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Step 1: Identify the Known Quantities
• Mass of the marble block, $m = 2\,\text{kg}$
• Initial velocity, $u = 6\,\text{m/s}$
• Final velocity, $v = 0\,\text{m/s}$
• Time taken to stop, $t = 10\,\text{s}$
• Acceleration due to gravity, $g = 10\,\text{m/s}^2$ (as used in the problem)
Step 2: Apply the Kinematic Equation
We use the linear motion equation:
$v = u + at$
Here, $v = 0$, $u = 6$, and $t = 10\,\text{s}$. Solving for $a$:
$0 = 6 + a \times 10$
$\implies a = \frac{0 - 6}{10} = -0.6\,\text{m/s}^2$
Step 3: Relate Acceleration to Frictional Force
The only retarding force is friction, given by:
$F_{\text{friction}} = \mu m g$
Since $F = m a$, we have:
$m a = -\mu m g$
(The negative sign indicates that friction acts opposite to the direction of motion.)
Step 4: Solve for the Coefficient of Friction ($\mu$)
From $a = -\mu g$, substitute $a = -0.6\,\text{m/s}^2$ and $g = 10\,\text{m/s}^2$:
$-0.6 = -\mu \times 10$
$\mu = \frac{0.6}{10} = 0.06$
Final Answer
The coefficient of friction is $0.06$.
