Consider a perfectly inelastic head-on collision between a small car and a large truck traveling at the same speed. Which vehicle has a greater change in kinetic energy as a result of the collision?
Since the vehicles stick together after the collision and take the direction of the large truck (greater momentum), I guessed that the small car would have a greater change in kinetic energy.
I can easily use formulas to find answers, but I always have trouble with conceptual questions like this.
In a perfectly inelastic collision, the two objects stick together after colliding and move as one unit. The kinetic energy is not conserved in this type of collision, and some of it is converted into other forms of energy, such as heat or deformation of the objects involved.
To determine which vehicle has a greater change in kinetic energy, we need to analyze the factors that contribute to the final outcome of the collision.
1. Mass: The larger the mass of an object, the greater its kinetic energy for a given speed.
2. Speed: The faster an object is moving, the greater its kinetic energy.
Based on these factors, we can conclude that the vehicle with the greater change in kinetic energy would be the one that has the higher initial kinetic energy.
In this scenario, both the small car and the large truck are traveling at the same speed before the collision. However, the large truck has a greater mass than the small car. Therefore, the large truck has a higher initial kinetic energy.
During the perfectly inelastic collision, the two vehicles stick together and move in the direction of the large truck. Since the small car has a lower initial kinetic energy, the change in its kinetic energy is smaller compared to the large truck.
Therefore, in a head-on collision between a small car and a large truck traveling at the same speed, the large truck would have a greater change in kinetic energy as a result of the collision.
To answer this conceptual question, let's break it down step by step.
In a perfectly inelastic collision, the objects stick together and move as one object after the collision. This means that both the small car and the large truck will have the same final velocity after the collision.
When we consider the change in kinetic energy, we need to think about the initial and final kinetic energies of the objects involved. The initial kinetic energy is given by the equation K = 0.5 * m * v^2, where m is the mass and v is the velocity.
Since the small car and the large truck are traveling at the same speed, their initial kinetic energies will be equal, assuming their masses are not equal. However, after the collision, their masses combine into one object, so the final kinetic energy will depend on the final velocity of this combined object.
In a head-on collision, the direction of the larger momentum object will dominate, meaning that the smaller car will take the direction and velocity of the truck. Since the final velocity after the collision is the same for both the car and the truck (the velocity of the truck), the final kinetic energy will also be the same for both objects.
Therefore, the change in kinetic energy after the collision will be the same for both the small car and the large truck.
Hmmmm. What is a perfectly inelastic collision as compared to an inelastic collision?
Momentum is conserved.
Mv-mv= initial momentum
after the collision...
Mv-mv=(M+m)v'
now which is greater?
v-v', or -v-v' Obviously, the smaller mass is greater (-v-v').