Calculate Crate Mass With 12 N Force And 0.20 M/s^2 Acceleration

Understanding Newton's Second Law of Motion

To determine the mass of the crate, we need to delve into the fundamental principles of physics, specifically Newton's Second Law of Motion. This law forms the bedrock of classical mechanics and provides a direct relationship between force, mass, and acceleration. In essence, it states that the net force acting on an object is directly proportional to the object's mass and the acceleration it experiences. Mathematically, this law is expressed as:

F = ma

Where:

• F represents the net force acting on the object, measured in Newtons (N).
• m represents the mass of the object, measured in kilograms (kg).
• a represents the acceleration of the object, measured in meters per second squared (m/s²).

This equation is a cornerstone of physics, allowing us to quantitatively analyze the motion of objects under the influence of forces. It highlights the crucial interplay between force, mass, and acceleration: a greater force will produce a greater acceleration for a given mass, while a greater mass will require a greater force to achieve the same acceleration. Understanding this relationship is key to solving a wide range of physics problems, from simple scenarios like pushing a crate to complex situations involving celestial mechanics. In the context of this problem, we are given the net force acting on the crate and its resulting acceleration. Our goal is to utilize Newton's Second Law to determine the crate's mass, which is a direct application of the law's principles.

Applying Newton's Second Law to the Crate Problem

In this specific problem, we are presented with a scenario where a net force of 12 N is applied to a crate, resulting in an acceleration of 0.20 m/s². Our objective is to find the mass of the crate. To achieve this, we will employ Newton's Second Law of Motion, which, as we established earlier, is mathematically expressed as F = ma. This equation provides a direct link between the force acting on an object, its mass, and its acceleration. Given that we know the net force (F) and the acceleration (a), we can rearrange the equation to solve for the mass (m). The rearrangement involves isolating 'm' on one side of the equation. Dividing both sides of the equation by 'a', we get:

m = F / a

This rearranged equation is now in a form that directly allows us to calculate the mass. We simply need to substitute the given values of force and acceleration into the equation. The net force (F) is given as 12 N, and the acceleration (a) is given as 0.20 m/s². By plugging these values into the equation, we can compute the mass of the crate. This step-by-step approach ensures that we are applying the fundamental principles of physics in a logical and methodical manner, leading us to the correct solution. The ability to rearrange equations and apply them to specific scenarios is a crucial skill in physics, and this problem provides a clear example of its application. Once we have substituted the values, the final calculation will reveal the mass of the crate in kilograms, which is the standard unit of mass in the International System of Units (SI).

Calculating the Mass

Now, let's proceed with the calculation. We have established the formula for mass as m = F / a, where F is the net force and a is the acceleration. We are given that the net force (F) is 12 N and the acceleration (a) is 0.20 m/s². Substituting these values into the formula, we get:

m = 12 N / 0.20 m/s²

To perform this division, we can think of it as dividing 12 by 0.20. A helpful way to simplify this is to multiply both the numerator and the denominator by 100 to remove the decimal. This gives us:

m = (12 * 100) / (0.20 * 100) m = 1200 / 20

Now, the division is much simpler. 1200 divided by 20 is 60. Therefore,

m = 60 kg

This result indicates that the mass of the crate is 60 kilograms. It's important to note the units in the final answer. Since we used Newtons (N) for force and meters per second squared (m/s²) for acceleration, the resulting unit for mass is kilograms (kg), which is the standard unit of mass in the International System of Units (SI). This calculation demonstrates the direct application of Newton's Second Law of Motion to a practical problem. By understanding the relationship between force, mass, and acceleration, we can quantitatively determine the mass of an object given the force acting upon it and its resulting acceleration. This skill is fundamental to solving many problems in mechanics and physics in general. The result we obtained, 60 kg, is one of the options provided, confirming our calculation.

Analyzing the Answer Choices

Having calculated the mass of the crate to be 60 kg, we can now analyze the answer choices provided to determine the correct one. The answer choices are:

A. 2.4 kg B. 6 kg C. 12.2 kg D. 60 kg

Comparing our calculated mass of 60 kg with the answer choices, we can clearly see that option D, 60 kg, matches our result. This confirms that our calculation is correct and that option D is the correct answer. The other options (A, B, and C) represent incorrect masses for the crate, based on the given force and acceleration. Option A, 2.4 kg, is significantly lower than our calculated mass, suggesting a much larger acceleration for the given force. Option B, 6 kg, is also considerably lower, indicating a similar discrepancy. Option C, 12.2 kg, is closer to the correct mass but still significantly different, highlighting the importance of accurate calculations in physics problems. This process of comparing the calculated result with the answer choices is a crucial step in problem-solving. It allows us to verify our solution and ensure that we have not made any errors in our calculations or reasoning. In this case, the clear match between our calculated mass and option D provides confidence in our solution and reinforces our understanding of Newton's Second Law of Motion. This methodical approach to problem-solving, involving careful calculation and verification, is essential for success in physics and other quantitative disciplines.

Conclusion

In conclusion, by applying Newton's Second Law of Motion (F = ma) and performing the necessary calculations, we have determined that the mass of the crate is 60 kg. This result was obtained by rearranging the formula to solve for mass (m = F / a) and substituting the given values of force (12 N) and acceleration (0.20 m/s²). The calculated mass aligns perfectly with answer choice D, confirming it as the correct answer. This problem serves as a clear illustration of the practical application of Newton's Second Law in determining the mass of an object given the net force acting upon it and its resulting acceleration. The process involved understanding the fundamental principles of physics, applying the relevant formula, performing the calculations accurately, and verifying the result against the provided answer choices. This methodical approach is crucial for solving physics problems effectively and accurately. Furthermore, this exercise reinforces the importance of understanding the relationship between force, mass, and acceleration, which are fundamental concepts in classical mechanics. The ability to apply these concepts to real-world scenarios is a key skill for students and professionals in physics and related fields. The solution not only provides the correct answer but also demonstrates the underlying principles and problem-solving strategies involved, making it a valuable learning experience.

Therefore, the correct answer is D. 60 kg.