Physics
Collisions
Elastic Potential Energy and Collisions
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⚡ Quick Summary
When objects collide, kinetic energy can be converted into elastic potential energy, especially if a spring is involved. During the collision, the objects may deform, storing energy. How the objects behave after this point depends on whether they are elastic or inelastic. Elastic collisions conserve kinetic energy, while inelastic collisions do not.
['1/2 * m1 * u1^2 + 1/2 * m2 * u2^2 + 1/2 * k * x^2 = E (Energy conservation with spring)', "m1v1 + m2v2 = m1v1' + m2v2' (Conservation of Kinetic Energy)", 'm1v1 + m2v2 = (m1+m2)V (Conservation of momentum in inelastic collision)']
Elastic Potential Energy in Collisions: When two objects collide, and a spring is involved, the kinetic energy is converted to elastic potential energy as the spring compresses. The total energy of the system is conserved. The kinetic energy changes during the interval of compression. The compression is maximum when the velocities of the objects are equal.
Collisions without a Spring: During a collision, the objects deform, and kinetic energy is converted into elastic potential energy of the deformed objects. The deformation is maximum (kinetic energy is minimum) when the two objects attain equal velocities. Total momentum is always conserved.
Elastic Collisions: If the colliding objects are perfectly elastic, they regain their original shapes after maximum deformation, converting the elastic potential energy back into kinetic energy. Kinetic energy is conserved overall (initial KE = final KE), although it changes during the collision.
Inelastic Collisions: If the colliding objects are perfectly inelastic, they do not regain their original shapes. They continue to move together with a common velocity after deformation. Kinetic energy is not conserved; it decreases during the deformation and remains constant at the decreased value after that.
Elastic and Inelastic Collisions
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⚡ Quick Summary
Collisions can be elastic (kinetic energy conserved) or inelastic (kinetic energy not conserved). Momentum is always conserved in collisions.
None explicitly stated in the extract.
- Elastic Collision: A collision in which the total kinetic energy of the system is conserved.
- Inelastic Collision: A collision in which the total kinetic energy of the system is not conserved (typically converted to heat or other forms of energy).
- Momentum Conservation: The total momentum of a closed system remains constant if no external forces are acting on the system.
Coefficient of Restitution
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⚡ Quick Summary
The coefficient of restitution (e) is a measure of how much kinetic energy is conserved in a collision. It's the ratio of the relative velocity of separation to the relative velocity of approach.
e = |(v2f - v1f)| / |(v1i - v2i)|
The coefficient of restitution (e) is defined as: e = (Relative velocity of separation) / (Relative velocity of approach) = |(v2f - v1f)| / |(v1i - v2i)|, where v1i and v2i are the initial velocities of the two objects before collision, and v1f and v2f are their final velocities after collision.
Inelastic Collision
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⚡ Quick Summary
In an inelastic collision, kinetic energy is not conserved. Some of the kinetic energy is converted into other forms of energy such as heat or sound.
Conservation of Momentum: m1v1i + m2v2i = m1v1f + m2v2f
In an inelastic collision, momentum is conserved, but kinetic energy is not. Some kinetic energy is lost, often converted to heat, sound, or deformation of the objects involved.