Two blocks of mass 2kg each are connected by a spring of constant 1000 N/m. Initially, the spring is at the natural length. A force of 10 N is applied to the 1st block. At 0.1 sec, the extension in the spring is seen to be 1 cm. What is the displacement of the block A (in cm) till that time as seen from ground.

Engineering

Physics

Center of Mass

Question

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$a_{cm} = \frac{F}{m + m} = \frac{F}{2 m}$

$\frac{1}{2} \times 2.5 \times (0.1)^{2} = s_{c}$

$\frac{5}{400} m = s_{c}$

In C-frame

Displacement of A in C-fram

$s_{ac} - s_{bc} = s_{ab} = \frac{1}{100}$

2s_ac + 2s_bc = 0
s_ac = –s_bc

$2 s_{ac} = \frac{1}{100}$

$s_{ac} - s_{c} = s_{ac} = \frac{1}{200}$

$s_{a} = \frac{5}{400} + \frac{1}{400} = \frac{7}{400}$

Total displacement A = s_c + s_ac