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 applied, \( m \) is the mass, and \( a \) is the acceleration.
First, we need to calculate the net force acting on each box. The net force can be found by subtracting the weight of the box (which is mass times gravity, with \( g \approx 9.8 , \text{m/s}^2 \)) from the lifting force applied by the mover.
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For the 10 kg box lifted with 40 N of force:
- Weight = \( 10 \text{ kg} \times 9.8 \text{ m/s}^2 = 98 \text{ N} \)
- Net Force = \( 40 \text{ N} - 98 \text{ N} = -58 \text{ N} \) (negative indicates it's not enough to lift)
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For the 10 kg box lifted with 60 N of force:
- Weight = \( 10 \text{ kg} \times 9.8 \text{ m/s}^2 = 98 \text{ N} \)
- Net Force = \( 60 \text{ N} - 98 \text{ N} = -38 \text{ N} \) (still not enough to lift)
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For the 20 kg box lifted with 40 N of force:
- Weight = \( 20 \text{ kg} \times 9.8 \text{ m/s}^2 = 196 \text{ N} \)
- Net Force = \( 40 \text{ N} - 196 \text{ N} = -156 \text{ N} \) (not enough to lift)
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For the 20 kg box lifted with 60 N of force:
- Weight = \( 20 \text{ kg} \times 9.8 \text{ m/s}^2 = 196 \text{ N} \)
- Net Force = \( 60 \text{ N} - 196 \text{ N} = -136 \text{ N} \) (still not enough to lift)
All the boxes in this example have negative net force, which means none are being lifted at all. However, in terms of potential acceleration:
- Of the boxes being moved, the 10 kg box with 60 N of force has the least negative net force. It is technically closer to lifting than the others but still not enough to create upward acceleration.
So, if we look only in terms of which box has the least resistance and produces more upward force, the 10 kg box lifted with 60 N is the closest to being able to accelerate upward but is still not able to, as it remains below gravitational pulling.
To summarize, none of the boxes will actually accelerate upward due to insufficient lifting force. However, the box with the potential to accelerate most (if the forces were higher) would be the one where the force exceeds the weight, which in our scenario is still not achieved, but theoretically considering proximity, it could be imagined that the last one could lift earlier.