Questions: How does the magnitude of acceleration of the rifle compare with the magnitude of acceleration of the bullet, and why?

Solution Steps

We need to compare the magnitudes of acceleration of a rifle and a bullet when they experience the same magnitude of force. The key point here is to understand the relationship between force, mass, and acceleration.

Newton's Second Law states that \( F = ma \), where \( F \) is the force applied, \( m \) is the mass, and \( a \) is the acceleration. Given that the force \( F \) is the same for both the rifle and the bullet, we can write: \[ F = m_{\text{rifle}} a_{\text{rifle}} = m_{\text{bullet}} a_{\text{bullet}} \]

Since the force is the same, we can compare the accelerations by rearranging the equation: \[ a_{\text{rifle}} = \frac{F}{m_{\text{rifle}}} \] \[ a_{\text{bullet}} = \frac{F}{m_{\text{bullet}}} \]

The mass of the rifle (\( m_{\text{rifle}} \)) is much greater than the mass of the bullet (\( m_{\text{bullet}} \)). Therefore, for the same force: \[ a_{\text{rifle}} < a_{\text{bullet}} \]

Final Answer