Finding how long a collision lasts

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In summary, a truck with a mass of 2000 kg and a velocity of 23 m/s collides head-on with a concrete wall, causing the truck to crumple and become 0.67 m shorter. The average velocity during the collision is 11.5 m/s and the question asks for the duration of the collision and the magnitude of the average force exerted by the wall on the truck, which is found to be a large ratio compared to the gravitational force on the truck. The rear bumper only travels 0.67 m during the collision, and the problem can be solved by assuming constant acceleration, although this assumption may not accurately reflect real-life scenarios.
  • #1
Ghost4512
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Homework Statement


In a crash test, a truck with mass 2000 kg traveling at 23 m/s smashes head-on into a concrete wall without rebounding. The front end crumples so much that the truck is 0.67 m shorter than before.

Homework Equations


About how long does the collision last? (That is, how long is the interval between first contact with the wall and coming to a stop?)
Δt = (c) What is the magnitude of the average force exerted by the wall on the truck during the collision?
Fwall, avg = N(d) It is interesting to compare this force to the weight of the truck. Calculate the ratio of the force of the wall to the gravitational force mg on the truck. This large ratio shows why a collision is so damaging.
[Fwall, avg]/mg =


The Attempt at a Solution


Well I figured out that the Average velocity during the collision was 11.5 m/s. But after this I am stuck.
 
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  • #2
Ok, how far does the rear bumper travel during the collision?
 
  • #3
Wouldn't it have only traveled .67 m?
 
  • #4
Yes, so now can you solve for Δt?
 
  • #5
Oh, duh. Thanks.
 
  • #6
paisiello2 said:
Yes, so now can you solve for Δt?
Not so fast, literally.
The speed will not be constant. The acceleration will not be constant either, but you will have to assume a particular time profile for the acceleration in order to solve the problem. The questioner probably expects you to assume constant acceleration.
 
  • #7
I believe the OP did this already.
 
  • #8
Yep.
 
  • #9
O
Ghost4512 said:
Yep.
Ok, but my point is that to do this you had to make an assumption that was not only unjustified but in practice likely to be false.
 

1. How do you determine the duration of a collision?

The duration of a collision can be determined by analyzing the velocity and acceleration of the objects involved in the collision. By measuring the change in velocity over time, the duration of the collision can be calculated.

2. What instruments are used to measure the duration of a collision?

In order to accurately measure the duration of a collision, high-speed cameras and sensors are commonly used. These instruments can capture the movement and velocity of the objects involved in the collision at a very high rate, allowing for precise calculations of the duration.

3. How does the mass of the objects affect the duration of a collision?

The mass of the objects involved in the collision can have a significant impact on the duration. Generally, the greater the mass of the objects, the longer the collision will last. This is because objects with more mass have more inertia, and therefore require more time to change their velocity.

4. Is the duration of a collision the same for all types of collisions?

No, the duration of a collision can vary depending on the type of collision. For example, an elastic collision, where kinetic energy is conserved, will have a shorter duration compared to an inelastic collision, where kinetic energy is lost due to deformation of the objects.

5. How does the speed of the objects affect the duration of a collision?

The speed of the objects involved in a collision can impact the duration, as well. Generally, the faster the objects are moving, the shorter the collision will last. This is because higher speeds result in greater forces and therefore quicker changes in velocity.

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