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In an elastic collision between two objects do both objects have the same kinetic energy after the collision as before?
Wiki User
∙ 14y ago
In an elastic collision between two objects do both objects have the same kinetic energy after the collision as before?
Let's do the problem and see
The problem below will prove that in an elastic collision between two objects the objects do not have the same kinetic energy after the collision as before?
But the KE before collision = KE after collision
A 2 kg object with velocity of 8 m/s E hits a 5 kg object with a velocity of 5m/s W. What is the velocity of both objects after colision?
East is positive, West is negative
Draw a picture showing the 2 objects before and after collisions.
…..8 m/s……………....-5 m/s………….V2…………….V5
...2kg object..-->….<--5 kg object…..2kg object…….5kg object W……………………………………………………………….E
Mom = +16………..Mom = -25………..2V2……………5V5
Momentum = mass * velocity
Since the 5 kg object has more momentum, both objects will continue to move West. They should have negative velocities!!
Momentum = mass * velocity
Total momentum before collision = (2 * 8) + (5 * -5) =
Total momentum before collision = 16 + -25 = -9
Total momentum before collision = -9
Total momentum after collision = (2 * V2) + (5 * V5)
Momentum is always conserved.
Total momentum after collision = Total momentum before collision
2V2 + 5V5 = -9 = (add - 2V2 and +9 to both sides)
2V2 = -9 - 5V5 , (divide by -2)
V2 = -4.5 - 2.5V5
Eq. momentum = V2 = -4.5 - 2.5V5
Since the collision is elastic, kinetic energy is conserved
KE before collision = KE after collision
KE ½ mass * velocity ^2
KE before collision = ½ * 2* 8^2 + ½ * 5 * 5^2 =
KE before collision = 64 + 62.5 =
KE before collision = 126.5
KE after collision = ½ * 2 * V2^2 + ½ *5 *V5^2
KE before collision = KE after collision
126.5 = ½ * 2 * V2^2 + ½ *5 *V5^2
126.5 = V2^2 + 2.5 *V5^2
Eq. energy = V2^2 + 2.5 *V5^2 -126.5 =0
Now we have 2 equations in 2 unknowns
Substitute the value of V2 from Eq.m into Eq.e
V2 = -4.5 - 2.5V5
(-4.5 - 2.5V5)^2 + 2.5V5^2 -126.5 = 0
(20.25 + 22.5V5 + 6.25V5^2) + 2.5V5^2 -126.5 =0
Add (6.25V5^2 + 2.5V5^2) = 8.75V5^2
Subtract (20.25 - 126.5) = -106.25
8.75V5^2 + 22.5V5 -106.5 =0
Use quadratic equation to solve for V5
V5 =[ -22.5 ± [22.5^2-(4 * 8.75 * -106.25)]^0.5] ÷ (2 * 8.75)
V5 = [-22.5 ± [506.25 + 3718.75]^0.5] ÷ 17.5
V5 = [-22.5 ± [4225]^0.5] ÷ 17.5
The square root of 4225 = ± 65, I will try +65 first and try add +65 first.
V5 = [-22.5 + 65] ÷ 17.5
V5 = +42.5 ÷ 17.5
V5 = +2.42857
This means the 5 kg object is going East. I made this statement at the beginning. "Since the 5 kg object has more momentum, both objects will continue to move West." V5 = +2.4286 is wrong
I will try subtract +65.
V5 = [-22.5 - 65] ÷ 17.5
V5 = -87.5 ÷ 17.5
V5 = -5
That can not be true, because that was the velocity of the 5 kg in the beginning.
I will try using - 65 for the square root of 4225, and add.
V5 = [-22.5 + -65] ÷ 17.5
V5 = -87.5 ÷ 17.5
V5 = -5
That can not be true, because that was the velocity of the 5 kg in the beginning.
Last but not least, I will using - 65 for the square root of 4225, and subtract.
V5 = [-22.5 - -65] ÷ 17.5
V5 = +42.5 ÷ 17.5
V5 = +2.42857
I know the answer has to be V5 = -2.42857.
If the -22 was +22.5, I would get the correct answer..
If you find the mistake, email me at morrison60957@yahoo.com
V5 = [+22.5 - 65] ÷ 17.5
V5 = -42.5 ÷ 17.5
V5 = -2.42857
I will copy, paste the area where I believe my mistake is at the bottom of this work. If you find my mistake let me know!!
