To find the upward acceleration of the box, we can use Newton's second law of motion, which states:
\[ F_{net} = m \cdot a \]
Where:
- \( F_{net} \) is the net force acting on the object (in newtons),
- \( m \) is the mass of the object (in kilograms),
- \( a \) is the acceleration (in m/s²).
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Determine the weight of the box: The weight (\( W \)) of the box can be calculated using the formula:
\[ W = m \cdot g \]
Where \( g \) (acceleration due to gravity) is approximately \( 9.81 , \text{m/s}^2 \).
\[ W = 15 , \text{kg} \times 9.81 , \text{m/s}^2 = 147.15 , \text{N} \]
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Calculate the net force: The net force acting on the box (\( F_{net} \)) is the applied force minus the weight of the box:
\[ F_{net} = F_{applied} - W \] Given that the applied force is 18.0 N, we have:
\[ F_{net} = 18.0 , \text{N} - 147.15 , \text{N} \] \[ F_{net} = 18.0 , \text{N} - 147.15 , \text{N} = -129.15 , \text{N} \]
Here, we note that the 18 N is less than the weight of the box, which indicates that the box is not accelerating upward but is actually accelerating downward.
Since the box is not being lifted, this situation implies a downward acceleration instead. As such, we need to calculate the actual upward acceleration with respect to the net downward force (which results in a negative acceleration).
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Finding the upward acceleration: Using \( F_{net} = m \cdot a \):
\[ -129.15 , \text{N} = 15 , \text{kg} \cdot a \]
Solving for \( a \):
\[ a = \frac{-129.15 , \text{N}}{15 , \text{kg}} \approx -8.61 , \text{m/s}^2 \]
Finally, since we are referencing upward acceleration, the box is not accelerating upwards, but rather experiencing an upward net force of only 18 N, meaning it accelerates downward rather than upward.
If the box is lifted with insufficient force, thus, the box is falling.
This implies that upward acceleration is not happening and simply put it is accelerating downward.
Conclusion: The upward acceleration of the box is \( 0 , \text{m/s}^2\) (as it cannot lift off the ground as the lifting force is lower than the weight).
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