Perpendicular inelastic collision problem

In summary, the conversation is about finding the missing "v" value in a problem involving energy loss in a 1-dimensional inelastic collision. The steps to solve the problem include solving a system of equations and replacing the value of "v" in a specific equation. The final result is an equation for energy loss that includes the reduced mass and the relative velocity of the colliding objects.
  • #1
NODARman
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Homework Statement
Where did "v" go?
Relevant Equations
.
I still don't get it where did "v" go.
I'm trying to solve the problem that is on the second image.
1658833952271.png


Second image.
1658834059120.png
 
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  • #2
Yes well your book doesn't show all the in between steps on how exactly it derives that result. It just states "Sparing the reader the algebra".

What is done in the in between steps (which you should try to work out by yourself, I ll just outline the steps) is that the system of equations 4.5.18 (two equations with two unknowns, the common velocity and the angle) is solved and then once you solve it and find ##v## (##v## will be a function of ##m_1,m_2, v_1,v_2##) then ##v## it is replaced in equation 4.5.19 and then after some algebra you end up with equation 4.5.20.
 
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  • #3
NODARman said:
Homework Statement:: Where did "v" go?
Relevant Equations:: .

I still don't get it where did "v" go.
I'm trying to solve the problem that is on the second image.
View attachment 304812

Second image.
View attachment 304813
There's a general result (which can be derived) for energy loss in a 1 dimensional inelastic (collide and coalesce) collision: $$\Delta E= \frac{1}{2} \mu \Delta v^2$$ where ##\mu## is the reduced mass of the colliding objects and ##\Delta v## their relative velocity: $$\mu = \frac{m_1m_2}{m_1+m_2}$$It looks like there's nothing different here except that ##\Delta v## is replaced by the vector difference of the two velocities.
 
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FAQ: Perpendicular inelastic collision problem

1. What is a perpendicular inelastic collision problem?

A perpendicular inelastic collision problem is a type of collision in which two objects collide at right angles to each other and stick together after the collision, losing some of their initial kinetic energy. This type of collision is also known as a two-dimensional inelastic collision.

2. How is the momentum conserved in a perpendicular inelastic collision problem?

In a perpendicular inelastic collision problem, the total momentum of the system is conserved. This means that the total momentum of the two objects before the collision is equal to the total momentum of the combined object after the collision.

3. What is the equation for calculating the final velocity in a perpendicular inelastic collision problem?

The equation for calculating the final velocity in a perpendicular inelastic collision problem is:
Vf = (m1v1 + m2v2) / (m1 + m2)
where Vf is the final velocity, m1 and m2 are the masses of the two objects, and v1 and v2 are their initial velocities.

4. How is kinetic energy lost in a perpendicular inelastic collision problem?

In a perpendicular inelastic collision problem, kinetic energy is lost due to the deformation and heat generated during the collision. This loss of kinetic energy is represented by the decrease in the final velocity compared to the initial velocities of the two objects.

5. Can a perpendicular inelastic collision problem be solved using the conservation of energy principle?

No, a perpendicular inelastic collision problem cannot be solved using the conservation of energy principle because kinetic energy is not conserved in an inelastic collision. However, the conservation of momentum principle can be used to solve for the final velocities of the objects involved in the collision.

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