# Physics120 car collision question

• physics120
In summary: The net force on the person if they are wearing a seat belt and the air bag deploys correctly is 6716 N. The net force that ultimately stops the person is 9.4 N less than the weight of the person.
physics120

## Homework Statement

Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. Cars are designed with a "crumple zone" in the front of the car. In the event of an impact, the passenger compartment decelerates over a distance of about 1 meter as the front of the car crumples. An occupant restrained by seat belts and air bags decelerates with the car. By contrast, an unrestrained occupant keeps moving forward with no loss of speed (Newton's first law!) until hitting the dashboard or windshield. These are unyielding surfaces, and the unfortunate occupant then decelerates over a distance of only about 5 mm.
(a) A 60 kg person is in a head-on collision. The car's speed at impact is 15 m/s. Calculate the net force on the person if he or she is wearing a seat belt and the air bag deploys correctly.

(b) Calculate the net force that ultimately stops the person if he or she is not restrained by a seat belt or air bag.

(c) How do these two forces compare to the person's weight?

## Homework Equations

F= ma
Vf^2= V0^2 + 2ax
Vf= V0 + at
x= V0*t + .5a(t^2)

## The Attempt at a Solution

Well, for (a), what I thought you do is: Force of seatbelt and airbag = mass * acceleration

Then, using Vf^2= V0^2 + 2ax, make Vf = 0. Solve for ax.
So, ax= -(15^2)/(2*1.005) which equals -111.9 m/s^2

Btw, I got 1.005 because the passenger compartment decelerates over 1 m, and the airbag for 0.05mm, so I assumed adding those two nuumbers together, to give me 1.005 m will give me the distance. I am not sure about this, though.

Then, go back to the Force of seatbelt and airbag = mass * acceleration

F= 60 kg * -111.9 m/s^2
=-6716 N

Last edited:
Is the initial speed 17 m/s or 15 m/s?

As to your 5 mm, ignore it. The idea is that if restrained the person won't strike an unyielding surface.

Is the weight 50 kg or 60 as in your calculation?

LowlyPion said:
Is the initial speed 17 m/s or 15 m/s?

As to your 5 mm, ignore it. The idea is that if restrained the person won't strike an unyielding surface.

Is the weight 50 kg or 60 as in your calculation?

The initial speed is 15 m/s.

Also, the mass of the person is 60 kg.

The original statement of the problem says otherwise.

LowlyPion said:
The original statement of the problem says otherwise.

I apologize, here is the problem with the correct numbers:

Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. Cars are designed with a "crumple zone" in the front of the car. In the event of an impact, the passenger compartment decelerates over a distance of about 1 meter as the front of the car crumples. An occupant restrained by seat belts and air bags decelerates with the car. By contrast, an unrestrained occupant keeps moving forward with no loss of speed (Newton's first law!) until hitting the dashboard or windshield. These are unyielding surfaces, and the unfortunate occupant then decelerates over a distance of only about 5 mm.

(a) A 60 kg person is in a head-on collision. The car's speed at impact is 15 m/s. Calculate the net force on the person if he or she is wearing a seat belt and the air bag deploys correctly.

(b) Estimate the net force that ultimately stops the person if he or she is not restrained by a seat belt or air bag.

(c) How do these two forces compare to the person's weight?

NEVERMIND! I completely understand what I was not seeing before. I got the answers for all 3 parts! Thank-you for showing me that I had made an error when I wrote out the numbers in the problem!

## What is the Physics120 car collision question?

The Physics120 car collision question is a hypothetical scenario used to illustrate concepts of momentum, energy, and collisions in introductory physics courses. It typically involves two cars of different masses colliding with each other at different velocities.

## What is momentum?

Momentum is a measure of an object's motion, and is calculated by multiplying an object's mass by its velocity. In the Physics120 car collision question, momentum is conserved, meaning the total momentum of the system before and after the collision remains constant.

## What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. In the Physics120 car collision question, kinetic energy is also conserved, meaning the total kinetic energy of the system before and after the collision remains constant.

## How do you calculate the velocities of the cars after the collision?

To calculate the velocities of the cars after the collision, we can use the conservation of momentum and conservation of kinetic energy equations, along with the given masses and velocities of the cars before the collision. These equations can be solved simultaneously to determine the velocities of the cars after the collision.

## What other factors may affect the outcome of the collision?

In addition to momentum and kinetic energy, there are other factors that may affect the outcome of the collision in the Physics120 car collision question. These include the coefficient of restitution, which measures the elasticity of the collision, and external forces such as friction or air resistance. The angles of the cars' paths and the presence of any obstacles may also impact the outcome of the collision.

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