# Automobile drives into a brick wall

• bmoore509
In summary, an automobile with a mass of 3000 kg was driven into a brick wall in a safety test. The bumper of the car acted like a Hooke's-law spring with a spring constant of 6 × 10^6 N/m. The bumper compressed a distance of 4.23 cm as the car came to a stop. Using the formula for work (W=Fd) and the spring formula (F=kx), the energy stored in the bumper was calculated to be -10735.74 J. Equating this to the kinetic energy lost by the car before the collision (-0.5mv^2), the initial speed of the car was found to be 1.89 m/s.
bmoore509

## Homework Statement

An automobile of mass 3000 kg is driven into a brick wall in a safety test. The bumper behaves like a Hooke’s-law spring. It has an effective spring constant of 6 × 106 N/m, and is observed to compress a distance of 4.23 cm as the car is brought to rest. What was the initial speed of the automobile?

F=-kx
Ke=(1/2)mv^2
U=(1/2)kx^2
Kf+Uf=Ki+Ui
W=Kf-Ki+Uf-Ui

## The Attempt at a Solution

I'm really not sure where to start. I tried doing KE=U but I know that's not right.

The kinetic energy of the car is absorbed by the bumper.
Use the spring formula (F=kx) and spring constant given to calculate the energy "stored" in the bumper when compressed 4.23cm
Energy stored will be average force times distance compressed.
Equate this to the kinetic energy of the car before collision.

I got it. I had a way to do it but the answer never seemed right. I didn't think about the fact that I needed to convert the 4.23 cm.

I did:
F=-kx = -253800
W=Fd = -10735.74
W=-.5mv^2+.5kx^2
-10735.74=-.5(3000)v^2-.5(6X10^6)(0.0423^2)
V=1.89m/s

Good.
It was just a case of putting ½Fx² equal to ½mv²
Kinetic energy lost by the car is "absorbed" by the bumper.

I would approach this problem by first identifying the relevant equations and variables. In this case, we have the mass of the car (m = 3000 kg), the spring constant (k = 6 × 106 N/m), and the distance the spring compressed (x = 4.23 cm or 0.0423 m). We also know that the car came to rest, so the final kinetic energy (Kf) is 0.

Next, I would use the equation F = -kx to find the force applied to the car by the spring. Plugging in the values, we get:

F = -kx = -(6 × 106 N/m)(0.0423 m) = -25400 N

We can then use the equation W = Kf - Ki + Uf - Ui to find the initial kinetic energy of the car (Ki). Since the car is initially at rest, Ui = 0. Plugging in the values, we get:

W = Kf - Ki + Uf - Ui
0 = 0 - Ki + (1/2)kx^2 - 0
Ki = (1/2)kx^2 = (1/2)(6 × 106 N/m)(0.0423 m)^2 = 254 N

Finally, we can use the equation Ke = (1/2)mv^2 to solve for the initial velocity (v) of the car. Plugging in the values, we get:

Ke = (1/2)mv^2
254 N = (1/2)(3000 kg)v^2
v = √(2(254 N)/(3000 kg)) = 2.53 m/s

Therefore, the initial speed of the automobile was 2.53 m/s. This means that the car was traveling at a relatively low speed before it hit the brick wall, which is why the compression distance of the bumper was relatively small. This information can be useful for designing safer cars and understanding the impact of collisions.

## 1. What are the potential causes of an automobile driving into a brick wall?

There are several potential causes for an automobile driving into a brick wall, including driver error, mechanical failure, road conditions, and external factors such as weather or distractions.

## 2. What safety features can prevent an automobile from crashing into a brick wall?

Modern automobiles are equipped with various safety features that can help prevent crashes, such as anti-lock braking systems, airbags, and electronic stability control. Proper maintenance and attentive driving can also play a role in preventing accidents.

## 3. How does the speed of the automobile affect the impact of a crash into a brick wall?

The speed of the automobile can greatly impact the severity of a crash into a brick wall. The higher the speed, the greater the force of impact, which can result in more damage to the vehicle and potential injuries to the occupants.

## 4. Can an automobile survive a crash into a brick wall?

It is highly unlikely for an automobile to survive a crash into a brick wall due to the immense force of impact. However, the design and safety features of the automobile, as well as the speed and angle of impact, can affect the outcome of the crash.

## 5. What steps should be taken after an automobile crashes into a brick wall?

If an automobile crashes into a brick wall, the first priority should be to ensure the safety of all individuals involved. Call for medical assistance if needed and report the accident to the authorities. It is also important to document the incident, gather information from witnesses, and contact your insurance company.

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