Travis is sliding a moving box across his bedroom floor. If the box is 52.5 kilograms and he slides it with a net force of 105 N, what is the acceleration of the moving box?
To determine the acceleration of the box, we use Newton's Second Law of Motion. This law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The mathematical relationship is expressed as:
\[F = m \cdot a\]
where \(F\) is the net force measured in Newtons (N), \(m\) is the mass of the object measured in kilograms (kg), and \(a\) is the acceleration measured in meters per second squared (\(m/s^2\)).
We are given the mass of the box, \(m = 52.5 \text{ kg}\), and the net force applied, \(F = 105 \text{ N}\). To find the acceleration, we rearrange the equation \(F = m \cdot a\) to solve for \(a\):
\[a = \frac{F}{m}\]
Substituting the known values into this equation, we have:
\[a = \frac{105 \text{ N}}{52.5 \text{ kg}}\]
Performing the division, we find that:
\[a = 2 \text{ m/s}^2\]
Therefore, the acceleration of the box is \(\boxed{2 \text{ m/s}^2}\).
In everyday life, understanding Newton's Second Law helps in various scenarios, such as determining how much force to apply to push a shopping cart in a grocery store or calculating the acceleration of a car when the engine exerts force. By knowing the mass of an object and the force acting upon it, one can predict how quickly its motion will change, which is essential for designing vehicles, sports equipment, and even planning efficient logistics in daily tasks.