To find which box has the greatest acceleration, we can use Newton's second law, which states:
\[ F = m \cdot a \]
Where:
- \( F \) is the net force applied,
- \( m \) is the mass of the box,
- \( a \) is the acceleration.
We can rearrange this to find acceleration:
\[ a = \frac{F}{m} \]
Now let's analyze each option and calculate the acceleration:
-
10 kg box lifted with 40 N of force:
- Weight of the box = \( 10 , \text{kg} \times 9.8 , \text{m/s}^2 = 98 , \text{N} \)
- Net force = \( 40 , \text{N} - 98 , \text{N} = -58 , \text{N} \) (the box will not accelerate up)
- Acceleration = 0 (since the force isn’t sufficient to lift the box).
-
20 kg box lifted with 60 N of force:
- Weight of the box = \( 20 , \text{kg} \times 9.8 , \text{m/s}^2 = 196 , \text{N} \)
- Net force = \( 60 , \text{N} - 196 , \text{N} = -136 , \text{N} \) (the box will not accelerate up)
- Acceleration = 0 (since the force isn’t sufficient to lift the box).
-
20 kg box lifted with 40 N of force:
- Weight of the box = \( 20 , \text{kg} \times 9.8 , \text{m/s}^2 = 196 , \text{N} \)
- Net force = \( 40 , \text{N} - 196 , \text{N} = -156 , \text{N} \) (the box will not accelerate up)
- Acceleration = 0 (since the force isn’t sufficient to lift the box).
-
10 kg box lifted with 60 N of force:
- Weight of the box = \( 10 , \text{kg} \times 9.8 , \text{m/s}^2 = 98 , \text{N} \)
- Net force = \( 60 , \text{N} - 98 , \text{N} = -38 , \text{N} \) (the box will not accelerate up)
- Acceleration = 0 (since the force isn’t sufficient to lift the box).
None of the options provides sufficient force to counteract the weight of the boxes, meaning they will not accelerate upward in any case. Among all the movers, the box that has the greatest net force where \( F > m \cdot g \) does not exist in the given options.
For actual upward acceleration, a greater net force than the weight of the box is needed. Therefore, none of the boxes will exhibit any upward acceleration as described.
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