Two children of different masses are sitting on identical swings. To impart identical initial acceleration, for which child would you require to apply a larger force? Explain why.
A larger force would be required for the child with the larger mass.
The context states that for the same force, a larger mass has a smaller acceleration. Since the goal is to impart identical initial acceleration to both children, the applied force must be adjusted based on their masses.
From the relationship a = F / mass, if the acceleration (a) is identical for both, the force (F) must be directly proportional to the mass. Therefore, to achieve the same acceleration, a larger force must be applied to the child with the larger mass compared to the child with the smaller mass.
Explanation
The textbook context establishes the relationship between force, mass, and acceleration, noting that for the same force, a larger mass has a smaller acceleration. Using the formula a = F / mass, to keep acceleration (a) constant, force (F) must increase as mass increases. Thus, the child with the larger mass requires a larger force to achieve the identical initial acceleration.