If An Object Weighs 48 N On The Moon, What Would Its Weight Be On Earth? The Gravity On The Moon Is About 1/6th That Of Earth. Calculate The Correct Option.
In the realm of physics, understanding the relationship between weight and gravity is fundamental. Weight, unlike mass, is not an intrinsic property of an object. Instead, it is the force exerted on an object due to gravity. This means that an object's weight can change depending on the gravitational field it is in. A classic example of this is comparing an object's weight on the Moon versus its weight on Earth. This article will delve into this concept by solving a specific problem: If an object weighs 48 N on the Moon, what would its weight be on Earth, given that the Moon's gravity is approximately 1/6th of Earth's gravity? We will explore the underlying physics principles, walk through the calculation step by step, and arrive at the correct answer. Furthermore, we will discuss the implications of this calculation in understanding gravitational forces and their effect on weight, providing a comprehensive explanation suitable for students and enthusiasts alike. This article not only serves as a problem-solving exercise but also as a deeper exploration into the fascinating world of physics and gravitational interactions. Understanding weight and gravity is crucial not only for academic pursuits but also for comprehending various real-world phenomena, from the motion of celestial bodies to the design of structures on different planets.
To accurately calculate the weight of an object on Earth, starting from its weight on the Moon, we must first understand the fundamental concepts of weight and gravity. Weight is the force exerted on an object due to gravity. It is a vector quantity, meaning it has both magnitude and direction. The magnitude of weight is typically measured in Newtons (N) in the International System of Units (SI). Gravity, on the other hand, is the force of attraction between any two objects with mass. The more massive an object, the stronger its gravitational pull. Similarly, the closer two objects are, the stronger the gravitational force between them. These principles are encapsulated in Newton's Law of Universal Gravitation, which provides a mathematical framework for understanding gravitational interactions. The law states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This understanding is crucial because the gravitational force exerted by a celestial body, like the Earth or the Moon, determines the weight of an object on its surface. Since the Moon has significantly less mass than the Earth, its gravitational pull is weaker. Specifically, the gravity on the Moon is approximately 1/6th of the gravity on Earth. This difference in gravitational force is the key to solving the problem at hand. We will use this ratio to determine how the weight of an object changes as it moves from the Moon to Earth, demonstrating the practical application of these fundamental physics concepts. Recognizing the direct relationship between gravity and weight allows us to accurately predict and calculate weight variations across different celestial bodies, enhancing our understanding of the cosmos and the forces that govern it.
The core of our discussion lies in solving the problem: If an object weighs 48 N on the Moon, what would its weight be on Earth? Given that the gravity on the Moon is approximately 1/6th of the gravity on Earth, we can approach this problem systematically. The weight of an object is given by the formula:
Weight (W) = mass (m) × gravitational acceleration (g)
On the Moon, the object's weight (_W_Moon) is 48 N. Let's denote the gravitational acceleration on the Moon as _g_Moon and on Earth as _g_Earth. We know that _g_Moon = (1/6) _g_Earth.
So, we can write the equation for the weight on the Moon as:
48 N = m × _g_Moon
Since _g_Moon is (1/6) _g_Earth, we can substitute this into the equation:
48 N = m × (1/6) _g_Earth
Now, we want to find the weight on Earth (_W_Earth), which is given by:
_W_Earth = m × _g_Earth
To find _W_Earth, we need to find the value of m × _g_Earth. From the equation for the weight on the Moon, we can rearrange to find this value:
m × _g_Earth = 48 N × 6
m × _g_Earth = 288 N
Therefore, the weight of the object on Earth is 288 N. This calculation underscores the principle that weight is directly proportional to gravitational acceleration. By understanding this relationship and applying the given ratio of lunar to terrestrial gravity, we have successfully determined the object's weight on Earth. The correct answer, therefore, is A) 288 N. This step-by-step solution not only provides the answer but also reinforces the importance of understanding the underlying physics principles and applying them in a logical and methodical manner.
