What do you say?

 

[ergospherical]

Say, the astronaut can leave the ground at a speed $v$ in a direction of his choosing. (In other words, he can exert an impulse of fixed magnitude on the ground). How do the parameters of the resulting parabolic trajectory change as you vary the gravitational acceleration $g$?

 

[russ_watters]

Let’s take atmosphere out of the question. Then I think if a person jumps on moon with some force making an angle of 45 with horizontal then he will surely go higher on moon but the horizontal distance covered will be same. In other words he cannot run faster on moon but surely he can run longer. What do you say?

That's still wrong/a mess. How can he go higher if he doesn't also go further? And you should go reread the posts about net force.

 

[phinds]

@rudransh verma it is very annoying that you rarely seem to answer questions that people ask you, you just ignore us and keep posting nonsense. You would be better off trying to figure out why we ask what we ask rather than ignoring our questions.

 

[Arjan82]

Let’s take atmosphere out of the question. Then I think if a person jumps on moon with some force making an angle of 45 with horizontal then he will surely go higher on moon but the horizontal distance covered will be same. In other words he cannot run faster on moon but surely he can run longer. What do you say?

So, I hope it's clear by now that the gravitational force on Mars is lower than on earth. Gravitational force, or mass times the acceleration of gravity, is what we call weight. Weight is a force.

Mass on the other hand is a measure for the amount of 'stuff' (let's keep it classical to not further confuse things). So, that's the difference between mass and weight. Mass is what resists acceleration. A more massive thing needs a higher force for the same acceleration. This is the same on Mars, the Moon, Earth or Jupiter for that matter.

Let's say you have a car and it can do 0 to 60 in 4 seconds in a vacuum on Earth (just to exclude aerodynamic drag, which just further confuses things). How would it perform on Mars? Exactly the same! (assuming enough grip of course). And on Jupiter? Again: the same!*)

The reason why you can jump higher on the moon is actually more complicated than you might think:
First, getting off the ground: the gravitational force (weight) keeping you on the surface is lower, this lower force is what you have to work against with your legs when jumping. But a lower force means you have higher 'excess force' on your body, since the sum of all forces on your body, so its weight and the force generated by your legs, is what is determining your acceleration. The higher net force means a higher acceleration and therefore a higher velocity the moment you leave the ground.
Then, returning to the ground: when you are airborne there is only one force acting on you: the gravitational force, or your weight. This is lower on the moon, but your mass is the same, therefore your acceleration back to the surface is lower on the moon, giving you more hang-time.*) you can throw in all kinds of other secondary order effects like the resistance of the tires due to its weight and all that, but let's keep it simple, we are talking about the fundamentals.

 

[phinds]

Then I think if a person jumps on moon with some force making an angle of 45 with horizontal then he will surely go higher on moon but the horizontal distance covered will be same.

Once again you do not seem to have actually thought about the physical meaning of what you say. This seems to be a persistent problem that you have. For some reason you can't seem to connect concepts to the physical world. You should give this some thought.

 

[rudransh verma]

it is very annoying that you rarely seem to answer questions that people ask you, you just ignore us and keep posting nonsense.

For some reason you can't seem to connect concepts to the physical world.

I am not smart as you guys. That was foolish. Instead of thinking in velocity I was thinking in terms of force but the force stops acting as soon as we lift of the ground.

 

[rudransh verma]

How do the parameters of the resulting parabolic trajectory change as you vary the gravitational acceleration g?

You are right. I should be watching for the parabola. That will be bigger as we lower the value of g. But do we actually make parabolas when running? Is running actually repeated jumping?

 

[russ_watters]

I am not smart as you guys.

It's not your intelligence, it's your approach/attitude (this has been pointed out to you before...). These concepts are successfully taught to schoolchildren.

But do we actually make parabolas when running? Is running actually repeated jumping?

When we're in the air, yes.

 

[phinds]

I am not smart as you guys.

That may or may not be but it has nothing to do with anything. As @russ_watters just said, your intelligence is not the problem. The problems, as I see it, are that
(1) you don't seem to make any attempt to connect concepts to the physical world even to the application of trivial every-day actions.
(2) you ignore good advice when it is given
(3) you don't seem to believe that we know what we are talking about
(4) you don't answer direct questions that are put to you.

 

[ergospherical]

I can see why some advisors are frustrated, but making mistakes (and crucially learning from them) is one of, if not the most, important part of the learning process. I think there's some good evidence of that in this thread, e.g. #10, #15 and #22. And our job is to be that helping hand guiding you along the path. That said, I do agree you should try really hard to focus your enquiries.

Back to the point...

You are right. I should be watching for the parabola. That will be bigger as we lower the value of g. But do we actually make parabolas when running? Is running actually repeated jumping?

