According to Newton's second law of motion, the acceleration of an object is inversely proportional to its mass when applying the same force. The law is expressed by the formula:
\[ F = m \cdot a \]
Where:
- \( F \) is the force applied,
- \( m \) is the mass of the object,
- \( a \) is the acceleration.
If you apply the same force \( F \) to both boxes:
- Let's say the mass of the box full of books is \( m_1 \),
- And the mass of the box with fewer books is \( m_2 \) (where \( m_2 < m_1 \)).
The acceleration of each box can be calculated as:
For the full box: \[ a_1 = \frac{F}{m_1} \]
For the box with fewer books: \[ a_2 = \frac{F}{m_2} \]
Since \( m_2 < m_1 \), it follows that:
\[ a_2 > a_1 \]
Thus, the box with fewer books will have a greater acceleration than the box full of books when the same amount of force is applied.
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