Question

Consider two less-than-desirable options. In the first you are driving 30 mph and crash head-on into an identical car also going 30 mph. In the second option you are driving 30 mph and crash head-on into a stationary brick wall. In neither case does your car bounce off the thing it hits, and the collision time is the same in both cases. Which of these two situations would result in the greatest impact force?

Answer 1

These two situations would result in the greatest impact force: The force would be the same in both cases.

Explanation:

Consider two less-than-desirable options. In the first you are driving 30 mph and crash head-on into an identical car also going 30 mph. In the second option you are driving 30 mph and crash head-on into a stationary brick wall. In neither case does your car bounce off the thing it hits, and the collision time is the same in both cases. Which of these two situations would result in the greatest impact force?

$F \Delta t= m \Delta V$ where

• The force would be the same in both cases.
• Hitting the brick wall
• Hitting the other car
• None of the above choices are correct

Newton 3rd law stated that for every action, there is an equal and opposite reaction.

For example the forces on the trucks are equal but opposite in the direction. Newton 3rd law of impulse stated about momentum formula.  Impulse is force multiplied by time, whereas the time of contact is the same for both, therefore the impulse is the same in magnitude for the two trucks.

Let's look on the attached picture. The case of hitting the brick wall have the same impact force as hitting the other car, because they have the same change in momentum and it doesn't matter what the source is. In first case both the cars are identical and have same velocity whereas in the second case, the wall is stationary.  Also, in both the cases the car does not bounces off the things it hit.

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Answer 2

Answer:

The impact force will be same for both the cases.

Explanation:

The rate of change of momentum is known as the Impulse and is given by:

$I = \frac{\Delta p}{\Delta t}$

where

I = Impulse

$\Delta p = change in momentum$

$\Delta t = time interval$

Now,

In first case both the cars are identical and have same velocity and in the second case, the wall is stationary.

Also, in both the cases the car does not bounces off the things it hit.

Thus

$\Delta p = 0 - m\times v = - mv$

Thus

Impact force, $F = \frac{\Delta p}{\Delta t} = \frac{m\Delta v}{\Delta t}$

Therefore, impact force is same for both the cases.