Inertia in the case of sudden stops?

[lokifenrir96]

Hi, imagine two cars traveling at the same velocity in the same direction. One car carries a heavy man and the other a light man. Both are not buckled by seatbelts to the car, and the roof of the car is open. If both cars slam into a wall at the same time, which man will be more prone to continue moving forward (assuming he does not hit against the wall and windshield)?

Is it the heavy man because the higher the mass the greater the inertia so he'll be more prone to continue moving forward?

Or is it the light man because the lighter the mass, the greater the acceleration?

Or am I just confused about this? I don't know if I'm approaching this question the right way.

Please help me if you can, and thanks in advance! :)

 

[timthereaper]

So are the masses of the cars the same? It seems you're making the assumption that each car+man object weigh the same, i.e the lighter man has a heavier car and vice versa, so that the car+man kinetic energies are the same. If that is the case, the forces needed to decelerate the cars would be equal, and the heavier man would feel a greater force since the deceleration would be the same for each man.

 

[Jocko Homo]

Hi, imagine two cars traveling at the same velocity in the same direction. One car carries a heavy man and the other a light man. Both are not buckled by seatbelts to the car, and the roof of the car is open. If both cars slam into a wall at the same time, which man will be more prone to continue moving forward (assuming he does not hit against the wall and windshield)?

Is it the heavy man because the higher the mass the greater the inertia so he'll be more prone to continue moving forward?

Or is it the light man because the lighter the mass, the greater the acceleration?

Or am I just confused about this? I don't know if I'm approaching this question the right way.

Please help me if you can, and thanks in advance! :)

If you have a really heavy cannonball and a really light cannonball and you drop them from a bridge, which one will fall faster?

 

[nitsuj]

If you have a really heavy cannonball and a really light cannonball and you drop them from a bridge, which one will fall faster?

Good answer!

Btw what is the answer to that?

Given the information, I'd say the light cannonball floats into the sky never to be seen again.

 

[nitsuj]

Hi, imagine two cars traveling at the same velocity in the same direction. One car carries a heavy man and the other a light man. Both are not buckled by seatbelts to the car, and the roof of the car is open. If both cars slam into a wall at the same time, which man will be more prone to continue moving forward (assuming he does not hit against the wall and windshield)?

Is it the heavy man because the higher the mass the greater the inertia so he'll be more prone to continue moving forward?

Or is it the light man because the lighter the mass, the greater the acceleration?

Or am I just confused about this? I don't know if I'm approaching this question the right way.

Please help me if you can, and thanks in advance! :)

The heavier person due to what you said, inertia (i think the definition of inertia is resistance to force)

 

[OnlyMe]

If both vehicles were traveling at the same velocity and neither driver's path of continued motion is obstructed.., they wil both continue forward at the same velocity.

Only when you begin to account for things like wind resistance will there be a difference their continued motion.., the post wall velocity of the drivers.

 

[Drakkith]

Hold on all, we have a mix of a couple of different things here. First, let's break them up.

1. Inertia
2. Resistance

For the case of inertia, the heavier man (who has more mass) WILL have more kinetic energy than the lighter man. If we could measure the total energy of each as they splat against the wall, and account for things such as elasticity of the person and wall, we would see that the larger man applied a greater amount of kinetic energy to the wall.

Now, if NEITHER hit the wall nor the windshield, we are dealing with a case of wind resistance. The resistance from the air is based purely on the aerodynamics of the two men.(Or so we'll assume for this discussion.) If we assume that the air resistance is equal for both men, the again the larger man will take longer to slow down as he has more inertia, more energy. However, a more realistic case would be very hard to discuss as the aerodynamics of each person is unknown and subject to many different variables. It could be that the larger man is "denser" and the increased drag due to his size is less than the increased inertia. Or it could be that he is not "denser" and that the increased drag is more than the increase in inertia.

 

[lokifenrir96]

Okay, so you're saying that since the heavier man has higher inertia due to his greater mass, he will be flying forward with greater force than the lighter man?

Then does F=ma apply to this scenario? Since the mass of the heavier man is higher... o.0 I think I'm confused between what applies to this scenario: is it the force the man is flying forward with or his acceleration? And are you applying the law of inertia or f=ma?

 

[Drakkith]

Okay, so you're saying that since the heavier man has higher inertia due to his greater mass, he will be flying forward with greater force than the lighter man?

To avoid getting too nit picky, I'll answer yes to that.

Then does F=ma apply to this scenario?

Of course! The heavier man took more energy to accelerate to the same speed as the lighter man when they drove off in their cars. If they both had their engines apply the same amount of force then the larger man took longer to accelerate to the same speed.

