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?
Sure! I can explain why the forces in both scenarios A and B are equal, resulting in choice C.
To understand this, we need to consider the concept of momentum. Momentum is the product of an object's mass and velocity. In the case of a collision, momentum is conserved, which means that the total momentum before the collision is equal to the total momentum after the collision.
In scenario A, your car is running at 20 mph into a solid wall. Let's assume your car has a mass of M and a velocity of 20 mph. The wall is immovable, so its mass is considered infinite. Before the collision, the total momentum is M * 20 mph. After the collision, your car comes to a stop, so its final velocity is 0 mph. The wall remains motionless, so its velocity remains 0 mph. Therefore, the total momentum after the collision is 0 mph, which is equal to the total momentum before the collision.
In scenario B, your car is running head-on at 20 mph into an identical car also driving at 20 mph in the opposite direction. Let's assume both cars have a mass of M. The total momentum before the collision is (M * 20 mph) + (M * (-20 mph)) = 0 mph. This is because the momentum of your car in the positive direction is canceled out by the momentum of the other car in the negative direction. After the collision, both cars come to a stop, so their final velocities are 0 mph. Therefore, the total momentum after the collision is also 0 mph, which is equal to the total momentum before the collision.
Since the total momentum before and after the collisions in both scenarios A and B is the same (0 mph), the forces exerted on the cars are equal in magnitude. Hence, the correct answer is choice C: the forces are equal in both scenarios.