- Use Newton's Second Law formula \(a = F / m\) to relate force, mass, and acceleration.
- Calculate the acceleration for each egg type: \(a_{\text{Chicken}} = 750 \text{ m/s}^2\), \(a_{\text{Ostrich}} = 1000 \text{ m/s}^2\), and \(a_{\text{Quail}} = 2500 \text{ m/s}^2\).
- Compare the results to identify the greatest acceleration.
- The highest acceleration is \(\boxed{2500 \text{ m/s}^2}\).
Explanation
- Problem Analysis and Formula Setup
To identify which egg experiences the greatest acceleration, we use Newton's Second Law of motion, which is given by the equation \[F = m \cdot a\] where \(F\) is the force in Newtons (N), \(m\) is the mass in kilograms (kg), and \(a\) is the acceleration in \(m/s^2\). By rearranging this formula to solve for acceleration, we get: \[a = \frac{F}{m}.\] We are given the mass and force data for three types of eggs:
- Chicken: mass \(m = 0.06 \text{ kg}\), force \(F = 45 \text{ N}\).
- Ostrich: mass \(m = 1.4 \text{ kg}\), force \(F = 1400 \text{ N}\).
- Quail: mass \(m = 0.02 \text{ kg}\), force \(F = 50 \text{ N}\).
We will calculate the acceleration for each egg individually to compare them.
- Calculation of Acceleration Values
Using the formula \(a = \frac{F}{m}\), we compute the acceleration for each egg:
- For the Chicken egg: \[a_{\text{Chicken}} = \frac{45}{0.06} = 750 \text{ m/s}^2.\]
- For the Ostrich egg: \[a_{\text{Ostrich}} = \frac{1400}{1.4} = 1000 \text{ m/s}^2.\]
- For the Quail egg: \[a_{\text{Quail}} = \frac{50}{0.02} = 2500 \text{ m/s}^2.\]
Comparing these values, we find that \(2500 \text{ m/s}^2 > 1000 \text{ m/s}^2 > 750 \text{ m/s}^2\). The Quail egg has the greatest acceleration.
- Conclusion
The calculations demonstrate that the Quail egg, having a mass of \(0.02 \text{ kg}\) and experiencing a force of \(50 \text{ N}\), undergoes an acceleration of \(2500 \text{ m/s}^2\). This is the highest acceleration among the three types of eggs provided. Therefore, the greatest acceleration is \(\boxed{2500 \text{ m/s}^2}\).
Examples
Newton's Second Law is fundamental to understanding motion in our daily lives. For example, when you push a grocery cart, the force you apply causes the cart to accelerate depending on how much food is inside (its mass). If the cart is heavy, it requires more force to achieve the same acceleration as a lighter cart. This relationship helps engineers design everything from safe cars, which need to accelerate efficiently, to playground equipment where controlling the acceleration of swings or slides is crucial for safety. Understanding these physics principles allows us to predict and control the movement of objects accurately.