Since the mass of the heavier man is higher... o.0 I think I'm confused between what applies to this scenario: is it the force the man is flying forward with or his acceleration? And are you applying the law of inertia or f=ma?

Ugh, time to get nit picky! The man isn't flying forward WITH force, he is flying forward at a certain velocity and has a certain mass (which determines inertia). When he hits something he will exert a greater force on it due to F=ma than the lighter man. Because of air resistance he is accelerating, but in the opposite direction to his velocity. He is decelerating. And just like the scenario with the two men accelerating in their cars, the larger man requires a longer time to decelerate to the same speed as the smaller man did because of his inertia. (Assuming things like aerodynamics between the two are equal)

 

[lokifenrir96]

So, basically what you're saying is:

Since the mass of the heavier man is higher, than it would take longer to accelerate to the same speed as the lighter man if the same force is applied to the car by the engines.

So if both cars hit the wall and both men fly out, then the heavier man would decelerate at a slower rate by the same theory, and fly forward for a longer period of time than the lighter man. Is this also related to inertia in that the heavier man would "want" to continue moving forward due to his higher mass?

Also, in a separate scenario, if both cars are traveling at the same acceleration, then when they are both sent flying out and hit a random object, the heavier man would hit it with more force.

Have I got it? Thanks :)

 

[Drakkith]

Pretty much loki.

Also, in a separate scenario, if both cars are traveling at the same acceleration, then when they are both sent flying out and hit a random object, the heavier man would hit it with more force.

Do you mean the same velocity?

 

[OnlyMe]

So if both cars hit the wall and both men fly out, then the heavier man would decelerate at a slower rate by the same theory, and fly forward for a longer period of time than the lighter man. Is this also related to inertia in that the heavier man would "want" to continue moving forward due to his higher mass?

This is where I believe there is some confussion. Once both men are in motion the only part that inertia plays a role in is that they will both keep moving at the same velocity when their cars hit the wall. Both are equal in that respect.., unless you start adding additional information.

There is no way from the information in the OP to assert that either man would travel furred than the other given that neither hits any stationary object. To better understand this let us replace the men with two balls of lead. One with a mass equal to 100 kg and one with a mass of 200 kg. Both balls would have the same aerodynamic properties so any difference in mass would have no affect on how far either travels. The larger ball would meet with greater wind resistance due to it's larger surface area, however the difference would be offset by its greater inertia.

Until they "hit" something stationary like the wall their forward velocity is unchanged. At any point of impact with, say a wall, the more massive ball, or man, would hit with a greater force, proportional to its/his greater mass.

The answer to the question in the OP,

... If both cars slam into a wall at the same time, which man will be more prone to continue moving forward (assuming he does not hit against the wall and windshield)?

Is that they both fly forward at the same velocity. There is not enough information given to introduce the affect of wind resistance into the answer.

 

[OnlyMe]

Also, in a separate scenario, if both cars are traveling at the same acceleration, then when they are both sent flying out and hit a random object, the heavier man would hit it with more force.

The acceleration would have no affect, as it would not continue beyond the time the cars hit the wall. Both men would continue forward at what ever velocity they were traveling when their cars hit the wall. And, yes if after that they both hit a random object, the heavier man would hit it with more force. F=mv in this case as neither would continue to accelerate after their car's initial impact with the wall.

This result would be no different than if they cars were both traveling at a constant velocity. The only difference would be that some portion of the force accelerating the cars would potentially add to each cars inertia.

An object has an inertia proportional to its [strike]velocity and[/strike] mass. If it is accelerating there is an additional force involved, the force responsible for the acceleration. In this case think of it as the cars motor and wheels are still trying to accelerate the cars forward. This would be a relative component of the force that each car transfers to the wall. It would not have any affect on the [strike]inertia[/strike] velocity of the men after the cars hit the wall. As soon as the car hits the wall it will begin to slow down, rapidly, even when accounting for the addition of the force of acceleration. As soon as the cars hit the wall, the men and the cars become inertially separated, they are no longer moving together. The cars slowing down and the men continuing forward at their velocity just prior to impact.

 

[Drakkith]

An object has an inertia proportional to its velocity and mass.

I believe inertia is only propotional to an objects mass, not its velocity.

 

[OnlyMe]

I believe inertia is only propotional to an objects mass, not its velocity.

Correct!

 

[Drakkith]

Correct!

Woohoo! Give me a cupcake!

 

[lokifenrir96]

This is where I believe there is some confussion. Once both men are in motion the only part that inertia plays a role in is that they will both keep moving at the same velocity when their cars hit the wall. Both are equal in that respect.., unless you start adding additional information.

