Calculating Force of Impact: Solving for F in a Collision with a Steel Wall

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Homework Help Overview

The discussion revolves around calculating the force of impact when a car collides with a steel wall. The scenario involves a 1000 kg car traveling at 20 meters/second, with a collision duration of 0.5 seconds. Participants are exploring the relationship between force, momentum, and time in the context of this collision.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss whether to use momentum equations and how to apply the time duration of the collision. Questions arise about the definitions of velocity and acceleration, as well as the correct formulas to use for calculating force and momentum changes.

Discussion Status

The discussion is progressing with participants clarifying concepts of momentum and force. Some have suggested using the impulse-momentum theorem, while others are working through the implications of negative values in their calculations. There is a focus on understanding the relationship between the average force, change in momentum, and time.

Contextual Notes

Participants are navigating the definitions of initial and final momentum, as well as the implications of vector quantities in their calculations. The problem does not specify whether the force should be expressed as a magnitude or with direction, leading to further exploration of the signs in their answers.

Sarah
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Hey everyone so I'm having trouble figuring out this problem, it's for HW and I don't want to get an answer I just need help having it explained. I wasn't sure if I needed to use the momentum equation to figure it out.
Suppose a 1000kg car is traveling at 20 meters/second before experiencing a collision. (a) If the car runs into a steel wall and the collision occurs over the course of 0.5 seconds, then what is the resulting force of impact?


So I'm trying to figure out F right? So m=1000 kg, a= 20 m/s or do I need momentum? I'm just confused and need help breaking it down. I don't know where to plug in the 0.5 sec. The car is going from 20 m/s and is stopping but where do I put in the 0.5 sec?
Thanks!
 
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Welcome to PF.

Sarah said:
car is traveling at 20 meters/second ...

So m=1000 kg, a= 20 m/s

Does the 20 m/s represent a velocity or an acceleration?
 
Oh! I think velocity!
 
Sarah said:
Oh! I think velocity!
Yes.
 
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would the correct formula be F x change in time = change in momentum
then J=change in momentum ?
 
and would 0.5 sec be considered the change in time?
 
Sarah said:
would the correct formula be F x change in time = change in momentum
Yes. F is the average force of the collision.
 
so then F=ma therefore it would be (1000 kg) (change in velocity/time) = change in momentum?
Thank you for your help:)
 
Sarah said:
so then F=ma therefore it would be (1000 kg) (change in velocity/time) = change in momentum?
Thank you for your help:)
No. You're mixing the two formulas F = ma and F Δt = change in momentum.

You can just work with F Δt = change in momentum. Can you calculate the change in momentum of the car?
 
  • #10
Would the change in momentum be p=MV so (1000 kg) (20 m/s) ? so 20000 kg m/s?
 
  • #11
I can't tell if you're thinking about this correctly.

So just to be clear, note that "change in momentum" means the difference between the final momentum and the initial momentum:
change in momentum = Δp = pf - pi.

What is the initial momentum?
What is the final momentum?
What is the change in momentum?
 
  • #12
ok. this is getting much clearer I think...haha
ok so then the pi would = 20000 kg m/s and pf= 0 m/s therefore it would be -20000 kg m/s for the final momentum?
 
  • #13
Sarah said:
ok. this is getting much clearer I think...haha
ok so then the pi would = 20000 kg m/s and pf= 0 m/s therefore it would be -20000 kg m/s for the final momentum?
Yes. Good. Except your final number is the change in momentum, right?
 
  • #14
No because I'm trying to find the final force right? So where the heck does the 0.5 sec fit? change of time??
 
  • #15
thank you for helping me btw
 
  • #16
You are trying to determine the (average) force, F, that acts on the car during the time interval, Δt, of the collision.
(Once the collision is over, there is no force. So, the final force is zero.)

The formula states that the impulse F Δt is equal to the change in momentum. Here, F is the average force during the collision (which is what you want to find). You correctly found the initial and final momenta. You are given the time interval of the collision. So, you're almost there.
 
  • #17
oh! so would the formula be f 0.5 sec=-20000 kg/ms and then do the calculations to it?
 
  • #18
Yes.
 
  • #19
yay! so subtract 0.5 sec to -20000?
 
  • #20
Subtract?
 
  • #21
divide! sorry its been a while with math and science for me lol
 
  • #22
F=40000 kg m/s
 
  • #23
OK. I think you have it. If you get a negative answer for F, you should try to interpret the meaning of the negative answer.
 
  • #24
yes meant to put a negative so would it be F= -40000
 
  • #25
OK. In post # 22 you did not quite get the correct units and you didn't specify the units for F in your last post.

Should the negative result for F be of concern?
 
  • #26
No it shouldn't shoot haha, I wrote down in my notebook that units should be N/ S does that seem right?
 
  • #27
Sarah said:
No it shouldn't shoot haha, I wrote down in my notebook that units should be N/ S does that seem right?
You're calculating a force. What is the SI unit for force?
 
  • #28
N ??
 
  • #29
Yes. You should get Newtons. To see how this comes about, note that solving the formula F Δt = Δp for F gives F = Δp/Δt. Δp has units of mass times velocity, or kg m/s. When you divide by Δt (which has units of seconds), you get that Δp/Δt has units of kg m/s2. You should be able to see that these units are equivalent to Newtons (Think F = ma).
 
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  • #30
I'm not quite sure how to make it not negative
 

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