# Amount of Force felt in impact

1. May 15, 2012

### centrix

1. The problem statement, all variables and given/known data
A 15000 kg train traveling at 30m/s collides with a 2500 truck with a 90 kg man going at 22m/s in the opposite direction. The time of collision is 1.5 seconds. After collision, both objects are moving in the same direction with a velocity of 22 m/s. What is the size of the force felt by the man

2. Relevant equations
ft=mΔv
f=ma

3. The attempt at a solution
I tried to use the impulse equation, but can't seem to get a reasonable answer from it. I tried to find the acceleration then the next force, but still couldn't find a reasonable answer for the force.

I first tried to find acceleration using Vf=Vi+at.
22=-22+1.5a
a=29.2 m/s/s

f=90*29.2
f=2640 N

that force seems to small for a collision like this. would it be reasonable to assume the force felt by the car is about equal to what the person will feel?

Last edited: May 15, 2012
2. May 15, 2012

### Staff: Mentor

Hi centrix, welcome to Physics Forums.

You should obtain the same result from either the impulse or acceleration methods. Be sure to keep track of the velocity and momentum directions.

The man was lucky that the collision occurred over a relatively long timespan (1.5 seconds is practically an eternity in a collision. His truck must have excellent crumple zones!). What force would he experience if the time were only 1/10 second?

3. May 15, 2012

### centrix

The force felt would definitely increase because the acceleration would increase while mass stays constant.

How long does a collision normally last?

4. May 15, 2012

### Staff: Mentor

It depends upon the nature of the bodies involved. The more rigid the bodies, the smaller the deformation and the more brief the interaction. Vehicles are often designed to lengthen the collision time by the use of crumple zones which absorb energy as they 'fail', lengthening the time. Think in terms of fractions of a second.