91Ó°ÊÓ

When we talk about force and acceleration, it's essential to understand how closely linked they are through Newton's Second Law. In simple terms, this law states that an object will accelerate when a force is applied to it, and the extent of this acceleration is dependent on the object's mass.
A fact-filled way to remember this relationship is by using the equation: \[ F = m \cdot a \]where:

• \( F \) is the force applied, measured in newtons (N),
• \( m \) is the mass of the object, measured in kilograms (kg),
• \( a \) is the acceleration, measured in meters per second squared (m/s²).

In practical terms, if you exert a greater force, the acceleration increases, provided the mass remains constant. This is why pulling a sled with a constant force, as in our problem, results in a steady acceleration. Understanding this relationship helps us determine how objects move, crucial when calculating either force, mass, or acceleration in physical problems.

Mass calculation becomes essential when you want to understand the total 'weight' or amount of matter an object or group of objects possess. In our exercise, to find the mass of the little sister, we must first calculate the total mass of the system (sled plus sister).
The formula derived from Newton’s Second Law allows us to find total mass using known values of force and acceleration: \[ m = \frac{F}{a} \]Substituting the given values yields:\[ m = \frac{120\, \text{N}}{2.5\, \text{m/s}^2} = 48\, \text{kg} \]This number, 48 kg, represents the combined mass of both the sled and your sister. To isolate the mass of your sister, we subtract the sled's mass:\[ m_{sister} = 48\, \text{kg} - 7.4\, \text{kg} = 40.6\, \text{kg} \]Thus, through basic algebra and physics, we discover the sister's mass, emphasizing how forces and motions interconnect with mass determination.

A frictionless surface represents an idealized condition in physics where an object moves without any resistance caused by friction. Imagine a perfectly smooth icy surface where a sled slides effortlessly.
On such a surface, the only force needed is the one that changes the object's speed or direction. There is no energy lost to frictional forces, leading to:

• Greater efficiency in motion – all applied force contributes to acceleration.
• Simplification of calculations, as you don't need to account for frictional force.
• Ideal conditions to vividly see principles of physics, such as Newton’s laws, in action without external interferences.

The notion of a frictionless surface is useful when we wish to simplify problems and better understand the core physics at play, as it allows us to isolate forces and accelerations without worrying about unwanted distractions. However, in real life, complete frictionless scenarios are rare, but in physics problems, they are a great tool for learning the basics.