Conservation of kinetic energy

In summary, the conservation of kinetic energy states that in an elastic collision, there is no loss of kinetic energy, while in an inelastic collision, part of the kinetic energy is converted into other forms of energy. This principle is useful in calculating the final velocities of objects involved in a two-body collision, assuming conservation of momentum as well. In ideal gases and sub-atomic particle interactions, collisions can approach perfect elasticity, while in large-scale interactions like gravitational interactions, perfect elasticity is possible. The principle can be applied to calculate the kinetic energy before and after a collision, as shown in the example provided.
  • #1
kreb11
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Homework Statement


I am asked to explain the conservation of kinetic energy

I am having trouble finding this..I do know that kinetic eneergy is conserved in an elastic collision and part of the KE is changed to some other form of energy in an inelastic collision
 
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A perfectly elastic collision is defined as one in which there is no loss of kinetic energy in the collision. An inelastic collision is one in which part of the kinetic energy is changed to some other form of energy in the collision. Any macroscopic collision between objects will convert some of the kinetic energy into internal energy and other forms of energy, so no large scale impacts are perfectly elastic. Momentum is conserved in inelastic collisions, but one cannot track the kinetic energy through the collision since some of it is converted to other forms of energy. Collisions in ideal gases approach perfectly elastic collisions, as do scattering interactions of sub-atomic particles which are deflected by the electromagnetic force. Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are perfectly elastic.

Collisions between hard spheres may be nearly elastic, so it is useful to calculate the limiting case of an elastic collision. The assumption of conservation of momentum as well as the conservation of kinetic energy makes possible the calculation of the final velocities in two-body collisions.

We are now going to see an example of how to use this “principle” which i am going to call the “principle of conservation of kinetic energy”.

Fig 1 below shows two objects traveling towards each other and fig 2 shows the two objects separating after the two objects have separated.

So if the principle of conservation of kinetic energy applies then it means that Sum of kinetic energy before collision = sum of kinetic energy after collision

http://lh3.ggpht.com/_MLcxcpYx4ws/S4iqI2bfwVI/AAAAAAAAAbI/zY5-598E6dQ/s1600-h/clip_image001%5B5%5D.gif

Fig 1 Before collision

Before the collision

Sum of kinetic energy before collision = kinetic energy of object 1 + kinetic energy of object 2

= 1/2m1u12 + 1/2m2v12

http://lh3.ggpht.com/_MLcxcpYx4ws/S4iydzx3GVI/AAAAAAAAAbQ/YgNllKXs98c/s1600-h/clip_image001%5B6%5D%5B4%5D.gif

Fig 2 After collision


After the collision
Sum of kinetic energy after collision = kinetic energy of object 1 + kinetic energy of object 2

= 1/2m1u22 + 1/2m2v22

If you refer back to the principle then

Sum of kinetic energy before collision = sum of kinetic energy after collision

1/2m1u12 + 1/2m2v12 = 1/2m1u22 + 1/2m2v22
 
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1. What is the definition of conservation of kinetic energy?

The conservation of kinetic energy is a fundamental principle of physics which states that the total amount of kinetic energy in a closed system remains constant over time. This means that energy cannot be created or destroyed, only transferred from one form to another.

2. How does the conservation of kinetic energy relate to the law of conservation of energy?

The conservation of kinetic energy is a specific application of the law of conservation of energy. The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. The conservation of kinetic energy specifically refers to the transformation of kinetic energy within a closed system.

3. Does the conservation of kinetic energy apply to all types of energy?

No, the conservation of kinetic energy only applies to mechanical energy, which includes the energy of an object in motion. Other forms of energy, such as thermal energy or chemical energy, do not necessarily follow the principle of conservation of kinetic energy.

4. Is the conservation of kinetic energy affected by external forces?

No, the conservation of kinetic energy is not affected by external forces as long as the system remains closed. External forces may change the amount of kinetic energy within the system, but the total amount of kinetic energy will remain constant.

5. What are some real-life examples of the conservation of kinetic energy?

One example of the conservation of kinetic energy is a pendulum. As the pendulum swings back and forth, the potential energy at the top of the swing is converted into kinetic energy at the bottom of the swing and vice versa. The total amount of kinetic energy remains constant throughout the motion. Another example is a rollercoaster, where the potential energy gained from climbing to the top of a hill is converted into kinetic energy as the car moves down the hill.

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