V5 = -2.42857
Eq. momentum = V2 = -4.5 - 2.5V5
V2 = -4.5 - (2.5* -2.42857)
V2 = -10.5714
Let's see if the momentum = -9
Total momentum after collision = (2 * -10.5714) + (5 * -2.42857)
Total momentum after collision = -21.142853 + 12.14285 = -9.000003
Now let's see if the Kinetic energy is conserved
KE before collision = 126.5
KE after collision = ½ * 2 * V2^2 + ½ *5 *V5^2
126.5 = ½ * 2 * (-10.5714)^2 + ½ *5 *(-2.42857)^2
126.5 = 111.754498 + 14.75588061
126.5 ≈ 126.49993786 OK
KE before collision = 64 + 62.5
KE of 2 kg object = 64 J
KE of 5 kg object = 62.5 J
Sum of KE = 126.5
KE after collision = 64 + 62.5
KE of 2 kg object after collision = 111.754498 J
KE of 5 kg object after collision = 14.75588061 J
Sum of KE after collision = 126.49993786
I have proved that in an elastic collision between two objects the objects do not have the same kinetic energy after the collision as before?
But the KE before collision = KE after collision
Below is the work where I suspect I have made a mistake, If you find the mistake, email me at morrison60957@yahoo.com
Momentum = mass * velocity
Total momentum before collision = (2 * 8) + (5 * -5) =
Total momentum before collision = 16 + -25 = -9
Total momentum before collision = -9
Total momentum after collision = (2 * V2) + (5 * V5)
Momentum is always conserved.
Total momentum after collision = Total momentum before collision
2V2 + 5V5 = -9 = (add - 2V2 and +9 to both sides)
2V2 = -9 - 5V5 , (divide by -2)
V2 = -4.5 - 2.5V5
Eq. momentum = V2 = -4.5 - 2.5V5
V2 = -4.5 - 2.5V5
(-4.5 - 2.5V5)^2 + 2.5V5^2 -126.5 = 0
(20.25 + 22.5V5 + 6.25V5^2) + 2.5V5^2 -126.5 =0
Add (6.25V5^2 + 2.5V5^2) = 8.75V5^2
Subtract (20.25 - 126.5) = -106.25
8.75V5^2 + 22.5V5 -106.5 =0
Wiki User
∙ 14y ago
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What is perfectlyinelastic collision?
I'm not sure what you mean by "stronger" A perfectly inelestic collision is an ideal event in which none of the kinetic energy of the colliding bodies id tranferred into them as vibrations of their own molecules, i.e. transformed into heat. In an elastic collision, which always happens in the real world, some, or even all, of the kinetic energy of the two objects will be transformed into heat vibrating their molecules. This means that in an inelastic cillision, the bodies final velocities will add up to less than the total velocities that had before the collision, In the ideal state of an inelastic collision though, the sum of their final velocities must equal the sum of their final velocities.
What happens when another object collides with another object?
Newton's Third Law is closely related to Conservation of Momentum. When objects collide, whether the collision is elastic or not, momentum is conserved. (An elastic collision is one in which mechanical energy is conserved. In an elastic collision, after the collision, the objects go away at the same relative speed at which they approached before the collision.)
Is The gravitational force between two objects depends on the distance between the objects and each objects what?
Mass
Objects that are able to fall have what type of energy?
When a body is supported at a height, it has potential energy. When it is released, it will start to fall. As the downward velocity increases, so kinetic energy increases. The potential energy is reduced as the height of the body decreases.
What happens when sound waves from one object cause another object to vibrate?
When two objects collide they can undergo three possible collisions: perfectly inelastic, inelastic, and perfectly elastic. The first type, perfectly inelastic, is when the two objects stick together and become one, like the collusion of two cars and their hoods scrunch up. Perfectly elastic, on the other end of the scale, results in rebound of the two objects without any lost to kinetic energy, these collisions only occur at the atomic level. The third category is everything that lies between the two: inelastic. The objects do rebound to a certain degree, but kinetic energy is not conserved. Thus, the energy of motion must be converted to another type of energy. Thus, when two object collide, the most common forms of energy that kinetic energy is converted to are sound energy and thermal energy. A simple proof of the energy conversion is the simple clapping of hands, if you clap long enough, your hands get warmer, and of course sound is produced.
What is elastic and inelastic collision?
In an elastic collision, no kinetic energy is lost, and the relative speed of separation of the objects after the collision is the same as the relative speed before the collision. In an inelastic collision, part of the elastic energy is lost, and the relative speed after the collision is less.
What is kinetic to kinetic energy?
same if none has been lost. ke=0.5Xmv(squared) GPE=massxgravityxheight
Comparison between elastic and inelastic collision?
