(C) For the $1 \ kg$ block to never move,the maximum spring force must be less than or equal to the limiting friction acting on it.$F_{s,max} \le f_{l

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(C) For the $1 \ kg$ block to never move,the maximum spring force must be less than or equal to the limiting friction acting on it.$F_{s,max} \le f_{l} = \mu m_{2} g$$kx = \mu m_{2} g$$8 \times x = 0.8 \times 1 \times 10$$8x = 8 \implies x = 1 \ m$Now,apply the work-energy theorem to the $2 \ kg$ block system. The work done by friction on the $2 \ kg$ block as it moves by distance $x$ is $W_{f} = -\mu m_{1} g x$.The energy balance is: $\frac{1}{2} m_{1} u^{2} = \frac{1}{2} k x^{2} + \mu m_{1} g x$$\frac{1}{2} \times 2 \times u^{2} = \frac{1}{2} \times 8 \times (1)^{2} + 0.8 \times 2 \times 10 \times 1$$u^{2} = 4 + 16$$u^{2} = 20$$u = \sqrt{20} \ m/s$

Class 11 Physics Newton's Laws of Motion and Friction Mix Examples-Newton's Laws of Motion and Friction

Difficult

Two blocks of mass $2 \ kg$ and $1 \ kg$ are connected by an ideal spring on a rough surface. The spring is unstretched. The spring constant is $8 \ N/m$. The coefficient of friction is $\mu = 0.8$. Now,the $2 \ kg$ block is imparted a velocity $u$ towards the $1 \ kg$ block. Find the maximum value of velocity $u$ of the $2 \ kg$ block such that the $1 \ kg$ block never moves.

A
$\sqrt{10} \ m/s$
B
$\sqrt{15} \ m/s$
C
$\sqrt{20} \ m/s$
D
$\sqrt{30} \ m/s$

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Newton's Laws of Motion and Friction

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Mix Examples-Newton's Laws of Motion and Friction

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Medium

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$A$ particle initially at rest is subjected to two forces. One is constant,the other is a retarding force proportional to the particle velocity. In the subsequent motion of the particle,

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