Calculating Weight And Mass: A Physics Problem

Hey guys! Let's dive into a classic physics problem where we'll be calculating weight and mass. This is a fundamental concept in physics, and understanding how these two are related is super important. We'll use the equation Weight (N) = mass (kg) × 9.8 m/s² to fill in the missing values in the table. So, grab your calculators and let's get started!

Understanding Weight and Mass

Before we jump into the calculations, let's quickly recap what weight and mass actually are. This will help solidify our understanding and make the problem even easier to tackle. Mass is a measure of how much matter an object contains. It's a fundamental property of the object and doesn't change unless you physically add or remove matter. We typically measure mass in kilograms (kg). Think of it as the object's resistance to acceleration. The more massive an object is, the harder it is to push or stop.

On the other hand, weight is the force of gravity acting on an object's mass. It's the pull that the Earth (or any other celestial body) exerts on the object. Weight is measured in Newtons (N). Since weight is a force, it depends on both the object's mass and the gravitational acceleration. That's why the equation we're using includes the value 9.8 m/s², which is the approximate acceleration due to gravity on Earth. This means that your weight can change depending on where you are in the universe, but your mass will stay the same. For example, you would weigh less on the Moon because the Moon's gravitational pull is weaker than Earth's, but your mass would still be the same.

It's a common mistake to use the terms mass and weight interchangeably, but they represent different concepts. Mass is an intrinsic property, while weight is a force that depends on gravity. Understanding this difference is crucial for solving physics problems correctly. This distinction becomes especially important when dealing with scenarios in different gravitational environments, like space travel or planetary comparisons. Imagine comparing the weight of an astronaut on Earth versus on Mars. Their mass remains constant, but their weight changes dramatically due to the different gravitational forces. So, always remember: mass is what you are, and weight is the force acting upon you due to gravity!

Filling in the Missing Values

Now, let's get to the core of the problem. We have a table with missing values for mass and weight, and we need to use the equation Weight (N) = mass (kg) × 9.8 m/s² to complete it. This is a straightforward application of the formula, but we'll go through each step to make sure we understand the process. The table looks like this:

We already have one weight value, which serves as a good initial check to ensure we understand the relationship between mass and weight. Object C, with a mass of 60 kg, has a weight of 588 N. If we were to quickly calculate using our equation, 60 kg * 9.8 m/s^2 equals 588 N, which matches what's in the table. This confirmation gives us confidence that we're on the right track and that the provided data is consistent with the physics principles we're applying.

Calculating the Weight of Object A

Let's start with Object A. We know the mass is 25 kg, and we need to find the weight. We can directly apply the formula:

Weight (N) = 25 kg × 9.8 m/s²

Weight (N) = 245 N

So, the weight of Object A is 245 N. It's as simple as plugging in the known values and solving for the unknown. Remember, the units are important! We're multiplying kilograms (kg) by meters per second squared (m/s²), which gives us Newtons (N), the unit of force. Always keep track of your units to ensure your answer makes sense physically.

Calculating the Mass of Object B

Next up is Object B. This time, we know the weight (294 N) and need to find the mass. We'll need to rearrange the formula to solve for mass:

Mass (kg) = Weight (N) / 9.8 m/s²

Mass (kg) = 294 N / 9.8 m/s²

Mass (kg) = 30 kg

Therefore, the mass of Object B is 30 kg. Notice how we rearranged the equation. Instead of multiplying, we're dividing the weight by the gravitational acceleration. This is a crucial skill in physics – being able to manipulate equations to solve for different variables. Don't just memorize the formula in one form; practice rearranging it to solve for any of the variables involved. This will make you a much more confident and capable problem solver!

Completed Table

Now that we've calculated the missing values, let's complete the table:

We've successfully filled in all the missing values using the equation Weight (N) = mass (kg) × 9.8 m/s². This exercise demonstrates the direct relationship between mass and weight. As you can see, a larger mass results in a greater weight, which makes intuitive sense since weight is the force of gravity acting on that mass. This simple calculation is a cornerstone of physics, and mastering it will open the door to understanding more complex concepts later on.

Key Takeaways

Let's quickly summarize the key takeaways from this problem. First, remember the difference between mass and weight. Mass is the amount of matter in an object, while weight is the force of gravity acting on that mass. They are related but distinct concepts. Second, the equation Weight (N) = mass (kg) × 9.8 m/s² is fundamental for calculating weight on Earth. Third, be comfortable rearranging the equation to solve for different variables, like we did when finding the mass of Object B. Finally, always pay attention to units! They are crucial for ensuring your answer makes sense and is physically accurate.

By understanding these concepts and practicing applying the formula, you'll be well-equipped to tackle similar problems involving weight and mass. Physics can seem intimidating at first, but by breaking down problems into smaller steps and understanding the underlying principles, you can conquer any challenge. So keep practicing, keep asking questions, and keep exploring the amazing world of physics!

Practice Problems

To further solidify your understanding, try these practice problems:

1. An object has a mass of 50 kg. What is its weight on Earth?
2. An object weighs 735 N on Earth. What is its mass?
3. What would the weight of a 100 kg object be on a planet with a gravitational acceleration of 3.7 m/s²?

Work through these problems, and you'll be a pro at calculating weight and mass in no time. Remember, physics is all about practice and application. The more you work with these concepts, the more comfortable and confident you'll become.

So, guys, that's it for this problem! I hope this explanation was helpful. Remember, physics is a journey, and every problem you solve brings you one step closer to mastering the subject. Keep up the great work, and I'll see you in the next problem!