# What is the Average Force During a Collision?

• FrostyMan
In summary, we are given a problem involving an 18-wheeler being shot into a concrete wall at 80mph and causing a deformation of 0.1m. We are asked to draw free body diagrams and find the average acceleration and force during the collision. However, the given information does not allow us to accurately calculate the average force over time, so an energy approach is suggested as an alternative.
FrostyMan

## Homework Statement

As part of a safety test, an eighteen wheeler is being shot down a track by a rocket into a solid concrete wall. The truck is fully loaded, for a total weight of 95,000lbs. If the truck hits the wall at 80mph and causes a deformation of .1m in the wall before coming to a halt:

a. Draw two free body diagrams, one of the truck and the other of the wall, during the crash.
b. What is the average acceleration of the truck during the collision?
c. what is the average force on the truck during the collision?

## Homework Equations

SumofF=ma
Vf=Vo+2a(Xf-Xo)
Xf=Xo+Vot+(1/2a)t^2

## The Attempt at a Solution

I drew two free body diagrams: (_ is for formatting purposes)

______^________________________________^
______| Fn(Ground->Truck)________________|Fn(Ground-->Wall)
____Truck-->Fp(Rocket->Truck)___________Wall-->Fp(Truck-->Wall)
______|Fg(Earth->Truck)__________________|Fg(Earth-->Wall
______v________________________________v

I'm having trouble finding the average acceleration and the average force, however. I converted the lbs to kg (95,000lbs to 43091.24kg) and the mph to m/s (80mph to 35.7632m/s). I tried treating it as a 1D problem to find acceleration and wrote a table of variables but did not have enough knowns to finish the equations.

Any suggestions would be greatly appreciated.

I often see this question in different guises. It is an error on the part of the poser of the question.
You are given a stopping distance and asked about a force. Since force x distance = energy, the obvious approach is to compute the KE and divide by the distance. That gives an average force in a sense, but it is an average over a distance, not an average over time. When we talk of average acceleration (and thus of average force) we mean the change in velocity divided by the time taken, so it's an average over time.
In practice, the force during a collision tends to increase more or less linearly from 0 to a maximum, then may stay at that maximum (as objects crumple) for a while, then quickly fall away to nothing. However, that makes it impossible to calculate the average over time without further information.
Sorry I can't be more helpful. I suggest you use the energy approach to get the answer expected, but please understand that it is wrong.

## What is Newton's Second Law Problem?

Newton's Second Law Problem is a physics concept that describes the relationship between an object's mass, acceleration, and the net force acting upon it. It states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass.

## What is the formula for Newton's Second Law Problem?

The formula for Newton's Second Law Problem is F = ma, where F represents the net force, m represents the mass of the object, and a represents the acceleration.

## How do you solve a Newton's Second Law Problem?

To solve a Newton's Second Law Problem, you must first identify the known values, including the mass, acceleration, and net force. Then, use the formula F = ma to calculate the missing value. Be sure to use consistent units for all values.

## What is an example of a Newton's Second Law Problem?

An example of a Newton's Second Law Problem is a car accelerating down a straight road. The mass of the car is 1000 kg, and the net force acting upon it is 5000 N. What is the acceleration of the car? Using the formula F = ma, we can calculate the acceleration to be 5 m/s^2.

## How does Newton's Second Law Problem relate to everyday life?

Newton's Second Law Problem is applicable to everyday life in many ways, such as understanding the forces that act upon objects in motion, calculating the acceleration of a moving object, and determining the necessary force to move an object at a desired acceleration. It is also used in fields such as engineering and sports to optimize performance and design.

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