According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This can be expressed with the formula:
\[ F = m \cdot a \]
Where:
- \( F \) is the force applied,
- \( m \) is the mass of the object,
- \( a \) is the acceleration of the object.
In this scenario, both footballs (A and B) are thrown with the same amount of force. However, football A has a greater mass than football B.
Let's denote:
- \( F \) as the force exerted on both footballs,
- \( m_A \) as the mass of football A,
- \( m_B \) as the mass of football B (where \( m_B < m_A \)),
- \( a_A \) as the acceleration of football A,
- \( a_B \) as the acceleration of football B.
According to the formula, we can express the acceleration of each football as follows:
For football A: \[ a_A = \frac{F}{m_A} \]
For football B: \[ a_B = \frac{F}{m_B} \]
Since \( m_A > m_B \), it follows that:
\[ \frac{F}{m_A} < \frac{F}{m_B} \]
Thus, the acceleration of football A (\( a_A \)) will be less than the acceleration of football B (\( a_B \)).
In summary:
- Football A (greater mass) will have less acceleration.
- Football B (less mass) will have more acceleration.
This means that even though the same force is applied, the heavier football (A) accelerates slower than the lighter football (B).
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