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In an elastic collision between two objects do both objects have the same kinetic energy after the collision as before?
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
What else can I help you with?
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 happens to the kinetic energy in a perfectly elastic collision between two perfectly rigid objects?
In a perfectly elastic collision between two perfectly rigid objects, the kinetic energy is conserved. This means that the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
How is energy conserved in an elastic collision between two objects?
In an elastic collision between two objects, energy is conserved because the total kinetic energy before the collision is equal to the total kinetic energy after the collision. This means that no energy is lost or gained during the collision, and it is transferred between the objects without any loss.
How is energy conserved in an elastic collision?
In an elastic collision, energy is conserved because the total kinetic energy before the collision is equal to the total kinetic energy after the collision. This means that the energy is not lost or gained during the collision, but rather transferred between the objects involved.
What factors must be considered in analyzing a head-on elastic collision between two objects?
When analyzing a head-on elastic collision between two objects, factors to consider include the masses of the objects, their velocities before and after the collision, the angle of impact, and the coefficient of restitution. These factors help determine the conservation of momentum and kinetic energy in the collision.
What does it mean when a collision is elastic and how does it differ from an inelastic collision?
In an elastic collision, kinetic energy is conserved and the objects bounce off each other without losing energy. In an inelastic collision, kinetic energy is not conserved and some energy is lost as the objects stick together or deform.
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.
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 are the characteristics and outcomes of a partially elastic collision between two objects?
In a partially elastic collision between two objects, some kinetic energy is conserved while some is lost as heat or sound. The objects may stick together briefly before separating. The outcome depends on the masses and velocities of the objects involved.
What is the final velocity of two objects after an elastic collision?
In an elastic collision, the final velocity of two objects can be calculated using the conservation of momentum and kinetic energy principles. The final velocities depend on the masses and initial velocities of the objects involved in the collision.
What is elastic and inelastic collisions in terms of momentum?
In elastic collisions, both momentum and kinetic energy are conserved. This means that momentum before and after the collision is the same, and the objects bounce off each other without any loss of kinetic energy. In inelastic collisions, momentum is conserved but kinetic energy is not. Some kinetic energy is converted into other forms of energy, such as heat or sound, during the collision.
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.
What is the difference between an elastic collision and an inelastic collision?
No loss in energy due to collision is for elastic collision. But there will be a loss during collision in case of in-elastic collision. So KE will remain constant before and after collision in case of elastic collision.
