To determine which box will have the greatest acceleration, we can use Newton's second law of motion, which states that \( F = m \cdot a \) or rearranged, \( a = \frac{F}{m} \). Here, \( F \) is the net force applied, \( m \) is the mass of the box, and \( a \) is the acceleration.
Let’s analyze the options given:
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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 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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20 kg box lifted with 60 N of force: \[ a = \frac{60 , \text{N}}{20 , \text{kg}} = 3 , \text{m/s}^2 \]
Now we compare the accelerations:
- For the 10 kg box lifted with 60 N: 6 m/s²
- For the 20 kg box lifted with 40 N: 2 m/s²
- For the 10 kg box lifted with 40 N: 4 m/s²
- For the 20 kg box lifted with 60 N: 3 m/s²
The first box (10 kg box lifted with 60 N) has the greatest acceleration of 6 m/s².
So, the box with the greatest acceleration is the 10 kg box lifted with 60 N of force.
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