To determine which box will have the greatest acceleration, we can use Newton's second law of motion, which states that \( F = ma \), where \( F \) is the net force, \( m \) is the mass, and \( a \) is the acceleration.
First, we need to calculate the net force for each box. The weight of each box (the force exerted by gravity) can be calculated using \( F_{\text{gravity}} = mg \), where \( g \) (acceleration due to gravity) is approximately \( 9.8 , \text{m/s}^2 \).
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10 kg box lifted with 60 N of force:
- Weight: \( F_{\text{gravity}} = 10 , \text{kg} \times 9.8 , \text{m/s}^2 = 98 , \text{N} \)
- Net force: \( F_{\text{net}} = 60 , \text{N} - 98 , \text{N} = -38 , \text{N} \) (not accelerating upward)
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20 kg box lifted with 60 N of force:
- Weight: \( F_{\text{gravity}} = 20 , \text{kg} \times 9.8 , \text{m/s}^2 = 196 , \text{N} \)
- Net force: \( F_{\text{net}} = 60 , \text{N} - 196 , \text{N} = -136 , \text{N} \) (not accelerating upward)
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10 kg box lifted with 40 N of force:
- Weight: \( F_{\text{gravity}} = 10 , \text{kg} \times 9.8 , \text{m/s}^2 = 98 , \text{N} \)
- Net force: \( F_{\text{net}} = 40 , \text{N} - 98 , \text{N} = -58 , \text{N} \) (not accelerating upward)
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20 kg box lifted with 40 N of force:
- Weight: \( F_{\text{gravity}} = 20 , \text{kg} \times 9.8 , \text{m/s}^2 = 196 , \text{N} \)
- Net force: \( F_{\text{net}} = 40 , \text{N} - 196 , \text{N} = -156 , \text{N} \) (not accelerating upward)
Analysis: All calculations show that the net force is negative, indicating that none of the boxes are accelerating upward; they are all being lifted with insufficient force to overcome their weight.
However, if we look at the net force magnitudes for the situations where there is some lifting force:
- 10 kg box at 60 N has a net force of -38 N,
- 20 kg box at 60 N has -136 N,
- 10 kg box at 40 N has -58 N,
- 20 kg box at 40 N has -156 N.
The box with the least negative net force (meaning it is closer to zero) will have the greatest potential acceleration upward (if it were lifted with enough force).
Thus, if the goal is to find which box would have the greatest acceleration if we could apply appropriate lifting forces:
- The 10 kg box lifted with 60 N of force shows the smallest net force value, indicating it would accelerate upward the best if sufficient force could overcome its weight.
Conclusion: The box with the greatest acceleration (if it could be lifted effectively) is the 10 kg box lifted with 60 N of force.