The net force on a racecar that is accelerating at a rate of 2.5 m/s² is 2,000 newtons. What is the mass of the racecar in kilograms?
The problem asks for the mass \(m\) of a racecar, given that the net force \(F\) acting on it is \(2,000 \text{ newtons}\) and its acceleration \(a\) is \(2.5 \text{ m/s}^2\). According to Newton's Second Law of Motion, the relationship between these quantities is defined by the equation \(F = m \cdot a\). Our goal is to solve for the mass \(m\).
To find the mass, we rearrange Newton's Second Law, \(F = m \cdot a\), to isolate \(m\):
\[m = \frac{F}{a}\]
Given the values:
\(F = 2,000 \text{ N}\)
\(a = 2.5 \text{ m/s}^2\)
Substituting these values into our equation gives:
\[m = \frac{2,000}{2.5}\]
Calculating this division:
\[m = \frac{2,000}{2.5} = 800\]
Thus, the mass of the racecar is \(800 \text{ kilograms}\).
Newton's Second Law is essential in various fields, such as automotive engineering and sports science. For instance, when designing a car, engineers must calculate the force required to accelerate a vehicle of a specific mass at a desired rate. Similarly, a runner's performance can be analyzed by understanding the relationship between the force they exert on the track and their resulting acceleration. By applying \(F = m \cdot a\), one can predict how changes in mass or force will impact motion.