Momentum

[Guest Synapse]

Hi, here is my question...

 

Two cars travelling toward each other each at the same velocity (100km/h).

 

They collide head-on. What speed to the passengers leave their seats?

Does the weight of the cars have any baring on the answer?

 

Please discribe which laws of physics support the answer.

 

Thank you.

[Primarygun]

1.If you are finding the speed of the passengers to the man on the ground relatively.

His speed is 100ms^-1 when the car hits the other at the particular short time interval.

2.If you are finding the speed of the passengers to the seats relatively. That's a bit difficult. The speed of the car varies as time passes. You need to specify the particular time moment first.

 

The weight of the car for case 2 has effects on the "relative" speed of the passengers.

It has no effects in case 1.

[Guest Synapse]

Is there a principle/law that states why the wieght of the car does not have an effect on the speed of the passenger relative to the road?

[[Tycho?]]

Depends on how the cars move after they hit. If they are the same mass they will move in the same way.

 

Why are there two cars? Will your little experiment change if its just a single car that hits a wall? This would be a more simple example if it fits.

[Guest Synapse]

The issue was, does the weight of the cars have any effect on the speed of the passengers at the time of the accident? I'm sure it doesn't but I was hoping someone could name the law/principle that applies here.

[albertlee]

Synapse,

Let's assume each of the cars has a mass of x kg at the same velocity

 

when they collide, their momentum will be 0, according to the laws of conservation of momentum

 

now, both cars stay at rest

 

Thinking back again, if 1 car has a momentum of y kgm/s, its passenger is also travelling at a momentum of y kgm/s, so

 

the velocity of a passenger after the car collides is y / the mass of the passenger, and another passenger's velocity will be negative, ie, in opposite direction

 

Albert

[albertlee]

and, Synapse, back to your question on whether there is an effect on the velocity of passenger by the mass of the cars or not, just consider the formula for the momentum

 

p = mv

 

if the velocity of the car is a constant, then the increase of car's mass will increase its momentum, so, it deduces that, when the car's mass increases, the passenger's momentum increases, hence, the passenger's velocity after the car collides increases, in your particular question

 

Albert

[swansont]

Synapse' date='

Let's assume each of the cars has a mass of x kg at the same velocity

 

when they collide, their momentum will be 0, according to the laws of conservation of momentum

 

now, both cars stay at rest

[/quote']

 

That's only true if the collision is completely inelastic and the cars have the same mass. If the collision is not, then they will rebound from each other. If the masses are different the more massive one will continue to move forward.

 

The passengers have to have the same veocity as the cars at the time of the collision. If they didn't they would have to be moving relative to the car. Passengers generally aren't.

[albertlee]

so, swansont, you mean that when the collision takes place, even the momentum of cars is zero, will the passengers stay at rest as well??

 

Albert

[The Rebel]

Do we consider the passenger to be isolated from the car, in which case (assuming the car comes to a dead stop) the passenger will leave at the speed before the collison (100km/h]. Because in essence the car and the passenger are different elements only related by what speed they were travelling.

 

The difficulty comes in including components such as the seatbelt, the structure of the passenger, and the behaviour of the crumple or bounce of the collision.

[Primarygun]

, I got a bad glance on the unit

[swansont]

so' date=' swansont, you mean that when the collision takes place, even the momentum of cars is zero, will the passengers stay at rest as well??

 

Albert[/quote']

 

It depends on if they're restrained. I was simplifying and objecting to your conclusion that the cars will automatically come to rest. That includes some assumptions. That part wasn't supposed to be part of any solution to the original problem. Sorry if I was unclear.

 

If you model the system as two cars, each with a passenger, and know all the masses and velocities, you are going to have four unknowns - the final velocities of the four objects. You will need four equations in order to solve the problem. More information is needed.

 

That's why in physics class, it's generally two objects, and the collision is either elastic or completely inelastic, to give you two equations for your two unknowns.

[albertlee]

yeah, Synapse's question wasn't fully defined.....

[RICHARDBATTY]

Provided they are not attached to the cars in anyway they would continue at the same speed. Inertia.