How Much Force Does a Man Feel in a Train-Truck Collision?

[centrix]

Homework Statement

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

Homework Equations

ft=mΔv
f=ma

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?

 

[gneill]

Homework Statement

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

Homework Equations

ft=mΔv
f=ma

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?

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?

 

[centrix]

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

How long does a collision normally last?

 

[gneill]

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

How long does a collision normally last?

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.

 

[asteriatic]

I would approach this problem by first considering the conservation of momentum principle. This states that the total momentum before a collision is equal to the total momentum after the collision. In this case, the total momentum before the collision is (15000 kg * 30 m/s) + (2500 kg * 22 m/s) = 465000 kg*m/s. After the collision, the total momentum is (15000 kg + 2500 kg) * 22 m/s = 396000 kg*m/s. Since the total momentum before and after the collision must be equal, we can set these two values equal to each other and solve for the final velocity of the combined objects.

465000 kg*m/s = (15000 kg + 2500 kg) * vf
vf = 22.5 m/s

We can then use this final velocity to calculate the change in momentum of the man, which is equal to the impulse experienced by the man.

Δp = mvf - mvi
Δp = 90 kg * (22.5 m/s - 22 m/s)
Δp = 45 kg*m/s

Finally, we can use the impulse equation to calculate the force experienced by the man.

F = Δp/t
F = 45 kg*m/s / 1.5 s
F = 30 N

This result does seem small, but it is important to remember that the man's mass is much smaller than the train and truck, so he will experience a much smaller force. Additionally, the force experienced by the man may also be distributed over a larger area (such as the seat or airbag), which would further decrease the perceived impact force. It is also possible that the man's body may have some resistance or ability to absorb the force, which would also reduce the perceived impact force. Overall, while the calculated force may seem small, it is still a reasonable result given the variables and assumptions of the problem.