A soccer player kicks the ball towards the goal. The ball accelerates towards the goal at $600 m / s ^2$. If the ball has a mass of 0.2 kilogram, at what net force was the soccer ball kicked?
The problem asks us to determine the net force applied to a soccer ball that is being kicked. We are provided with the mass of the ball, \(m = 0.2 \, \text{kg}\), and its acceleration, \(a = 600 \, \text{m/s}^2\). According to Newton's Second Law of Motion, the net force \(F\) acting on an object is equal to the product of its mass and its acceleration:
\[F = m \cdot a\]
This relationship allows us to find the force simply by multiplying the given mass and acceleration values.
Now, we substitute the given values into the formula:
\[F = 0.2 \, \text{kg} \times 600 \, \text{m/s}^2\]
Performing the multiplication, we get:
\[F = 120 \, \text{kg} \cdot \text{m/s}^2\]
Since \(1 \, \text{kg} \cdot \text{m/s}^2\) is equivalent to one Newton (\(1 \, \text{N}\)), the net force applied to the soccer ball is:
\[F = 120 \, \text{N}\]
Thus, the soccer ball was kicked with a net force of \(120 \, \text{N}\).
Understanding Newton's Second Law is essential in many everyday situations involving motion. For example, when you push a shopping cart in a grocery store, applying a force causes the cart to accelerate. If the cart is heavy (large mass), you need to apply more force to achieve the same acceleration compared to an empty, lighter cart. By calculating these forces, engineers can design safer vehicles, sports equipment, and various machinery that rely on controlled motion.