# Car hits brick wall, find inital speed of car

• AHinkle
In summary, a 2000 kg car is driven into a brick wall and the bumper compresses a distance of 1.67 cm. The car's initial speed is 0 m/s.
AHinkle

## Homework Statement

An automobile of mass 2000 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 5 × 106 N/m, and
is observed to compress a distance of 1.67 cm
as the car is brought to rest.
What was the initial speed of the automo-
bile?

## Homework Equations

$$\Delta$$KE = (1/2)mvf2-(1/2)mvi2
Wapplied to spring=(1/2)kxf2-(1/2)kxi2

## The Attempt at a Solution

$$\Delta$$x = -0.167m

Wapp=(1/2)kxf2-(1/2)kxi2
Wapp=(1/2)(5x106)(-0.167)2-(1/2)(5x106)(0)2

Wapp = 69722.5 J

Vf = 0 (because the car is brought to rest)
m = 2000 Kg

$$\Delta$$KE = 69722.5 J =(1/2)(2000)(0)2-(1/2)(2000)vi2

69722.5 J = -(1000)vi2
vi2 = (69722.5/-1000)

vi = (-69722.5/1000)1/2

and here i came to a dead end with a non-real answer. Err..
am I at least going in the right direction. I must have my sign off somewhere. I just want to know if I'm approaching the problem correctly.

The change in the kinetic energy of the car, the energy it loses, is transferred to the buckle.
The car goes from v to zero so its change in kinetic energy is simply ½mv²
If the bumper behaves as a Hooke's Law spring, then the energy absorbed by it is given by a formula involving k, the spring constant, and x the distance it compresses.
You have all the information [m,k and x] to calculate v.
Do you know the spring formula?

do you mean
Fspring=-kx

and the work done by a spring is
Ws=$$\int$$(-kx) dx = 1/2kxf2-1/2kxi2

Last edited:
AHinkle said:
do you mean
Fspring=-kx

and the work done by a spring is
Ws=$$\int$$(-kx) dx = 1/2kxf2-1/2kxi2

That's it. It's just ½kx² here where x is the compression. Equate the work done to the loss in k.e. of the car.

1/2kxf2-1/2kxi2=1/2mvi2

1/2(5x106)(-.0167)2-1/2(5x106)(0)2=1/2(2000)vi2

vi = .835m/s? aww crap... i got a sign or something mixed up somewhere or i just don't understand what orientation i need to put all the parts together in

actually i checked the answer and .8350 m/s is correct! I found out what i did wrong. I converted from centimeters to meters incorrectly in my first work calculation and that threw everything off.

Yes, the answer is fine. :)

## 1. What is the formula for finding the initial speed of a car that hits a brick wall?

The formula for finding the initial speed of a car is v0 = √(2gh), where v0 is the initial velocity, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the wall.

## 2. How do you determine the height of the wall in the equation?

The height of the wall can be measured or estimated using a measuring tape or ruler. Alternatively, if the wall is not accessible, you can use the distance between the point of impact and the point where the car came to a stop as the height.

## 3. Can this formula be used for any type of collision?

No, this formula is specifically for calculating the initial speed of a car that hits a brick wall. It assumes that the car was traveling horizontally before the collision and that the only force acting on the car was gravity.

## 4. Is this equation affected by the weight of the car?

Yes, the weight of the car can affect the outcome of this equation. A heavier car will have a higher initial speed than a lighter car if all other factors remain constant.

## 5. Are there any other factors that can affect the accuracy of this calculation?

Yes, there are several other factors that can affect the accuracy of this calculation, such as air resistance, friction, and the condition of the car and the road. These factors may not be accounted for in the equation and can affect the actual initial speed of the car.

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