(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two bodies [tex]A[/tex] and [tex]B[/tex] of mass [tex]m_1[/tex] and [tex]m_2[/tex] are connected via a spring of natural longitud [tex]l_0[/tex] and elastic constant [tex]k[/tex]. Both bodies are free of net force until at an instant [tex]t_i[/tex] something applies a constant force [tex]F[/tex] to the body [tex]A[/tex], in the direction of [tex]B[/tex]. (see the diagram)

a)Calculate the initial acceleration of the center of mass of the system

b)Calculate the initial acceleration of each of the 2 bodies

c)Calculate the respective accelerations in the instant in which the spring is compressed by a length x.

d)Indicate all the pars of action-reaction forces in the moment in which the spring is compressed by a length x.

2. Relevant equations

[tex]F_{spring}=k \varedelta x[/tex]

[tex]\sum \vec{F}=m\vec{a}[/tex].

3. The attempt at a solution

a)Just for fun I calculated the center of mass to be at [tex]\frac{l_0}{m_1+m_2}[/tex] if the origin is situated at body [tex]A[/tex] in instant [tex]t_i[/tex].

I think I've read somewhere that if an external force is applied, then it will modify the acceleration of the center of mass of the system following Newton's second law.

So [tex]\vec{a}_{CM}=\frac{F}{m_1+m_2}i[/tex]. Am I right?

b)Using Newton's second law, [tex]\vec{a}=\frac{F}{m_1+m_2}i[/tex] for the body [tex]A[/tex].

And here start my problems. I'm not sure how to find the acceleration of the body [tex]B[/tex] at [tex]t_i[/tex]. I'm tempted to go against my intuition and say that it will be the same as the center of mass of the system, but I don't think it's possible. Please help me going further this.

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# Homework Help: Problem: two bodies linked via a spring

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