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When understanding **Newton's Second Law**, it's important to grasp how force and acceleration are connected. This law tells us that the force applied on an object is equal to the mass of the object multiplied by its acceleration. The formula is:\[ F = ma \]Here:

• \( F \) stands for the force applied, measured in Newtons (N).
• \( m \) is the mass, which we aim to find in this problem.
• \( a \) is the acceleration, measured in meters per second squared (m/s²).

When a force is applied to an object like the box in our problem, it causes the box to accelerate in the direction of that force. The greater the force, the greater the acceleration, provided the mass remains constant. Conversely, for the same force, a more massive object will accelerate less compared to a lighter one. This relationship is crucial for solving physics problems dealing with motion.

**Calculating mass** becomes straightforward using Newton's Second Law when given force and acceleration. All we need to do is rearrange the original formula \( F = ma \) to solve for the object's mass. The rearrangement goes like this:\[ m = \frac{F}{a} \]By substituting the given values from our exercise:

• Force \( F = 48.0 \, \mathrm{N} \)
• Acceleration \( a = 3.00 \, \mathrm{m/s}^2 \)

We plug these numbers into our mass formula:\[ m = \frac{48.0 \, \mathrm{N}}{3.00 \, \mathrm{m/s}^2} \]And we find:\[ m = 16.0 \, \mathrm{kg} \]This calculation reveals that the box has a mass of 16.0 kilograms. Using these straightforward steps helps verify that our comprehension of Newton's law holds, establishing a solid foundation for tackling more complex physics puzzles.

A **frictionless surface** is an ideal scenario often used in physics problems to simplify calculations. In reality, most surfaces exert some resistance against moving objects, known as friction. But in our exercise, considering a frozen pond as a frictionless horizontal surface, means this resistance is non-existent. This absence impacts motion, as it allows the force applied to wholly convert into movement without any loss. Without friction, there is no opposing force to counteract the applied force. Hence, all of the applied 48.0 N can be utilized to induce the motion of the box. This setup helps us directly observe the effect of force on an object, accentuating the principles outlined in Newton's Second Law. It also facilitates the calculations by eliminating any need to consider frictional forces, thus focusing purely on force, mass, and acceleration.