To find the acceleration of the sliding box, we need to determine the net force acting on it. The steps to solve this problem are as follows:
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Calculate the force of friction (F_friction): The force of friction can be calculated using the formula: \[ F_{\text{friction}} = \mu \cdot F_{\text{normal}} \] Here, \( \mu \) is the coefficient of sliding friction (0.2) and \( F_{\text{normal}} \) is the weight of the box (347 N).
\[ F_{\text{friction}} = 0.2 \cdot 347 , \text{N} = 69.4 , \text{N} \]
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Calculate the net force (F_net): The net force is the applied force minus the force of friction. \[ F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}} \] Given that the pushing force is 500 N, we can calculate \( F_{\text{net}} \): \[ F_{\text{net}} = 500 , \text{N} - 69.4 , \text{N} = 430.6 , \text{N} \]
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Calculate the acceleration (a): Now we can use Newton's second law to find the acceleration: \[ F_{\text{net}} = m \cdot a \] We need to find the mass (m) of the box first using its weight: \[ F_{\text{weight}} = m \cdot g \quad \text{(where } g \text{ is the acceleration due to gravity, approximately } 9.81 , \text{m/s}^2\text{)} \] Rearranging gives: \[ m = \frac{F_{\text{weight}}}{g} = \frac{347 , \text{N}}{9.81 , \text{m/s}^2} \approx 35.36 , \text{kg} \]
Now using \( F_{\text{net}} \) to find acceleration: \[ a = \frac{F_{\text{net}}}{m} = \frac{430.6 , \text{N}}{35.36 , \text{kg}} \approx 12.2 , \text{m/s}^2 \]
Since the closest answer choice is D:
Answer: D. 12 m/s²
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