To find 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). Rearranging this gives us the formula for acceleration:
\[ a = \frac{F}{m} \]
Where:
- \( F \) is the force applied,
- \( m \) is the mass of the box,
- \( a \) is the acceleration.
Now, 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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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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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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20 kg box lifted with 60 N of force: \[ a = \frac{60 , \text{N}}{20 , \text{kg}} = 3 , \text{m/s}^2 \]
Now, comparing the accelerations:
- 20 kg box with 40 N: \( 2 , \text{m/s}^2 \)
- 10 kg box with 40 N: \( 4 , \text{m/s}^2 \)
- 10 kg box with 60 N: \( 6 , \text{m/s}^2 \)
- 20 kg box with 60 N: \( 3 , \text{m/s}^2 \)
The box that has the greatest acceleration is the 10 kg box lifted with 60 N of force, which has an acceleration of \( 6 , \text{m/s}^2 \).