When two objects collide, their trajectories are determined by the interaction forces between them. If the objects are elastic, their relative velocity after the interaction is determined by the way the interaction force acts between them.
If the force is in the same direction as the relative velocity between the objects, then their velocities will be increased. If the force is in the opposite direction of their relative velocity, then their velocities will be decreased.
When calculating collision velocity outcomes, there are three important things to remember: 1) only perpendicular forces act on each other when objects collide, 2) only elastic collisions matter when determining final velocities, and 3) mass must be accounted for in all calculations (force = mass × acceleration).
This article will explain these concepts in detail and demonstrate how they apply in real-life scenarios.
Calculate the final distances
If the colliding objects stick together, as in the case of a bullet passing through a target before striking a second target behind it, the final velocity of the first target is the total velocity of both objects.
To find the final velocity of the second target, you must calculate the total velocity of both targets and then subtract that from the total velocity of both objects before they stuck together.
The math to figure this out is not simple, and it requires you to know some derivatives. There are many resources online that can help you with this if you are struggling.
If one object sticks to the other after collision, then their relative velocities before and after collision are equal. This is because they have both stopped moving, so their relative velocity is zero. By convention, we assume that the first object has a negative relative velocity prior to collision.
Calculate the final speed for object 1
The final speed of object 1 is calculated by adding the initial speed of object 1 to the final velocity of object 2.
In this case, the initial speed of object 1 is zero, so the final speed is simply the same as the final velocity of object 2. Because the collision was perfectly elastic, object 2 had infinite mass, so its own final velocity became object 1’s initial velocity.
Therefore, after the collision, both objects have the same velocity and are moving in the same direction. This is because both objects exchanged equal amounts of momentum with each other during the collision.
It is important to note that although both objects have identical velocities after a perfectly elastic collision, they do not have to be of the same magnitude as each other.
Calculate the final speed for object 2
Now let’s look at what happens when one object goes into a second object and the collison is elastic. In this case, the second object (object 2) will get a velocity in the opposite direction of object 1.
You can calculate this by using a formula called the law of conservation of momentum. This law states that the total linear momentum before a collision is equal to the total linear momentum after a collision.
Linear momentum is defined as mass times velocity, so you can rephrase this law as mass 1 + mass 2 = total mass × velocity 1 + velocity 2.
So how do we apply this to our If The Collision Is Perfectly Elastic, What Are The Final Velocities V1 And V2 Of Objects 1 And 2? question? Well, we need to know the masses of both objects and their initial velocities before the collision.
Know that the collision was perfectly elastic
When the collision is perfectly elastic, the resulting velocity of both objects is the same and it is the average of their initial velocities. Imagine that object 1 has velocity V1 initially and object 2 has velocity V2 initially.
If they collide and stick to each other, after the collision, object 1 has velocity V1 + V2 and object 2 has velocity V1 – V2.
Since they stuck to each other, they now constitute one new object. Its total initial velocity is the average of V1 and V2, which is (V1 + V2) / 2.
Therefore, after the collision, object 1 moves with average velocity (V1 + V2) / 2 and object 2 moves with average velocity (V1 -V2) / 2. Their final velocities are the same.
Share your knowledge of collisions with others
As we’ve seen, understanding collisions is fundamental to understanding physics. We’ve also seen how you can apply your knowledge of collisions to real-world situations.
If you find that you’re interested in collisions, there are many ways you can study the subject further. Some colleges offer collision studies as a separate department, while other colleges include collision studies as a part of another department, such as physics or engineering.
There are even online courses available for those who are interested in studying collisions further but don’t want to commit to a course load. There are both free and paid options available for those who are interested.
Whether you study collisions formally or just share your knowledge with others, you are helping others understand how they work.
See how much you learned from reading this post with this quiz!
Quiz: If the Collision Is Perfectly Elastic, What Are the Final Velocities V1 and V2 of Objects 1 and 2?
If the collision is perfectly elastic, what are the final velocities V1 and V2 of objects 1 and 2?
Answer: The answer is A. If the collision is perfectly elastic, then object 1 will have the same velocity as object 2. This is because in a perfectly elastic collision, both objects exchange kinetic energy. Therefore, they both have the same velocity after the collision.
It is important to note that this only happens if the collision is perfectly elastic. If there is any inelasticity, then neither object will have the same velocity as the other.
Elastically bound objects return to their original state after collision
If the collision between the two objects is elastic, then both objects will have the same velocity after the collision. This is because they will be forced back into their original positions as a result of the collision.
In other words, they will bounce off of each other and return to their original positions. The more elastic the collision is, the farther they will be pushed back into their original positions.
Imagine holding a ball in your hand and then throwing a second ball at it. If the throw is perfect, then the two balls will pass through each other and return to their original states. This is because of elastic collisions, which happen when the balls are made of similar materials.
Elastic collisions happen because objects with similar properties exchange kinetic energy. When one object passes through another, some of its kinetic energy is transferred to the other object, making it return to its original state as well.
Inelastically bound objects do not return to their original state after collision
If the collision is inelastic, then object 1 will have a higher velocity than object 2. This is because the energy loss from the collision is not in the form of vibration, but rather a transformation of energy to another form, usually thermal energy.
For example, if two balls collide and one ball loses its kinetic energy due to the collision, then after the collision, one ball will have a higher velocity than before because it has less kinetic energy.
By looking at the K-internal link, you can see that after the collision, one ball has a lower internal kinetic energy than before. This is because part of its kinetic energy was transformed to external kinetic energy during the collision.
If you were to weigh both balls after the collision, you would find that one ball is heavier than before, meaning it has less internal kinetic energy due to the inelasticity of the collision.
Leave a Reply