Would conservation of momentum apply in this vehicle accident homework problem?

[lioric]

Homework Statement

If there were two vehicles A and B
Mass of A = 1000kg
Mass of B = 500kg
Driver mass = 50kg
A driver was driving vehicle A at 20m/s. The vehicle collided in to a solid structure and the driver was thrown forward off the vehicle at v m/s.

If the same driver was driving the vehicle B at the same speed and collided into the same structure, would the driver be thrown at the same speed?

Relevant Equations

Law of conservation of momentum
Total momentum before a collision is equal to the total momentum after the collision

Momentum = Mass x velocity

Vehicle A
Before collision = (mass of driver + mass of vehicle A) x velocity
= (50+1000) x 20
=21000kgm/s

After collision = (mass of driver x v) + (mass of vehicle A x 0)
=50v +0
=50v
50v = 21000
v=420m/s

Vehicle B
Before collision = (mass of driver + mass of vehicle B) x velocity
= (50+500) x 20
=11000kgm/s

After collision = (mass of driver x v) + (mass of vehicle A x 0)
=50v +0
=50v

50v = 11000
v=220m/s

Does this make sense?????
Does this mean that as the vehicle becomes heavier, the people in the vehicle would be thrown at greater speeds in an event of a collision?
This is something that I was thinking about. It's not a homework. I can see the math, but something doesn't seem right.
Could you guys tell me if I'm missing something.
Thank you for your time.

 

[berkeman]

What does it mean to collide with a "solid structure"? If the solid structure does not move, who cares how massive your vehicle is?

 

[erobz]

Let's greatly simplify the situation. The driver is not restrained, and they are free to slide off the seat and out of the car unobstructed, what is the magnitude of force that is doing work on them and how long(time) or how far(distance) was it applied in either case? This will lead to more questions about the nature of each collision, but it's a place to start (I believe).

 

[kuruman]

What does Newton's first law have to say about the speed of the driver, who is foolishly not wearing a seat belt, have to say about this? A collision is not necessary for the driver to be thrown off. Sudden and (near) instant braking from 50 mph to zero will do the job just as well.

 

[lioric]

What does it mean to collide with a "solid structure"? If the solid structure does not move, who cares how massive your vehicle is?

Yes structure does not move. Just wondering if the vehicle stops instantly when it collides, and the driver is thrown out of the vehicle, in the same direction as he was moving, would his velocity after collision increase as the vehicle's mass increase?

 

[berkeman]

would his velocity after collision increase as the vehicle's mass increase?

What would be the accelerating force on their back to make their velocity increase?

 

[kuruman]

$\dots$ would his velocity after collision increase as the vehicle's mass increase?

Like I said, what does Newton's first law have to say about this?

 

[lioric]

What would be the accelerating force on their back to make their velocity increase?

These are two scenarios. Just wondering if such a collision happens the velocity at which the driver is thrown would change due to the mass of the vehicle. My mind says that in both cases the driver would be thrown at 20m/s. As the driver would be at that velocity when the crash happens. But I’m wondering, if the driver was considered to be moving with on the vehicle, then the vehicle and the driver would be considered as a combined mass. So the driver being thrown off would be like a piece of the vehicle, being thrown off.

 

[lioric]

Like I said, what does Newton's first law have to say about this?

An object would keep moving in a straight line until an external force is exerted on it

 

[berkeman]

These are two scenarios. Just wondering if such a collision happens the velocity at which the driver is thrown would change due to the mass of the vehicle. My mind says that in both cases the driver would be thrown at 20m/s. As the driver would be at that velocity when the crash happens. But I’m wondering, if the driver was considered to be moving with on the vehicle, then the vehicle and the driver would be considered as a combined mass. So the driver being thrown off would be like a piece of the vehicle, being thrown off.

And if the vehicle hits a "solid (immovable) object", it:

a) Accelerates

b) Decelerates

 

[lioric]

And if the vehicle hits a "solid (immovable) object", it:

a) Accelerates

b) Decelerates

What about the person on the vehicle?

 

[berkeman]

What about the person on the vehicle?

They might accelerate if they have one of these...

https://www.nbcnews.com/mach/science/iron-man-jet-pack-flier-just-set-new-world-speed-ncna819766

 

[lioric]

They might accelerate if they have one of these...

View attachment 338290
https://www.nbcnews.com/mach/science/iron-man-jet-pack-flier-just-set-new-world-speed-ncna819766

So what your saying is, because of Newton’s first law, when the vehicle meets an immovable solid object, it’ll stop, the person who did not meet the immovable object would continue to go at the speed they were traveling because there was no force which made the person to accelerate.

