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Step 1: Identify the Problem
We have a block of mass 1 kg placed on a horizontal surface of a truck. The coefficient of friction is given as $0.6$, and the truck accelerates at $5\,\text{m/s}^2$. We need to find the frictional force on the block.
Step 2: Determine the Maximum Possible Friction
The maximum static friction is given by:
$f_{\text{max}} = \mu\,m\,g$,
where $m = 1\,\text{kg}$, $\mu = 0.6$, and $g = 9.8\,\text{m/s}^2$.
Substituting the values:
$f_{\text{max}} = 0.6 \times 1 \times 9.8 = 5.88\,\text{N}$.
Step 3: Calculate the Required Friction to Accelerate the Block
To move with the truck at an acceleration of $5\,\text{m/s}^2$, the block needs a net force equal to $m\,a$, where $m = 1\,\text{kg}$ and $a = 5\,\text{m/s}^2$. Thus,
$F_{\text{required}} = m\,a = 1 \times 5 = 5\,\text{N}$.
Step 4: Compare Required Friction with Maximum Friction
The required friction ($5\,\text{N}$) is less than the maximum friction ($5.88\,\text{N}$). Hence, the frictional force that actually acts on the block will be $5\,\text{N}$ because it does not exceed the maximum limit.
Step 5: Conclusion
The frictional force on the block is $5\,\text{N}$, which is sufficient to keep the block moving with the truck at the given acceleration.
