To determine which box will have the greatest acceleration, we can use Newton's Second Law of Motion, which states that \( F = ma \) (Force equals mass times acceleration). We can rearrange this equation to find acceleration:
\[ a = \frac{F}{m} \]
Let's calculate the acceleration for each option:
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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: \[ a = \frac{40 , \text{N}}{10 , \text{kg}} = 4 , \text{m/s}^2 \]
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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: \[ a = \frac{60 , \text{N}}{20 , \text{kg}} = 3 , \text{m/s}^2 \]
Now we can summarize the calculated accelerations:
- 10 kg box with 60 N: 6 m/s²
- 10 kg box with 40 N: 4 m/s²
- 20 kg box with 40 N: 2 m/s²
- 20 kg box with 60 N: 3 m/s²
The box that has the greatest acceleration is the 10 kg box lifted with 60 N of force, with an acceleration of 6 m/s².
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