How Does Collision Time Affect Impulse and Momentum Change?

[Sylis]

Homework Statement

Consider the two examples that follow:

Example A. The figure below shows a truck coasting at a speed of 30mph just before it hits a large, impenetrable b ridge abutment. The truck's engine is off. The truck is brought very quickly to a complete stop in a time interval of Δt=0.020s when it has a collision with bridge abutment.

Example B. The figure below shows a truck, identical to the truck in Example A, coasting at a speed of 30 mph just before it hits a series of large barrels containing water or sand. The trucks engine is off. The truck is brought more slowly to a complete stop in a time interval of Δt=0.20s when it has a collision with the large barrels.

a) Which truck has a larger change in momentum during its collision when it is brought to a stop?

b) Which truck has a larger impulse during the collision when it is brought to a stop?

c) If you were a civil engineer trying to make bridge abutments safer for vehicles that collide with them what would you do? You should consider your answers to the previous two questions and the results of Exploration 20 (which we haven't done yet) as you formulate your answer to this question.

Homework Equations

J=ΔP=m(V_f-V_i)

The Attempt at a Solution

I wrote for problem a) that "Assuming the trucks have the same mass, considering that they each have identical initial and final velocities the two trucks would have the same change in momentum because of the formula ΔP=m(V_f-V_i)"

And problem b) I wrote " Impulse for each truck would be the same again assuming the masses are the same because of J=ΔP=m(V_f-V_i)".

I thought I had it questions a) and b) correct until I read c) and now I'm not so sure. In my notes I have that J=ΔP=m(V_f-V_i), however that F_avgΔt=m(V_f-V_i). I mean if questions a or b had asked about force, my answers to them would have been different because of the change in time interval for each scenario, but they didn't they specifically asked about impulse and change in momentum.

My answer to c would be something like "In order to make the bridge abutments safer I would increase the time interval and lessen the force of the impulse."

Am I correct in my statements considering the way the questions are worded? I don't think you need the figures and I haven't changed any wording.

 

[Doc Al]

Your answers to questions a) and b) are perfectly correct. And your answer to c is most reasonable.

 

[TSny]

Hello Sylis. Yes, you are thinking correctly! It's not impulse that causes injury, it's force.

 

[Sylis]

Thank you. I started to second guess myself there at the last part. Appreciate the reassurance.

 

[Nickie]

I would like to clarify some of the concepts and equations mentioned in this question.

Firstly, let's define impulse and change in momentum. Impulse (J) is the product of force (F) and time (Δt) and is represented by the equation J = FΔt. On the other hand, change in momentum (ΔP) is the difference between the final momentum (Pf) and initial momentum (Pi) of an object and is represented by the equation ΔP = Pf - Pi.

In Example A, the truck is brought to a complete stop in a very short time interval (Δt = 0.020s) when it hits the bridge abutment. This means that the force of the collision is very high, resulting in a large impulse and a large change in momentum. In Example B, the truck is brought to a complete stop in a longer time interval (Δt = 0.20s) when it hits the barrels. This means that the force of the collision is lower, resulting in a smaller impulse and a smaller change in momentum.

To answer question a), both trucks have the same mass and initial and final velocities, so their change in momentum would be the same. However, the truck in Example A experiences a higher force and a shorter time interval, resulting in a larger impulse.

For question b), the impulse would be the same for both trucks, as the mass and change in velocity are the same.

In regards to question c), as a civil engineer, I would consider increasing the time interval of the collision in order to reduce the force and impulse experienced by the truck. This could be achieved by implementing measures such as crash cushions, barriers, or other energy-absorbing materials to slow down the vehicle gradually and reduce the impact force. This would ultimately make the bridge abutments safer for vehicles that collide with them.