Question

Two identical particles $A$ and $B$, each of mass $m$, are interconnected by a spring of stiffness $k$. If the particle B experiences a force $F \&$ the elongation of the relative spring is $x$, the relative acceleration between the particles is equal to:

• A. $F / 2 m$
• B. $\frac{ F - kx }{ m }$
• C. $\frac{F-2 k x}{m}$
• D. $\frac{k x}{m}$

Answer 1

Answer: (C)

Equation of motion for $A: T=m a$
$\Rightarrow a =\frac{ T }{ m }=\frac{ kx }{ m }$ for $B : F - T = ma ^{\prime}$
$\Rightarrow a ^{\prime}=\frac{ F - kx }{ m }$
$\Rightarrow $ The relative acceleration
$a_{r}=\left|a^{\prime}-a\right|=\frac{F-2 k x}{m}$