Two masses m1 and m2 are connected by a massless spring of spring constant k and unstretched length ℓ. The masses are placed on a frictionless straight channel – which we consider our x - axis. They are initially at rest at x = 0 and x = ℓ, respectively. At t = 0, a velocity of v0 is suddenly imparted to the first mass. At a later time t, the center of mass of the two masses is at

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Physics

Center of Mass

Question

Two masses m₁ and m₂ are connected by a massless spring of spring constant k and unstretched length ℓ. The masses are placed on a frictionless straight channel – which we consider our x - axis. They are initially at rest at x = 0 and x = ℓ, respectively. At t = 0, a velocity of v₀ is suddenly imparted to the first mass. At a later time t, the center of mass of the two masses is at

$x = \frac{m_{2} l}{m_{1} + m_{2}} + \frac{m_{2} v_{0} t}{m_{1} + m_{2}}$

$x = \frac{m_{1} l}{m_{1} + m_{2}}$

$x = \frac{m_{1} l}{m_{1} + m_{2}} + \frac{m_{2} v_{0} t}{m_{1} + m_{2}}$

$x = \frac{m_{2} l}{m_{1} + m_{2}} + \frac{m_{1} v_{0} t}{m_{1} + m_{2}}$

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$x_{0 c} = \frac{m_{1} 0 + m_{2} l}{m_{1} + m_{2}}$

$v_{c} = \frac{m_{1} v_{0}}{m_{1} + m_{2}} \Rightarrow x_{c} = x_{0 c} + v_{c} t$ .

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