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Good morning,

i have a stationary vehicle weighing 1000 kg being hit by a truck weighing 17.000 kg at a speed of 86 kilometer per hour.

my question what is the force of the impact and what formula should i use to calculate this force.

Hello dirk,

The collision can not be analysed without making 2 assumptions. I will assume the stationary vehicle ended up being pushed along by the truck. The truck's initial velocity, in m/s, is

86 km/hr * (1000 m/1 km) * (1 hr/3600 s) = 23.9 m/s

Momentum is conserved throughout the collision. After the collision, the velocity, V, of the pair of vehicles will be given by

m1*U1 + m2*U2 = (m1+m2)*V

17,000 kg*23.9 m/s + 0 = (17,000 kg + 1000 kg)*V

V = 17,000 kg*23.9 m/s / 18,000 kg = 22.6 m/s

So the collision did not slow the truck significantly.

The truck gave the car an impulse equal to the change in momentum the car experienced.

Impulse = final momentum - initial momentum = 1000 kg*22.6 m/s - 0 = 2260 kg.m/s

Impulse is also calculated by multiplying the applied force and the time duration of the application of that force. The time duration is: how long did it take to change the car's velocity to 22.6 m/s? That is the other assumption and it is more difficult than the first assumption was.

I'll set this up for you and let you decide on the time duration and plug that time in.

Impulse = 2260 kg.m/s = Force*time duration

Force = (2260 kg.m/s) / time duration

(As an example, if you choose 1 s for the time duration, the force would be 2260 Newtons. But since the truck's speed, even after the collision, has it traveling about 23 meters in one second and the car's length is perhaps 5 meters, the car would have to accelerate to the final speed in much less than 1 second. Perhaps 0.1 s. The force is therefore much more than 2260 Newtons.)

I apologize for the delay in my reply. I hope this helps,

Steve

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Comment | thanks Steve. your explanation was very helpful. |

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