To find the acceleration of the box, we can start by calculating the net force acting on it. The net force \( F_{net} \) can be found by considering the applied force, the angle of the applied force, and the frictional force acting on the box.
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Calculate the horizontal component of the applied force \( F_A \): \[ F_{A_x} = F_A \cdot \cos(\theta) \] where:
- \( F_A = 85.0 , N \)
- \( \theta = 20.0^\circ \)
Using \( \cos(20^\circ) \) (which is approximately 0.9397): \[ F_{A_x} = 85.0 , N \cdot \cos(20^\circ) \approx 85.0 , N \cdot 0.9397 \approx 79.91 , N \]
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Determine the net force. The net force \( F_{net} \) acting on the box is given by: \[ F_{net} = F_{A_x} - F_{friction} \] where:
- \( F_{friction} = 21.0 , N \)
So, \[ F_{net} = 79.91 , N - 21.0 , N \approx 58.91 , N \]
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Calculate the acceleration using Newton's second law \( F = ma \): \[ a = \frac{F_{net}}{m} \] where \( m = 6.00 , kg \): \[ a = \frac{58.91 , N}{6.00 , kg} \approx 9.82 , m/s^2 \]
Thus, the acceleration of the box is approximately 9.82.