To determine which box will have the greatest acceleration, we can use Newton's second law of motion, which states that \( F = ma \) (force = mass × acceleration). From this equation, we can rearrange it to solve for acceleration:
\[ a = \frac{F}{m} \]
Where:
- \( a \) is the acceleration,
- \( F \) is the net force acting on the object, and
- \( m \) is the mass of the object.
In our case, we need to calculate the net force acting on each box, which is the applied force minus the weight of the box (which is the gravitational force acting downwards). The weight can be calculated using the formula:
\[ \text{Weight} = m \cdot g \]
Where \( g \approx 9.81 , \text{m/s}^2 \) (acceleration due to gravity).
Box Calculations
-
20 kg box lifted with 60 N of force:
- Weight: \( 20 , \text{kg} \cdot 9.81 , \text{m/s}^2 = 196.2 , \text{N} \)
- Net force: \( 60 , \text{N} - 196.2 , \text{N} = -136.2 , \text{N} \) (downward)
- Acceleration: Not possible upward (negative net force).
-
20 kg box lifted with 40 N of force:
- Weight: \( 20 , \text{kg} \cdot 9.81 , \text{m/s}^2 = 196.2 , \text{N} \)
- Net force: \( 40 , \text{N} - 196.2 , \text{N} = -156.2 , \text{N} \)
- Acceleration: Not possible upward (negative net force).
-
10 kg box lifted with 40 N of force:
- Weight: \( 10 , \text{kg} \cdot 9.81 , \text{m/s}^2 = 98.1 , \text{N} \)
- Net force: \( 40 , \text{N} - 98.1 , \text{N} = -58.1 , \text{N} \) (downward)
- Acceleration: Not possible upward (negative net force).
-
10 kg box lifted with 60 N of force:
- Weight: \( 10 , \text{kg} \cdot 9.81 , \text{m/s}^2 = 98.1 , \text{N} \)
- Net force: \( 60 , \text{N} - 98.1 , \text{N} = -38.1 , \text{N} \)
- Acceleration: Not possible upward (negative net force).
Additional Insight
None of the boxes would accelerate upward because the applied forces are not enough to overcome the weight of the 20 kg boxes and only partially overcome the weight of the 10 kg boxes. However, if we simplify our consideration to which one would have the highest upward acceleration if we ignore gravity temporarily and just assess the forces available at or above weight:
- The box with 10 kg and 60 N force will produce a smaller downward acceleration compared to the 10 kg box with 40 N.
Conclusion
Among the choices provided, the 10 kg box lifted with 60 N will provide the greatest upward acceleration, as it experiences less downward acceleration than the others will effectively have energy directed downward.
Therefore, while all boxes are unable to lift off the ground, the "10 kg lifted by 60 N" maximizes available upward force relative to its mass when considered from a purely comparative perspective with respect to attempted effort versus mass.