... you tell me! What does the velocity profile of the runner look like? Since gravity is vertical, their horizontal speed is unchanged whilst airborne in the absence of drag. The horizontal acceleration is confined to those times where there's a foot on the ground.

 

[rudransh verma]

Since gravity is vertical, their horizontal speed is unchanged whilst airborne in the absence of drag. The horizontal acceleration is confined to those times where there's a foot on the ground.

It’s horizontal velocity will be same. It looks like there will be no difference. But there is a drag on earth. So I think the person will move faster on moon.

 

[russ_watters]

It’s horizontal velocity will be same. It looks like there will be no difference. But there is a drag on earth. So I think the person will move faster on moon.

You're talking in half-completed thoughts. What is it that determines how fast someone can run? Think/talk it through.

 

[rudransh verma]

What is it that determines how fast someone can run?

Friction and your strength!

 

[russ_watters]

Friction and your strength!

Those are forces. What are they doing? What does your strength actually do? Does less friction (between what and what?) mean you can run faster? If so, why? Put more thought/effort into this.

 

[rudransh verma]

What are they doing? What does your strength actually do? Does less friction (between what and what?) mean you can run faster?

They are giving you forward momentum. My strength helps me to push the ground even harder. Without friction we can’t run.

 

[russ_watters]

They are giving you forward momentum.

Momentum? Why would that matter to how fast you can run? (hint: it really doesn't).

My strength helps me to push the ground even harder.

What direction are you pushing on the ground?

Without friction we can’t run.

You mean friction between your feet and the ground? Does that mean you run slower if there is less friction?

What does Newton's 2nd Law tell us about the net force required to run at constant speed?

Speak clearly and finish thoughts completely.

 

[russ_watters]

You're really not engaging your brain here to think this through, you're just doing one-line thoughts.

Newon's 2nd (and 1st, really) law tells us that running at constant speed doesn't require net force. So, what are our legs primarily doing when we run? They're bouncing us up and down. That's what we use most of our strength for. Lower weight means less strength required to bounce up and down, which means people would be able to run faster/for longer.

So, what effect does lower friction have? Since net force is only required for acceleration, lower friction means slower acceleration.

 

[jbriggs444]

So, what are our legs primarily doing when we run? They're bouncing us up and down.

It might be helpful to think about how a kangaroo moves.

Edit: Imagine my surprise when trying to look up some experimental detail to find:

Kuehnegger maintains the “kangaroo hop” was best. “By performing a kangaroo-type leaping and jumping, you require the least amount of energy, and consume the least amount of oxygen.”

 

[rudransh verma]

Then, returning to the ground: when you are airborne there is only one force acting on you: the gravitational force, or your weight. This is lower on the moon, but your mass is the same, therefore your acceleration back to the surface is lower on the moon, giving you more hang-time.

Lower weight means less strength required to bounce up and down, which means people would be able to run faster

Don’t you think in a single jump when the person is going up he is moving faster than on Earth because there is no drag and less gravity but when coming down he slows down because of low gravity. So net result is that the person is not actually gaining any speed over on earth.

 

[sysprog]

Then, returning to the ground: when you are airborne there is only one force acting on you: the gravitational force, or your weight. This is lower on the moon, but your mass is the same, therefore your acceleration back to the surface is lower on the moon, giving you more hang-time.

Your movement still has its horizontal component.

Don’t you think in a single jump when the person is going up he is moving faster than on Earth because there is no drag and less gravity but when coming down he slows down because of low gravity. So net result is that the person is not actually gaining any speed over on earth.

The vertical component of a leap off the ground must overcome both inertia and gravity; the horizontal component must overcome inertia alone.

 

[Arjan82]

Don’t you think in a single jump when the person is going up he is moving faster than on Earth because there is no drag and less gravity but when coming down he slows down because of low gravity. So net result is that the person is not actually gaining any speed over on earth.

You need to disconnect the horizontal movement from the vertical movement. As I said your takeoff velocity vertically can be faster*), but that doesn't say anything about how fast you go horizontally.

This is what I meant when mentioning the car going from 0 to 60 in 4 secs (in vacuum, to not be concerned with drag). That is horizontal movement, and thus, as @sysprog also pointed out, only susceptible to inertia. The car will always go 0 to 60 in 4 secs on any planet(oid), earth, the moon, mars, jupiter, anywhere (given enough drag, equal engine performance etc).

*) Also your hang-time is higher, so the time between jumps is longer and you get to a higher point above the ground.

 

[phinds]

Don’t you think in a single jump when the person is going up he is moving faster than on Earth because there is no drag and less gravity but when coming down he slows down because of low gravity. So net result is that the person is not actually gaining any speed over on earth.