To ensure clarity and understanding, let's break down the calculation into a step-by-step process. This will not only solidify the solution but also provide a template for tackling similar problems in the future. The initial information we have is:
- Weight on the Moon (_W_Moon) = 48 N
- Gravitational acceleration on the Moon (_g_Moon) = (1/6) × Gravitational acceleration on Earth (_g_Earth)
The objective is to find the weight on Earth (_W_Earth). Step 1: Write down the formula for weight on the Moon: 48 N = m × _g_Moon Step 2: Substitute _g_Moon with (1/6) _g_Earth: 48 N = m × (1/6) _g_Earth Step 3: Rearrange the equation to isolate m × _g_Earth, which represents the weight on Earth: m × _g_Earth = 48 N × 6 Step 4: Perform the multiplication: m × _g_Earth = 288 N Step 5: Recognize that m × _g_Earth is the weight on Earth: _W_Earth = 288 N Therefore, the weight of the object on Earth is 288 N. This step-by-step breakdown illustrates the logical progression from the given information to the final answer. Each step is clearly defined, making it easy to follow the reasoning and the mathematical operations involved. By breaking down the problem into manageable steps, we can better understand the underlying concepts and avoid errors. This method is particularly useful for students learning physics, as it promotes a systematic approach to problem-solving. Furthermore, this detailed calculation highlights the significance of each step, reinforcing the connection between weight, mass, and gravitational acceleration. This thorough approach ensures that the solution is not only correct but also well-understood.
Understanding the difference in weight due to varying gravitational forces has significant implications and applications in various fields. Firstly, it is crucial in space exploration. When planning missions to the Moon or other celestial bodies, engineers must account for the change in weight of equipment and astronauts. This affects the design of spacecraft, landing systems, and even the daily activities of astronauts. For instance, an object that is easily lifted on the Moon might be too heavy to move on Earth without assistance. Similarly, the reduced gravity on the Moon allows astronauts to perform tasks that would be impossible on Earth, such as leaping great distances. Secondly, this concept is vital in astrophysics and planetary science. By studying the gravitational forces on different planets and moons, scientists can infer information about their mass, density, and composition. This knowledge is essential for understanding the formation and evolution of the solar system. Furthermore, the principles of weight and gravity are fundamental in engineering and construction. When designing structures on Earth, engineers must consider the weight of materials and the forces acting upon them. This is even more critical when planning for structures on other planets, where gravitational forces may differ significantly. In addition, understanding weight and gravity helps us comprehend everyday phenomena. From the tides caused by the Moon's gravity to the trajectory of a ball thrown in the air, gravity plays a crucial role in our daily lives. The ability to calculate and predict weight changes in different gravitational environments is not just an academic exercise; it is a practical skill with far-reaching applications. By mastering these concepts, we gain a deeper understanding of the universe and our place within it. This knowledge empowers us to explore, innovate, and solve real-world problems across a variety of disciplines.
In conclusion, determining the weight of an object on Earth given its weight on the Moon is a fascinating exercise that underscores the fundamental principles of physics. By understanding the relationship between weight, mass, and gravitational acceleration, we successfully calculated that an object weighing 48 N on the Moon would weigh 288 N on Earth. This calculation, based on the Moon's gravity being approximately 1/6th of Earth's gravity, highlights the significant impact of gravitational force on an object's weight. The step-by-step solution provided a clear and methodical approach to solving the problem, reinforcing the importance of logical reasoning and the application of physics concepts. Furthermore, we explored the implications and applications of this knowledge in various fields, including space exploration, astrophysics, engineering, and our daily lives. The ability to accurately calculate weight changes in different gravitational environments is not only crucial for scientific endeavors but also enhances our overall understanding of the universe. This exercise serves as a valuable lesson in the power of physics to explain and predict real-world phenomena. It also demonstrates the interconnectedness of various scientific disciplines and the importance of a solid foundation in fundamental concepts. By mastering these principles, we can continue to explore the mysteries of the cosmos and push the boundaries of human knowledge. The study of weight and gravity is not just an academic pursuit; it is a gateway to understanding the forces that shape our universe and our place within it.