Erm by "same velocity" are you comparing the velocity of both men, or are you saying they'll move at the same velocity they were at upon hitting the wall? If it's the latter, I still don't really get why... how would it differ if you add air resistance (assume same surface area for both men) and if you don't?

Also, why is "Also, in a separate scenario, if both cars are traveling at the same acceleration, then when they are both sent flying out and hit a random object, the heavier man would hit it with more force" wrong? How does F=ma apply here? I thought if a is the same, and m is higher for the heavier man, then he would hit with the same force?

Woah I'm getting dizzy ><

 

[Drakkith]

Erm by "same velocity" are you comparing the velocity of both men, or are you saying they'll move at the same velocity they were at upon hitting the wall? If it's the latter, I still don't really get why... how would it differ if you add air resistance (assume same surface area for both men) and if you don't?

Let's assume a small wall, just high enough to stop the car but let the men fly forward past it, and that the cars were traveling the same velocity upon impact. Both men will start with the same velocity. The larger man, meaning he's more massive, will travel further because he has more inertia. It takes the same air resistance longer to slow him to the same speed compared to less massive man due to inertia. The larger man has more mass and therefor more inertia.

Also, why is "Also, in a separate scenario, if both cars are traveling at the same acceleration, then when they are both sent flying out and hit a random object, the heavier man would hit it with more force" wrong? How does F=ma apply here? I thought if a is the same, and m is higher for the heavier man, then he would hit with the same force?

Woah I'm getting dizzy ><

Acceleration isn't the correct word here. They were traveling at the same velocity. If both men hit the same object and experience the same deceleration after impact, then the man with more mass will impart a greater force on the object. F=ma applies perfectly.

Honestly the whole thing is easier to understand with something simple like a ball or whatever instead of two men. But that is the original example so let's just stick with it to avoid confusion.

 

[OnlyMe]

Woah I'm getting dizzy ><

Me too!

Drakkith did a good job of restating it...

One point I see differently is how far each man might fly after their cars hit the wall. If there were no external forces involved, air resistance, even gravity, they would both continue at the same velocity.

If you add air resistance you also have to define how the size of each man changes their individual aerodynamics. Which one is more affected by the wind or air resistance. It go either way.., too many variables unstated.

If you set aside air resistance and consider only the affect of gravity once they are thrown form their cars they should still both fly the same distance before landing on the ground. They both start with an equal velocity. The velocity of their cars just before impact with the wall. After impact and while they are both flying forward they will fall toward the ground at the same rate. Setting aside air resistance gravity acts the same on both men.

When they wind up hitting something the larger man will hit with a greater force. The m (mass) component of F=mv is larger for the large man while the v (velocity) component is the same. If you are allowing for gravity v would become a (acceleration) as there would be an element of acceleration due to the affect of gravity. In either case v or a, the net result would be the same for both men.

 

[Drakkith]

The distance one of them travels until they hit the ground is almost impossible to determine without stating the aerodynamic properties of each man. Without resistance each man would experience the same acceleration towards the ground and would impact at the same time. The heavier man is more massive and has more mass to respond to gravity. In essence he experiences more force, as you can see by weighing him. The higher mass causes him to have more inertia however, and the more force and more inertia cancel out and cause him to experience the same acceleration as the lighter man.

 

[lokifenrir96]

Okay so I reread the whole thing and I hope I've got it:

Since they were both traveling at the same velocity, and the same amount of force was driving them forward, then the heavier man with higher mass would take a longer time to accelerate to that velocity by F=ma. So when the car slams against the wall, it would also take a longer time for him to decelerate so if they don't hit anything he should be traveling further (if air resistance is the same for both men).

And in the scenario that they do hit something, since they are both traveling at the same velocity, and when they hit the object they suddenly decelerate at the same rate to 0, then by F=ma again the heavier man would exert a larger force...

I think I was getting confused because of F=mv. Isn't that momentum? I don't know O.O. I assume in this case that it is because after the men are removed from the car they no longer have any force causing them to accelerate, but instead decelerate to 0 upon hitting something. This is the only part I'm confused about (mv and not ma) if my parts above are correct, that is.

 

[OnlyMe]

This is the only part I'm confused about (mv and not ma) if my parts above are correct, that is.

You are right. In practice F=ma is the proper form for force.

I substituted F=mv (more appropriately p=mv for momentum) to make it consistent with the OP where the question was,

If both cars slam into a wall at the same time, which man will be more prone to continue moving forward (assuming he does not hit against the wall and windshield)?

In this question it is the momentum that is relevant and the balance between the momentum of each man and inertia. Abscent friction as in wind resistance their individual velocities do not change and are equal if their vehicles both hit the wal at the same speed/velocity.