Two students push two different boxes across a frictionless...

Two students push two different boxes across a frictionless floor. Both students exert a horizontal force of 50 $\mathrm{N}$ . If the first box has mass $m_{1}=$ 10 $\mathrm{kg}$ and the second box has mass $m_{2}=40 \mathrm{kg}$ , what is the value of $a_{1} / a_{2} ?$ (A) 1/4 (B) 1/2 (C) 2 (D) 4

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Key Concepts

Newton's Second Law

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This fundamental principle, expressed as F = ma, is central to understanding how varying masses respond differently when the same force is applied.

Inversely Proportional Relationship Between Mass and Acceleration

This concept highlights that when a constant force is applied to objects of different masses, the object with the smaller mass will experience a greater acceleration compared to the object with the larger mass. This inverse relationship is a direct consequence of Newton's Second Law.

Frictionless Surface

A frictionless surface implies that there is no opposing force due to friction, meaning that the net force acting on the objects is solely the applied force. This idealization simplifies the analysis by ensuring that all applied force contributes directly to accelerating the masses without any losses.

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