Calculating The Weight Of A 1.5 Kg Book On Earth A Physics Problem Solved

Understanding the relationship between mass and weight is fundamental in physics. While often used interchangeably in everyday language, these two terms represent distinct concepts. Mass is an intrinsic property of an object, representing the amount of matter it contains, and is measured in kilograms (kg). Weight, on the other hand, is the force exerted on an object due to gravity, and is measured in Newtons (N). This article delves into the calculation of weight, specifically addressing the question: What is the weight, on Earth, of a book with a mass of 1.5 kg? We will explore the underlying principles, the formula used, and the step-by-step calculation to arrive at the correct answer. This exploration will not only clarify the difference between mass and weight but also provide a practical application of the concepts of gravity and force.

It's crucial to differentiate between mass and weight. As mentioned earlier, mass is a measure of the amount of matter in an object. It remains constant regardless of the object's location. A book with a mass of 1.5 kg will have the same mass on Earth, on the Moon, or in the vacuum of space. Weight, however, is the force exerted on an object due to gravity. Since gravity varies depending on the celestial body and location, the weight of an object will also vary. For instance, the gravitational force on the Moon is about one-sixth of that on Earth. Therefore, an object will weigh significantly less on the Moon than on Earth, despite having the same mass. This difference highlights the importance of understanding the relationship between mass, weight, and gravity. To further illustrate, consider an astronaut. Their mass remains constant whether they are on Earth or in space. However, their weight changes drastically. On Earth, they experience the full force of Earth's gravity, giving them a certain weight. In the near-weightless environment of space, the gravitational force is significantly reduced, resulting in a much lower weight, even though their mass hasn't changed. This distinction is essential for accurate calculations and a proper understanding of physics principles. Another key difference lies in the units of measurement. Mass is measured in kilograms (kg), a fundamental unit in the International System of Units (SI). Weight, being a force, is measured in Newtons (N). One Newton is defined as the force required to accelerate a one-kilogram mass at a rate of one meter per second squared (1 N = 1 kg⋅m/s²). This difference in units further emphasizes that mass and weight are distinct physical quantities. Confusing these two concepts can lead to errors in calculations and a misunderstanding of physical phenomena. Therefore, it is essential to always clarify whether you are referring to the mass or the weight of an object, and to use the appropriate units.

To calculate the weight of an object, we use the following formula:

Weight (W) = mass (m) × acceleration due to gravity (g)

Where:

• W is the weight, measured in Newtons (N)
• m is the mass, measured in kilograms (kg)
• g is the acceleration due to gravity, which is approximately 9.8 m/s² on Earth

This formula is a direct application of Newton's Second Law of Motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). In the case of weight, the force is the gravitational force, and the acceleration is the acceleration due to gravity. The value of g (9.8 m/s²) represents the average acceleration experienced by objects near the Earth's surface due to the Earth's gravitational pull. It is a constant value that is widely used in physics calculations. However, it is important to note that g can vary slightly depending on the location on Earth, due to factors such as altitude and the Earth's rotation. For most practical purposes, 9.8 m/s² is a sufficiently accurate approximation. The formula W = mg is a powerful tool for understanding and calculating the weight of objects in various scenarios. It allows us to relate the mass of an object to the force that gravity exerts on it. By knowing the mass and the acceleration due to gravity, we can easily determine the weight. Conversely, if we know the weight and the acceleration due to gravity, we can calculate the mass. This formula is not only essential for academic physics problems but also has numerous practical applications in engineering, aerospace, and everyday life. For example, engineers use this formula to design structures that can withstand the gravitational forces acting on them. Aerospace engineers use it to calculate the weight of spacecraft and satellites. In everyday life, we use this concept to understand why objects fall to the ground and to estimate the force of gravity acting on ourselves and other objects.

Now, let's apply the formula to calculate the weight of a book with a mass of 1.5 kg on Earth. We'll use the formula: Weight (W) = mass (m) × acceleration due to gravity (g). Given the mass (m) = 1.5 kg and the acceleration due to gravity (g) = 9.8 m/s², we can substitute these values into the formula:

W = 1.5 kg × 9.8 m/s²

Performing the multiplication:

W = 14.7 kg⋅m/s²

Since 1 kg⋅m/s² is equivalent to 1 Newton (N), the weight of the book is:

W = 14.7 N

Therefore, the weight of a book with a mass of 1.5 kg on Earth is 14.7 N. This calculation demonstrates how straightforward it is to determine the weight of an object when its mass and the acceleration due to gravity are known. The key is to correctly apply the formula and use the appropriate units. In this case, the mass is in kilograms, the acceleration due to gravity is in meters per second squared, and the resulting weight is in Newtons. The step-by-step approach ensures that each component of the calculation is clearly understood, minimizing the chance of errors. This method can be applied to any object with a known mass to determine its weight on Earth or any other celestial body, provided the acceleration due to gravity is known for that location. It is a fundamental calculation in physics and a practical application of Newton's Second Law of Motion. Understanding this calculation helps to solidify the relationship between mass, weight, and gravity, and provides a foundation for more advanced physics concepts.

Looking at the answer choices provided:

A. 1.5 N B. 6.5 N C. 11.3 N D. 14.7 N

Based on our calculation, the correct answer is D. 14.7 N. The other options are incorrect because they do not accurately reflect the application of the formula Weight = mass × gravity. Option A (1.5 N) is simply the mass of the book, which is not the same as its weight. It neglects the effect of gravity. Option B (6.5 N) and Option C (11.3 N) are values that do not result from the correct calculation using the given mass and the acceleration due to gravity. These incorrect options might arise from common mistakes such as using the wrong formula, misinterpreting the units, or making errors in the multiplication. By understanding the concepts of mass and weight, the formula for calculating weight, and the value of the acceleration due to gravity, we can confidently eliminate the incorrect options and identify the correct answer. The process of analyzing answer choices is an important skill in physics problem-solving. It involves not only performing the calculation correctly but also understanding why the other options are incorrect. This deeper understanding strengthens the grasp of the underlying principles and prevents the repetition of common errors. In this case, the analysis highlights the importance of distinguishing between mass and weight and the necessity of including the acceleration due to gravity in the calculation. It also emphasizes the value of double-checking the calculations and ensuring that the units are consistent throughout the process.

In conclusion, the weight of a book with a mass of 1.5 kg on Earth is 14.7 N. This was determined by applying the formula Weight = mass × acceleration due to gravity (W = mg), where g is approximately 9.8 m/s² on Earth. This calculation underscores the fundamental difference between mass and weight, with mass being an intrinsic property and weight being the force exerted by gravity on that mass. Understanding this distinction and the formula for calculating weight is crucial for solving physics problems and grasping the principles of mechanics. The example of the book illustrates a practical application of these concepts. By correctly identifying the given values (mass and acceleration due to gravity) and applying the formula, we were able to accurately determine the weight. This process can be generalized to other objects and scenarios, as long as the mass and the acceleration due to gravity are known. The calculation not only provides a numerical answer but also reinforces the relationship between mass, weight, and gravity. It highlights how these three concepts are interconnected and how they influence the physical world around us. Moreover, the analysis of the answer choices demonstrates the importance of critical thinking and the ability to identify and correct potential errors. By understanding why certain options are incorrect, we deepen our understanding of the correct solution and the underlying principles. This problem-solving approach is valuable not only in physics but also in various other fields of science and engineering. Ultimately, mastering the calculation of weight and the distinction between mass and weight lays a solid foundation for further exploration of mechanics and other areas of physics.