Which results in a higher force of impact? Assume both collisions are completely inelastic (your car comes to a stop) and both take the same amount of time.
A) Running your car at 20 mph into a solid wall
B) Running your car head-on at 20 mph into an identical car also driving at 20 mph in the opposite
direction
C) The forces are equal
The answer is C but I don't understand why. Can someone explain this to me?
Force equals mass times acceleration...the mass of your vehicle is the same, always. The acceleration is also to be considered the same for both problems. So if both equations, (one for collision with wall, and one for other car) have the same numbers, then the forces are equal. Another way to look at it is to think about the collision itself: what is the speed at the point of impact? It is the same regardless of what object you hit, a wall, a car, or a semi truck...zero.
To understand why the forces in both scenarios are equal, we need to break down the concept of force and collisions.
Force is a measure of the interaction between two objects and is defined as the rate at which an object's momentum changes over time. When two objects collide, they exert forces on each other. In the context of this question, we are considering the force of impact during a collision.
In an inelastic collision, like the ones described, the objects stick together after the collision and come to a stop. This means that the final velocity of the combined mass of the objects is zero.
Now, let's analyze the given scenarios:
A) Running your car at 20 mph into a solid wall:
In this case, the car collides with the wall, comes to a stop, and subsequently, the combined mass of the car and the wall comes to rest. The final velocity of the combined mass is zero.
B) Running your car head-on at 20 mph into an identical car also driving at 20 mph in the opposite direction:
In this scenario, the two cars collide head-on, stick together after the collision, and come to a stop. Again, the final velocity of the combined mass is zero.
In both scenarios, the final velocities are the same, which means the change in momentum is the same. Since force is the rate of change of momentum, and the time taken for both collisions is the same, the force of impact in both cases will also be the same.
Therefore, the correct answer is C) The forces are equal.
By understanding the concept of momentum, inelastic collisions, and the relationship between force and momentum, we can determine that both scenarios will result in the same force of impact.