To determine which object will accelerate more when an equal amount of force is exerted on each, we can use Newton's second law of motion, which states that \( F = ma \) (force equals mass times acceleration).
Let's consider your two scenarios:
-
10 kg Box:
If a force \( F \) is applied to a 10 kg box, the acceleration \( a_1 \) can be calculated as: \[ a_1 = \frac{F}{m_1} = \frac{F}{10 , \text{kg}} \] -
Two 10 kg Boxes (totaling 20 kg):
If the same force \( F \) is applied to the combined mass of two boxes (20 kg), the acceleration \( a_2 \) would be: \[ a_2 = \frac{F}{m_2} = \frac{F}{20 , \text{kg}} \]
Now, we can compare the two accelerations:
- The 10 kg box has an acceleration of \( \frac{F}{10} \).
- The two 10 kg boxes, which total 20 kg, have an acceleration of \( \frac{F}{20} \).
Since \( \frac{F}{10} \) is greater than \( \frac{F}{20} \), the 10 kg box will accelerate more than the two 10 kg boxes when the same force is applied.
In conclusion, the 10 kg box will accelerate more than the two 10 kg boxes when equal force is applied.