Calculating Force & Impulse in Car Collision Situations

In summary, the conversation discusses a problem involving two cars with equal mass and speed crashing head on. The force and impulse on each driver during the collision is calculated, assuming constant forces and a deformation length of 0.5 meters. The two situations, one with a driver wearing a seat belt and the other without, are compared and it is concluded that the impulses will be the same but the forces and outcomes will differ. The conversation ends with a request for further help in solving the problem.
  • #1
Erik_at_DTU
28
0
Hey,

I've been looking on this problem:

"You have two cars with equal mass and speed (50km/h), which crash head on. One driver is wearing a seat belt (situation 1), the other not (situation 2). Calculate the force and impulse on each of the drivers during the collision. You can assume that the forces on the cars is constant (the deacceleration is constant). Make necessary assumptions."

My evaluation:
Both situations can be analysed as a car hitting a wall, because the cars have the same mass and speed. I assume that the car has a deformation length s=0.5 meter.
Situation 1:
The seat belt is a non stretching version, and calculate the acceleration a=192.9m/s^2. And the time it takes to stop t=0.072 s. Is this correct?

Situation 2:
This is a much more difficult situation to analyse, because the driver will be thrown out of his seat and hit the front window (which I assume is aligned vertical) with the same speed the car had before the crash (50km/h). But the car will have a different speed so relative to the car the person will have a speed=(the person's speed relative to the road) - (the cars speed relative to the road). So here I'm stuck, so I cry into the physics jungle for help :tongue2:

Anyone who have the opportunity to take a look at it?
 
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  • #2
Assume the change in momentum of both cars is the same, then the change in momentum of both drivers is also the same.

An impulse is needed to change the momentum. The impulses therefore must be the same. The impulse is a product of force and time. The seatbelt case will be more restrictive thus take less time. He will feel more force. The guy without the seatbelt will feel less force, but unfortunately he will be flying out the windshield into god knows what.

It'd be easier to assume an impact time, but using a deformation length is okay too ^_^
 
  • #3




Hi there,

Your analysis is on the right track. In both situations, the force and impulse on the drivers can be calculated using the principles of Newton's laws of motion.

In situation 1, the driver wearing a seat belt will experience a force equal to their mass multiplied by the acceleration, as you have calculated. This force will act for a very short amount of time, resulting in a relatively small impulse on the driver. The seat belt will also stretch slightly, increasing the time it takes for the driver to come to a stop and reducing the force on the driver.

In situation 2, the driver not wearing a seat belt will experience a much larger force and impulse. As you mentioned, the driver will continue moving forward at the same speed as the car before the crash, until they hit the front window. At this point, the driver will experience a sudden deceleration as they come into contact with the window. The force on the driver will be equal to their mass multiplied by the deceleration, which can be calculated using the distance the driver moves (0.5 meters) and the time it takes for them to stop (which can be estimated using the speed and distance). This force will act for a very short amount of time, resulting in a large impulse on the driver.

It is important to note that in both situations, the force and impulse on the drivers will be different from the forces and impulses on the cars. This is because the cars have different masses and are experiencing different forces during the collision.

I hope this helps with your analysis. Keep in mind that these calculations are based on simplified assumptions and real-life collisions can be much more complex. It is always important to wear a seat belt while driving to reduce the risk of injury in a car collision.
 

What is force and impulse in a car collision?

Force is a measure of the strength of an impact or push on an object. In a car collision, it is the amount of energy exerted on the car and its occupants. Impulse, on the other hand, is the change in momentum of an object due to an applied force. In a car collision, it is the change in the car's velocity caused by the impact.

How is force and impulse calculated in a car collision?

Force is calculated by multiplying the mass of the car by its acceleration, using the formula F=ma. Impulse is calculated by multiplying the force by the time it is applied, using the formula I=FΔt. Both force and impulse are vectors, meaning they have both magnitude and direction.

What factors affect the force and impulse in a car collision?

The force and impulse in a car collision are affected by several factors, including the mass and velocity of the car, the angle of impact, and the presence of safety features such as airbags and seatbelts. The type and condition of the objects involved in the collision can also impact the force and impulse.

Why is it important to calculate force and impulse in car collisions?

Calculating force and impulse in car collisions is crucial for understanding the severity of the impact and the potential injuries that may result. It also allows engineers to design safer cars and safety features, as well as providing valuable data for accident reconstruction and legal purposes.

Are there any limitations to calculating force and impulse in car collisions?

There are some limitations to calculating force and impulse in car collisions, as it is not always possible to accurately determine the exact conditions and variables involved in a collision. Additionally, human factors such as reaction time and the positioning of the occupants can also affect the force and impulse experienced in a car collision.

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