Solving Collison Equations: Step-by-Step Guide

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In summary, the conversation discusses the process of solving equations involving the conservation of momentum and energy. The equations are provided and it is mentioned that conservation of momentum is a vector equation while the energy equation is scalar. It is advised to start by factoring, expanding, or solving one equation and plugging it into the other.
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Super6
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Can anyone help show me the process of solving the equations
(m1*v1)+(M2*V2)=(m1*v1')+(M2*V2')
(.5m1*v1^2)+(.5M2*V2^2)=(.5m1*v1')+(.5M2*V2')

to get the equations

------(m1+M2) (2M2v)
v1'= --------- v1 + ----- V2
------(m1+M2) (m1+M2)


-------(2m1) (M2-m1)
V2'= --------- v1 + ----- V2
------(m1+M2) (m1+M2)


i need the algebra used or at least how i should start i know you solve one and plug it into the other, but I am not sure if i should start by factoring, expanding or what any help would be greatly appreciated
 
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Your equations are full of typographical errors, so it is to understand what you are trying to get.

One hint: conservation of momentum is a VECTOR equation, so it is actually three equations in the three components of velocity. On the other hand, the energy equation is scalar, where the velocity magnitude squared appears.
 

1. What are collision equations?

Collision equations are mathematical equations that are used to calculate the outcome of a collision between two objects. They take into account the mass, velocity, and direction of the objects involved in the collision to determine the resulting velocities and directions after the collision.

2. Why is it important to solve collision equations?

Solving collision equations is important because it helps us understand and predict the outcome of collisions, which occur frequently in the natural world and in various applications such as engineering and physics. By solving these equations, we can determine the forces and energy involved in a collision and make informed decisions about safety measures and design choices.

3. What are the steps involved in solving collision equations?

The steps involved in solving collision equations include identifying the variables, setting up the equations using conservation of momentum and conservation of kinetic energy principles, solving for the unknown variables, and checking the solution for accuracy. It is also important to use the correct units and apply appropriate mathematical operations.

4. Can you provide an example of solving collision equations?

Sure, let's say we have two cars, one with a mass of 1000 kg and a velocity of 20 m/s, and the other with a mass of 1500 kg and a velocity of -10 m/s. They collide head-on and stick together. To find the resulting velocity, we can use the equation (m1v1 + m2v2) / (m1 + m2) = vf, where m1 and v1 are the mass and velocity of the first car, m2 and v2 are the mass and velocity of the second car, and vf is the resulting velocity. Plugging in the values, we get (1000 kg x 20 m/s + 1500 kg x -10 m/s) / (1000 kg + 1500 kg) = vf. Solving for vf, we get a resulting velocity of 5 m/s.

5. Are there any limitations or assumptions when solving collision equations?

Yes, there are some limitations and assumptions when solving collision equations. Some of these include assuming that the collision is elastic (no energy is lost), the objects involved are rigid bodies, and there are no external forces acting on the objects. In reality, these assumptions may not hold true, but they provide a simplified model for solving collision equations.

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