Due to the much greater mass of the gun compared to the bullet, the acceleration of the gun is much less than the acceleration of the bullet, even though both experience equal and opposite forces according to Newton’s third law.
How does the mass of the gun and the bullet affect their accelerations during firing?
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According to Newton’s Second Law (F=ma), the acceleration (a) of an object is inversely proportional to its mass (m) when subjected to a constant force (F). In the context of a gun firing, the bullet and the gun experience equal and opposite forces during the action-reaction process (as per Newton’s Third Law). However, since the mass of the gun is typically much greater than that of the bullet, the gun’s acceleration is significantly smaller compared to the bullet. Therefore, the bullet accelerates more rapidly due to its lower mass, while the gun recoils with a much smaller acceleration due to its greater mass.