In an elastic collision, all initial kinetic energy is fully restored as final kinetic energy. where nothing is converted into noise, heat or any other form of energy. In an inelastic collision, kinetic energy is "lost" to thermal or sound energy.
Need an explanation why kinetic energy is always conserved during elastic collision what is meant by conserved?
In this context "conserved" means the total kinetic energy of all the objects is the same after the collision as before the collision. Note, the TOTAL is the same but the individual kinetic energies of each object may be different before and after. When two or more objects are about to collide they have a certain total kinetic energy. It is common that during the collision some of the kinetic energy is transformed into heat. So after the collision the total kinetic energy is less then before the collision. This is a non-elastic collision. There are some collisions, however, in which none of the kinetic energy is changed to heat. These are called ELASTIC collisions. So the total kinetic energy doesn't change, or is "conserved". There is another possible non-elastic collision. If during the collision there is an explosion, then its possible for the objects to have a larger total kinetic energy after the collision as they aquire some of the explosive energy. Finally note, that in all collisions the TOTAL vector momentum is the same just before and just after the collision. So in a collision momentum is always conserved.
What is the difference between elastic and inelastic collisions?
Elastic Collision is the collision in which colliding objects rebound without lasting deformation or heat generation.Inelastic collision is a collision in which the colliding objects become distorted and generate heat during collision and possibly stick together.
Can an object have momentum and kinetic energy but have no force?
Because momentum has a direction, it can be used to predict the resulting direction of objects. An elastic collision is one in which no kinetic energy is lost.
When a car hits another car what kind of energy is that?
There are two kinds of collision - elastic and inelastic. In an elastic collision, all the kinetic energy remains kinetic, though it might be transferred between objects in the collision. So the initially moving object could bounce back with the hit object staying in place, or the hit object might move and the initially moving object might stop. Or it might be a mix of both. Not only things that you think of as elastic have elastic collisions. Very hard things sometimes tend to have elastic collisions too. Not only rubber balls but also billiard balls and baseballs tend to have elastic collisions. The other type of collision is an inelastic collision. Some of the energy can remain in a kinetic form. The rest is converted to heat, sound, and breaking or deformation of the colliding objects.
What energy is in elastic objects?
kinetic and elastic potential energy
What is the difference between inelastic collision and perfectly inelastic collision?
In an inelastic collision kinetic energy is lost (generally through energy used to change an objects shape), but the two objects rebound off each other with the remaining kinetic energy. In a perfectly inelastic collision the two objects stick together after the collision.
When 2 objects of the same mass traveling at the same speed collide is the energy canceled out?
The answer depends on the material of the objects. In physics, one useful concept is the concept of a perfect elastic collision, which is an idealization of the real world. An elastic collision is a collision where no deformation of objects is taking place, and thus the kinetic energy of the moving objects is preserved as no kinetic energy is transformed to heat or work during an elastic collision. In short, for elastic collisions, kinetic energy is preserved and not canceled out. In reality, there will always be some (or a lot) loss of kinetic energy to heat or work done in deforming objects, think of a car crash where there is a lot of kinetic energy spent in deformation of the cars (modern cars are designed to absorb a maximum amount of kinetic energy to be converted into deformation of objects in order to save lives), but in practical life there are many situations where the fraction of kinetic energy lost to heat or work during a collision may be neglected as it is very small. A good demonstration in real world is colliding billiard balls, or the stones used in the sport of curling, these kind of collisions may for practical purposes be considered elastic. The sum of kinetic energy and the sum of momentum for the moving objects are the same before and after the collision. This means, if 2 equal objects of same mass and same speed but opposite direction of movement collide head on in an elastic collision, their direction of movement will be reversed and their speed will be the same as before collision. Think of two equal billiard balls travelling at same but opposite speed colliding head on. When a moving object hits a moving object at an angle, or at rest or travelling at different speed or is of different mass, that is a different story, but the same rules of physics apply of course, the speed and directions of movement of the objects after any elastic collision may be easily calculated using Newton's laws.
What would have happened to the gas if the molecular collisions were not elastic?
In an inelastic collision, part of the kinetic energy is absorbed by the colliding objects, and converted into heat. For an inelastic collision to occur between molecules, the energy would need to be absorbed at some lower level.
What collision produces more energy?
That depends what you mean by "produce". You may be aware that you can't create energy where there was none before.In a perfectly elastic collision, no kinetic energy is lost.In an inelastic collision (the objects stick together after the collision), much of the kinetic energy is converted into other forms of energy, mainly heat.
