Inelastic Collision with Spring

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Homework Help Overview

The problem involves a .2 kg mass colliding inelastically with a 1.3 kg mass at rest, which is connected to a spring. The scenario is set on a frictionless horizontal surface, and the objective is to analyze the linear momentum and kinetic energy of the combined masses immediately after the impact, while also considering the role of the spring.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply the conservation of momentum to find the final velocity after the collision and then calculate kinetic energy. However, they express uncertainty about how to incorporate the spring into their calculations.
  • Some participants clarify the momentum equation and confirm the known variables, while others suggest that the spring primarily serves to transfer energy rather than directly affecting the momentum calculation.
  • There is a discussion about equating kinetic energy of the masses to the potential energy stored in the spring, with one participant attempting to derive the spring compression and force.

Discussion Status

The discussion is active, with participants exploring different interpretations of how the spring affects the energy transfer during the collision. Some guidance has been offered regarding the relationship between kinetic and potential energy, but there is no explicit consensus on the next steps for solving the problem.

Contextual Notes

Participants are navigating the complexities of energy conservation in the context of an inelastic collision, with specific attention to the spring's role. The original poster's confusion about the spring's involvement indicates a need for further clarification on energy transformations in this scenario.

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Homework Statement


A .2kg mass traveling on a frictionless horizontal surface at a speed of 3 m/s. It hits a 1.3 kg mass at rest that is connected to a massless spring with a a spring constant of 100 Newtons per meter. The other end of the spring is fixed. Calculate the linear momentum and kinetic energy of the combined masses immediately after the impact.

Homework Equations


I can calculate the combined momentum of the masses but I don't know what to do with the spring.

The Attempt at a Solution



The inelastic equation formula is
(m1)(v1) + (m2)(v2) = (m1 + m2)(vf) where vf is the new velocity and then I would just plug in vf into:
KE = 1/2(m)(v)^2
as v and get the kinetic energy. My problem is I don't know what to do with the spring.
 
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So you know that (m1)(v1) + (m2)(v2) = (m1 + m2)(vf) from conservation of momentum.

You know m1,m2,v1 and v2 right? The question basically wants you to find the value of (m1+m2)(vf)
 
I get that but don't I have to do something with the spring?
 
Not really. The spring simply transfer the energy. Think of it as a mediator.

KE of car 1 collide with car 2 ==> KE becomes PE in the spring ==> Spring Potential Energy pushes the on car 2 and becomes potential energy

(assuming all energy is conserve and there is no heat loss anywhere)

So spring is just there.Now, the fun question is: calculate the kinetic energy when the spring is being compress. Now then, you need to account for it, since the spring is potential rather than kinetic energy
 
So do i just set the kinetic energy of the masses equal to the potential energy of the spring like so:
(1/2)mv^2 = (1/2)(k)(x)^2 ==> .5(1.5)(.4)^2 = .5(100)(x)^2
==> .12J = 50x^2 so .0024 = x^2 ==> and Squareroot(.0024) = .0489m = x

Then I plugged it in F = kx and got 4.89N which is the force of the spring.
Now I'm stuck, a little help on how this helps me solve for the linear momentum or kinetic energy of the masses after impact.
 

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