To find the acceleration of the box, we can follow these steps:
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Calculate the force of friction (F_friction): The force of friction can be calculated using the formula: \[ F_{\text{friction}} = \mu \cdot F_{\text{normal}} \] where \(\mu\) is the coefficient of sliding friction and \(F_{\text{normal}}\) is the normal force. For a box on a horizontal surface, the normal force is equal to the weight of the box (the gravitational force acting on it).
Given: \[ \mu = 0.15 \] \[ F_{\text{normal}} = 660 , \text{N} \]
Now we can calculate the force of friction: \[ F_{\text{friction}} = 0.15 \cdot 660 , \text{N} = 99 , \text{N} \]
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Determine the net force (F_net): The net force acting on the box can be found by subtracting the force of friction from the pushing force: \[ F_{\text{net}} = F_{\text{push}} - F_{\text{friction}} \]
Given: \[ F_{\text{push}} = 500 , \text{N} \]
Substituting in the values: \[ F_{\text{net}} = 500 , \text{N} - 99 , \text{N} = 401 , \text{N} \]
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Calculate the acceleration (a): To find the acceleration, we use Newton's second law: \[ F_{\text{net}} = m \cdot a \] where \(m\) is the mass of the box. First, we need to find the mass of the box using the weight (weight = mass × gravity): \[ F_{\text{gravity}} = m \cdot g \] where \(g\) is the acceleration due to gravity (approximately \(9.81 , \text{m/s}^2\)).
Thus, the mass \(m\) can be calculated as: \[ m = \frac{F_{\text{gravity}}}{g} = \frac{660 , \text{N}}{9.81 , \text{m/s}^2} \approx 67.14 , \text{kg} \]
Now we can find the acceleration: \[ a = \frac{F_{\text{net}}}{m} = \frac{401 , \text{N}}{67.14 , \text{kg}} \approx 5.96 , \text{m/s}^2 \]
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Round the acceleration: The calculated acceleration is approximately \(6 , \text{m/s}^2\).
Thus, the answer is:
D. 6 m/s²