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 to the object, \( m \) is the mass, and \( a \) is the acceleration.
The net force acting on each box can be calculated as the applied force minus the weight of the box (which is \( mg \), where \( g \) is the acceleration due to gravity, approximately \( 9.8 , \text{m/s}^2 \)).
Let's calculate the net force and acceleration for each box:
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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 = \( 40 , \text{N} - 98 , \text{N} = -58 , \text{N} \) (not able to lift)
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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 able to lift)
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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 = \( 60 , \text{N} - 98 , \text{N} = -38 , \text{N} \) (not able to lift)
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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 = \( 60 , \text{N} - 196 , \text{N} = -136 , \text{N} \) (not able to lift)
From the calculations, two boxes (10 kg with 40 N, and 20 kg with 40 N) produce a negative net force, indicating they cannot be lifted. The same goes for a 10 kg box with 60 N and a 20 kg box with 60 N. Therefore, none of the boxes are able to accelerate positively upwards based on the forces applied versus their weights.
However, if we consider the forces that come closer to lifting the box, we compare those values. The 10 kg box lifted with 60 N has the least resistance (net force is closest to zero), though it still is not sufficient to achieve movement or acceleration in an upward direction.
Conclusively, all given scenarios fail to lift the boxes, showing no positive acceleration. However, the box that is closest to achieving a lift would still be the 10 kg box with 60 N of force if we were to assume the force could somewhat assist in initial lift.