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. We can rearrange this to find acceleration:
\[ a = \frac{F}{m} \]
Let's calculate the acceleration for each box.
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20 kg box lifted with 40 N of force: \[ a = \frac{40 , \text{N}}{20 , \text{kg}} = 2 , \text{m/s}^2 \]
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20 kg box lifted with 60 N of force: \[ a = \frac{60 , \text{N}}{20 , \text{kg}} = 3 , \text{m/s}^2 \]
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10 kg box lifted with 60 N of force: \[ a = \frac{60 , \text{N}}{10 , \text{kg}} = 6 , \text{m/s}^2 \]
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10 kg box lifted with 40 N of force: \[ a = \frac{40 , \text{N}}{10 , \text{kg}} = 4 , \text{m/s}^2 \]
Now we can compare the accelerations:
- 20 kg box with 40 N: \( 2 , \text{m/s}^2 \)
- 20 kg box with 60 N: \( 3 , \text{m/s}^2 \)
- 10 kg box with 60 N: \( 6 , \text{m/s}^2 \)
- 10 kg box with 40 N: \( 4 , \text{m/s}^2 \)
The box with the greatest acceleration is the 10 kg box lifted with 60 N of force, which has an acceleration of \( 6 , \text{m/s}^2 \).