What acceleration is imparted to a football if a player kicks it with a force of 25 N? Assume that the mass of the football is 0.40 kg.
This problem involves an application of force (the kick) to an object of mass (the football).
The general formula relating force to mass and acceleration is called Newton's Second Law. This law of motion states that the net force is directly proportional to both mass and acceleration. That is, the greater the mass or acceleration of an object, the greater the force required to accelerate it. `F = m*a`, where F is the force exerted, m is the mass of a given object, and a is the acceleration of that object, expressed in meters per square second.
The kick is an exertion of force onto the football. Thus, according to the formula we just gave, the football will accelerate in inverse proportion to its mass (that is, some of the force will be "dissipated" by its mass and the remainder of the force will accelerate it). Now that we have established a good understanding of Newton's second law, let's calculate the acceleration of the ball using the equation:
`F = m*a`
`25 N = 0.40 kg * a`
Thus, we can divide both sides above by 0.40 kg, yielding this:
`62.5 (N)/(kg) = a`
To put this in terms of acceleration, we should remember that one Newton (N) is equivalent to `1 kg*m/(s^2)` .
Thus we have this:
`62.5 * (kg * m/(s^2))/(kg)`
The kilograms unit cancels out, and we are left with our final answer for the acceleration, `62.5 m/(s^2)` .