The total system momentum is conserved. An analysis of the kinetic energy of the two objects reveals that the total system kinetic energy before the collision is Joules J for the truck plus 0 J for the car. After the collision, the total system kinetic energy is Joules J for the truck and J for the car. The total kinetic energy before the collision is not equal to the total kinetic energy after the collision.
A portion of the kinetic energy is converted to other forms of energy such as sound energy and thermal energy. A collision in which total system kinetic energy is not conserved is known as an inelastic collision. For more information on physical descriptions of motion, visit The Physics Classroom Tutorial. Yes, this is a plot of velocity vs. Now for the next and more interesting question. Using the same situation we examined above, which vehicle stops in the shortest distance and why?
Figure it out and explain your answer. I'll wait. Do you have an answer? Are you sure about it? I really ought to just stop here, but I can't leave this question unanswered. I enjoy talking about it too much to do that. Instead of explaining the answer, I will show you the answer.
Here is a numerical calculation of the two vehicles stopping. It's basically the graph above, except you can see the motion of the two objects. Just press play to run it and the pencil to see and edit the code. The big red box represents the truck and the small blue box is the car. You'll notice the two vehicles leave a trail of dots. I did that so you see how fast they are moving.
An arrow represents the velocity of the car. Clearly, the red truck stops first. Let me explain why. When determining the time required to stop an object, it makes sense to use the momentum principle since it deals with time.
To find the distance it takes an object to stop, I must use the work energy principle. Since the two vehicles will have the same acting force on them, I can compare stopping distances by looking at the change in kinetic energy. If the vehicles started with the same kinetic energy, it would take the same amount of work to stop them.
With the same force, this would be the same stopping distance. The fact the two vehicles have the same starting momentum doesn't mean they have the same starting kinetic energy. The car has a lower mass, so it must have a higher velocity in order to have the same momentum as the truck.
But since kinetic energy depends upon the square of the velocity, the higher car velocity matters much more than the lower mass. Both the baseball and the catcher's mitt move with a velocity of The two collisions above are examples of inelastic collisions. Technically, an inelastic collision is a collision in which the kinetic energy of the system of objects is not conserved.
In an inelastic collision, the kinetic energy of the colliding objects is transformed into other non-mechanical forms of energy such as heat energy and sound energy. The subject of energy will be treated in a later unit of The Physics Classroom. To simplify matters, we will consider any collisions in which the two colliding objects stick together and move with the same post-collision speed to be an extreme example of an inelastic collision.
Now we will consider the analysis of a collision in which the two objects do not stick together. In this collision, the two objects will bounce off each other. While this is not technically an elastic collision, it is more elastic than the previous collisions in which the two objects stick together. In this collision, the truck has a considerable amount of momentum before the collision and the car has no momentum it is at rest.
After the collision, the truck slows down loses momentum and the car speeds up gains momentum. Observe in the table above that the known information about the mass and velocity of the truck and car was used to determine the before-collision momenta of the individual objects and the total momentum of the system.
The after-collision velocity of the car is used in conjunction with its mass to determine its momentum after the collision. To determine v the velocity of the truck , the sum of the individual after-collision momentum of the two objects is set equal to the total momentum.
The truck's velocity immediately after the collision is 5. As predicted, the truck has lost momentum slowed down and the car has gained momentum. The three problems above illustrate how the law of momentum conservation can be used to solve problems in which the after-collision velocity of an object is predicted based on mass-velocity information.
There are additional practice problems with accompanying solutions later in this lesson that are worth the practice. However, be certain that you don't come to believe that physics is merely an applied mathematics course that is devoid of concepts. For certain, mathematics is applied in physics. However, physics is about concepts and the variety of means in which they are represented.
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