 

[berkeman]

Yes, exactly. Well done.

 

[berkeman]

the person who did not meet the immovable object would continue to go at the speed they were traveling

Well, at least for a half meter or so...

[Gory medic pictures of car accidents deleted by the Mentors -- bad berkeman!]

 

[lioric]

Yes, exactly. Well done.

Thank you very much.
there was no action or reaction on the person. The action and the reaction happened to the vehicle, which was immov object, reaction was vehicle came to rest, the person had inertia so he kept on going. Hence the same speed as he was at the collision. It was funny to see that 20m/s before collision but 200 or 400 m/s right after. And the picture you showed explained it very well. There was no push from the person on the vehicle, for him to accelerate.
Thank you very much.

 

[berkeman]

You are welcome. To be clear, @kuruman posted the hint about Newton's First Law. I just like posting pictures of jetpacks and gory car accidents (now deleted by some obnoxious Mentor who will remain nameless).

 

[lioric]

Like I said, what does Newton's first law have to say about this?

Thank you for your hint. It was a well deserved lesson

 

[lioric]

You are welcome. To be clear, @kuruman posted the hint about Newton's First Law. I just like posting pictures of jetpacks and gory car accidents (now deleted by some obnoxious Mentor who will remain nameless).

Still this clears so much doubt.

 

[jbriggs444]

This thread began with a question about conservation of momentum. I want to make two points in that regard.

First, there was an assumption that the momentum of the car plus occupant should be conserved across the interaction. That assumption is false.

Momentum is conserved for isolated systems. In this situation "isolated" means that nothing new is added or removed from the system. It also means that there are no external forces acting on the system. If the car collides with an external object, there would be a very large external force acting for a very short time. Momentum for the car plus occupant would definitely not be conserved.

Second, there is a tendency to think about hypothetical immovable objects as if their momentum must necessarily be zero. Because their momentum is zero, one might incautiously reason that momentum can neither be added nor removed from such an object. However, this is not the case. The momentum of a hypothetical infinitely massive object which is at rest is indeterminate. Such an object can absorb momentum without changing its velocity. Its momentum remains indeterminate.

Of course, infinitely massive objects are unrealistic. If we think instead about a real world situation, we might have a very massive wall which attains a very small velocity as a result of a collision with a car. This real world wall (or wall plus earth) would move sightly as a result of the impact, gaining exactly as much momentum as the car had lost.

 

[lioric]

This thread began with a question about conservation of momentum. I want to make two points in that regard.

First, there was an assumption that the momentum of the car plus occupant should be conserved across the interaction. That assumption is false.

Momentum is conserved for isolated systems. In this situation "isolated" means that nothing new is added or removed from the system. It also means that there are no external forces acting on the system. If the car collides with an external object, there would be a very large external force acting for a very short time. Momentum for the car plus occupant would definitely not be conserved.

Second, there is a tendency to think about hypothetical immovable objects as if their momentum must necessarily be zero. Because their momentum is zero, one might incautiously reason that momentum can neither be added nor removed from such an object. However, this is not the case. The momentum of a hypothetical infinitely massive object which is at rest is indeterminate. Such an object can absorb momentum without changing its velocity. Its momentum remains indeterminate.

Of course, infinitely massive objects are unrealistic. If we think instead about a real world situation, we might have a very massive wall which attains a very small velocity as a result of a collision with a car. This real world wall (or wall plus earth) would move sightly as a result of the impact, gaining exactly as much momentum as the car had lost.

Thank you sir. That was very helpful

 

[kuruman]

So what your saying is, because of Newton’s first law, when the vehicle meets an immovable solid object, it’ll stop, the person who did not meet the immovable object would continue to go at the speed they were traveling because there was no force which made the person to accelerate.

Now you understand the role of seat belts and air bags in vehicles. I hope you will never have to experience that in a "real life" situation.

 

[haruspex]

there is a tendency to think about hypothetical immovable objects as if their momentum must necessarily be zero. Because their momentum is zero, one might incautiously reason that momentum can neither be added nor removed from such an object. However, this is not the case. The momentum of a hypothetical infinitely massive object which is at rest is indeterminate. Such an object can absorb momentum without changing its velocity. Its momentum remains indeterminate.

My attitude to idealisations, such as immovable masses, inelastic strings, etc., is that the only strictly valid treatment is to consider them as the limit of realistic versions.
If a body mass m, velocity v, coalesces with a body mass M at rest, the latter acquires momentum $\frac{Mmv}{M+m}$. In the limit as M tends to infinity this reduces to $mv$, even though the final velocity tends to zero.

 

[lioric]

Thank you all for your contributions. It’s always fun learning here.