Which graph represents the mass versus the acceleration of objects with different masses pulled by...

To determine which graph correctly represents the mass versus acceleration of objects with different masses pulled by the same net force, we must apply Newton's Second Law of Motion. Newton's Second Law states: \[ F = m \cdot a \] where \( F \) is the net force, \( m \) is the mass, and \( a \) is the acceleration. If we rearrange this equation to solve for acceleration, we get: \[ a = \frac{F}{m} \] This shows that acceleration is inversely proportional to mass when the net force is constant. Therefore, as mass increases, acceleration decreases, and this relationship is not linear but rather a hyperbolic curve. Let's analyze each graph: - **Graph A:** Shows a linear relationship between mass and acceleration, which contradicts the inverse relationship dictated by Newton's Second Law. - **Graph B:** Shows a curve where acceleration increases with mass, which again contradicts the expected inverse relationship. - **Graph C:** Shows a constant mass for all acceleration values, which is not applicable in this context. - **Graph D:** Shows a hyperbolic relationship, where acceleration decreases as mass increases, which is consistent with the equation \( a = \frac{F}{m} \). Thus, **Graph D** correctly represents the mass versus acceleration for objects pulled by the same net force, demonstrating the inverse relationship between mass and acceleration. **References:** - Newton's Second Law of Motion, Integrated Physical Sciences Learning Resources