- Identify the mass (\(m = 0.06 \text{ kg}\)) and acceleration (\(a = 13.7 \text{ m/s}^2\)) of the handball.
- Use Newton's Second Law of Motion: \(F = m \times a\).
- Calculate the force: \(F = 0.06 \times 13.7 = 0.822 \text{ N}\).
- The correct choice is \(\boxed{0.82 \text{ N}}\).
Explanation
- Problem Analysis and Data Identification
The problem involves calculating the force exerted on a handball based on its mass and acceleration. Newton's Second Law of Motion states that the force acting on an object is equal to the product of its mass and its acceleration, expressed by the formula:
\[F = m \times a\]
Given:
- Mass (\(m\)) = \(0.06 \text{ kg}\)
- Acceleration (\(a\)) = \(13.7 \text{ m/s}^2\)
Our objective is to find the magnitude of the force (\(F\)).
- Calculation and Comparison
Using the formula \(F = m \times a\), we substitute the given values:
\[F = 0.06 \text{ kg} \times 13.7 \text{ m/s}^2\]
Performing the multiplication:
\[F = 0.822 \text{ N}\]
Rounding this result to two decimal places, we get \(0.82 \text{ N}\). Comparing this to the given options:
- \(13.64 \text{ N}\)
- \(0.82 \text{ N}\)
- \(13.76 \text{ N}\)
- \(228 \text{ N}\)
The calculated force matches the option \(0.82 \text{ N}\).
- Final Answer
The force exerted on the handball is calculated to be \(\boxed{0.82 \text{ N}}\).
Examples
Understanding how force relates to mass and acceleration is fundamental in sports physics. For example, when a professional handball player throws the ball, the amount of force they generate determines how quickly the ball accelerates toward the goal. By applying \(F = ma\), players and coaches can analyze the dynamics of the throw to improve performance and precision in their movements.