1. What are the equations for linear momentum p and kinetic energy K? Please def

Question

1. What are the equations for linear momentum p and kinetic energy K? Please define the variables.

2. Please define concisely and in your own words the concept of conservation. Describe
conservation of momentum and kinetic energy.

3. Briefly describe the difference between elastic and inelastic collisions and give an example of each. Describe these collisions in terms of the kinetic energy and momentum.

4. A moving object collides with and sticks to a stationary object. Do the combined
objects move slower, faster or at the same speed as the original moving object?

5. What is the expected value of the ratio of the final and initial momenta, pf/pi?

Explanation / Answer

(1)

Linear momentum: P = mv

Here mass is m and velocity is v

Kinetic energy: K = 1/2 (m) (v)^2

Another form: K = P^2/ 2m

Here, P momentum

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(2) Conservation of a physical quantity represents that the particular quantity does not change

with respect time. Total quantity does not change.

Conservation of momentum represents total initial momentum is equal to total final momentum

Mathematically, dp/dt = 0 implies that p = constant

Conservation of kinetic energyrepresents total initial kinetic energy is equal to total final kinetic energy.

Mathematically, dK/dt = 0 implies that K = constant

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(3)

In elastic collsion, both momentum and kinetic energy are conserved

Ex: collision between atomic particles

In the case of inelastic collison, only momentum is conserved but not kinetic energy

Ex: collsion between bullet and wood

Note: THe linear momentum is conserved in every collsion, elastic as well as inelastic

In such collision, total energy is conserved.

Kinetic energy alone is not conserved in inelstic collision.

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(4) The given case is inelastic collison.In this case, the ratio of final to initial kinetic energy is less than 1. It represents objects move slower than the original speed after collision

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(5) As the momentum is conserved in every collision, the expected ratio of final momentum to initial momentum is 1.00

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