Personally, I have no interest at all in guessing, the way you do. If I actually wanted to figure out what was going on and what the answer definitely is, that's exactly what I would do ... FIGURE IT OUT.

The equation of motion is a parabola and gravity is involved. Assume a given mass for the runner/jumper, and assume a 45 degree takeoff with a specified force and then do the calculation given the different gravity on each planet.

You will, as you already understand, find that the jump is higher and longer under the lower gravity. As to whether it is faster or slower, I would leave that to the calculations and actually GET the answer rather than GUESS at the answer.

 

[Vanadium 50]

@rudransh verma you are not thinking about what other people are saying to you. The median time for you to respond is 14 minutes, with several being under 4. This is not enough time for you to consider what others are saying and trying to teach you.

Some people will find this rude, arrogant, snotty and/or disrespectful, and certainly not consistent with PF values. i won't speak to that and instead point out that it's ineffective. If you want to learn, you need to be engaged.

 

[rudransh verma]

The equation of motion is a parabola and gravity is involved. Assume a given mass for the runner/jumper, and assume a 45 degree takeoff with a specified force and then do the calculation given the different gravity on each planet.

O yes! You are right. I didn't realize i could do that sitting on my chair. By the way what will be the equation of parabola. The parabolas I know doesn't start at (0,0). Parabola should be in the first quadrant. If I know it I will be able to figure it out. $t^{2}=-x+1$ or $t^{2}=-x$ doesn't seem right.

 

[phinds]

O yes! You are right. I didn't realize i could do that sitting on my chair. By the way what will be the equation of parabola. The parabolas I know doesn't start at (0,0). Parabola should be in the first quadrant. If I know it I will be able to figure it out. $t^{2}=-x+1$ or $t^{2}=-x$ doesn't seem right.

You seem to have an extraordinarily poor understanding of math. I do not mean this as an insult, I mean it as a suggestion that perhaps you would be well-served to study a lot of basic math before you worry about physics problems since you can't do one without the other.

Parabolas don't "start" ANYWHERE. They have a particular shape but their equations are determined by, among other things, where they lie on an XY coordinate system and that can be anywhere and in any direction.

Take any specific parabolic shape and place it absolutely anywhere on an XY coordinate grid and oriented in any direction and you can write an equation that describes it.

The fact that you do not automatically realize that is the basis for my belief that you would be better off studying math than physics, until you understand math better.

 

[phinds]

@rudransh verma I see you have responded to my suggestion that you study math by tagging it indicating that you are skeptical. This is a perfect example of what I meant when I told you that you don't seem to believe that we here on PF know what we are talking about.

Continuing to rebuff our suggestions and/or treat them as invalid is not going to work well for you.

 

[rudransh verma]

Continuing to rebuff our suggestions and/or treat them as invalid is not going to work well for you.

I didn’t know the meaning of skeptical. I thought it means “I should think about it.”
As you said I am already going to study about parabolas and come back later.

 

[phinds]

I didn’t know the meaning of skeptical. I thought it means “I should think about it.”
As you said I am already going to study about parabolas and come back later.

Ah. Well, as I hope you have found out by now, it means "I think you are wrong".

You should be more careful that you know what you are saying.

 

[phinds]

Also, @rudransh verma parabolas are a very small part of math. You can't understand physics without all of basic math, so I continue to suggest that you make a systematic study of ALL of math up through at least calculus. Then you can decide if you want to go on to differential equations and beyond.

 

[Vanadium 50]

I didn’t know the meaning of skeptical.

And yet you neither apologized for nor removed the reaction,
I an skeptical of your explanation.

 

[sysprog]

O yes! You are right. I didn't realize i could do that sitting on my chair. By the way what will be the equation of parabola. The parabolas I know doesn't start at (0,0). Parabola should be in the first quadrant. If I know it I will be able to figure it out. $t^{2}=-x+1$ or $t^{2}=-x$ doesn't seem right.

I suggest that you should look up projectile motion (under gravity) $-$ here's an introductory-level example in a SciAm article: https://www.scientificamerican.com/article/football-projectile-motion

From that article:

The only choice he has to make to maximize distance, then, is the angle at which he kicks the ball. You can see from the equation above that the distance traveled by the ball will be greatest when sin(2θ) is greatest. The sine function reaches its largest output value, 1, with an input angle of 90 degrees, so we can see that for the longest-range punts 2θ = 90 degrees and, therefore, θ = 45 degrees. A projectile, in other words, travels the farthest when it is launched at an angle of 45 degrees.​

​

That's why @phinds suggested trying 45 degrees $-$ it produces the greatest distance for a single ballistic launch $-$ what is the greatest speed attainable for a specified distance is a different question.

 

[Doc Al]

Another useful site to explore: Trajectories - HyperPhysics