To determine the acceleration of the body being pressed against the wall, we can assess the forces acting on it.
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Given Data:
- Mass of the body \( m = 2 , \text{kg} \)
- Applied force \( F_{applied} = 100 , \text{N} \)
- Coefficient of friction \( \mu = 0.04 \)
- Gravitational acceleration \( g \approx 9.81 , \text{m/s}^2 \)
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Calculate the normal force \( F_N \): The normal force is equal to the applied force, as the body is pressed against the wall: \[ F_N = F_{applied} = 100 , \text{N} \]
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Calculate the frictional force \( F_f \): The maximum static friction can be calculated using the coefficient of friction and the normal force: \[ F_f = \mu \times F_N = 0.04 \times 100 , \text{N} = 4 , \text{N} \]
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Assess the forces acting on the body:
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The gravitational force acting downward: \[ F_{gravity} = m \times g = 2 , \text{kg} \times 9.81 , \text{m/s}^2 \approx 19.62 , \text{N} \]
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The frictional force acting upward (opposing the gravitational force): \[ F_f = 4 , \text{N} \]
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Calculate the net force acting on the body: The net force acting on the body can be calculated as the difference between the gravitational force and the frictional force: \[ F_{net} = F_{gravity} - F_f = 19.62 , \text{N} - 4 , \text{N} = 15.62 , \text{N} \]
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Calculate the acceleration \( a \) of the body: By applying Newton's second law \( F = m \times a \), we can find the acceleration: \[ a = \frac{F_{net}}{m} = \frac{15.62 , \text{N}}{2 , \text{kg}} \approx 7.81 , \text{m/s}^2 \]
Therefore, the car's acceleration is approximately \( 7.81 , \text{m/s}^2 \).