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Step-by-Step Solution
Step 1: Identify the given quantities
• Mass of the block, $m = 10\text{ kg}$
• Coefficient of friction, $\mu = 0.5$
• Applied horizontal force, $F = 100\text{ N}$
• Acceleration due to gravity, $g = 9.8\text{ m/s}^2$ (approx. can be taken as $10\text{ m/s}^2$ for rounded calculation)
Step 2: Calculate the frictional force
The frictional force, $f$, for an object on a horizontal surface is given by
$f = \mu \, N$. Here, $N = mg$ is the normal reaction on the block.
Thus, $f = 0.5 \times 10 \times 9.8 = 49\text{ N} \, (\text{approximately})$.
Step 3: Determine the net force on the block
The net horizontal force, $F_{\text{net}}$, acting on the block is:
$F_{\text{net}} = F - f$.
Substituting the values, $F_{\text{net}} = 100 \text{ N} - 49 \text{ N} = 51\text{ N}$.
Step 4: Calculate the acceleration of the block
From Newton's Second Law, $F_{\text{net}} = ma$, where $a$ is the acceleration.
Hence, $a = \frac{F_{\text{net}}}{m} = \frac{51}{10} = 5.1\text{ m/s}^2 \approx 5\text{ m/s}^2$.
Thus, the acceleration of the block is about $5\text{ m/s}^2$.
