Problem 34 - Algebra 1: Concepts and Skills

Question

Weight varies directly with gravity. With his equipment, Buzz Aldrin weighed 360 pounds on Earth but only 60 pounds on the moon. If Valentina V. Tereshkova had landed on the moon with her equipment and weighed 54 pounds, how much would she have weighed on Earth with her equipment?

Step-by-Step Solution

Answer

Valentina would have weighed 324 pounds on Earth with her equipment.

Step 1: Analyze the Given Information

First, we examine the information given. It is known that Buzz Aldrin's weight on Earth is 360 pounds, and on the moon, it is 60 pounds. This gives a ratio of Earth weight to moon weight.

Step 2: Find the Earth/Moon Weight Ratio

The ratio of Earth weight to moon weight is found by dividing the Earth weight by the Moon weight: \( \frac{360lbs}{60lbs} \) which equals 6. This implies that the gravity on Earth is six times stronger than on the moon.

Step 3: Use the Ratio to Find Valentina's Earth Weight

Knowing that Valentina weighed 54 pounds on the moon, to find her weight on Earth, we simply multiply this weight by the ratio calculated in step 2. So, Valentina's Earth weight is \( 54lbs * 6 = 324lbs \).

Key Concepts

Ratios

Ratios are a way of comparing quantities, often expressing how many times one value is contained within another. In our scenario with Buzz Aldrin, his weight on Earth compared to his weight on the moon can be represented as a ratio. This comparison shows us how much heavier objects would seem under Earth's stronger gravitational pull. To form a ratio, you would divide one quantity by another, as seen when we divide Buzz's 360-pound Earth weight by his 60-pound moon weight. This calculation gives us a ratio of 6:1.

• Ratios help understand relationships between values.
• They are useful in problems involving direct variation.
• In this context, they illustrate differences in gravitational strengths.

This capacity to compare quantities is vital for solving problems where relationships between different conditions, like gravity, must be considered. In our case, this ratio directly tells us how much Earth's gravity magnifies weight compared to the moon's.

Earth and Moon Gravity Comparison

In this topic, we take a closer look at the differences in gravity between Earth and the moon. The gravity on Earth is substantially stronger, which is why objects weigh more here than they do on the moon. We can understand this gravitational difference better by looking at the weight relationship shown in the given problem.
The ratio of 6:1 tells us that the force of gravity on Earth is six times more powerful than on the moon. This means if you were to take any object from the moon to Earth, it would weigh six times its moon weight. This difference is crucial for understanding how astronauts experience different weight conditions when they land on other celestial bodies.

• The gravity on Earth is 9.8 m/s², much stronger than the 1.6 m/s² on the moon.
• This is why Buzz, who weighed 360 pounds on Earth, saw his weight drop to 60 pounds on the moon.
• Astronauts must consider these differences for equipment and mission planning.

Weight Calculation

Weight calculation in this context refers to the ability to use known variables, like gravitational differences, to determine unknown values. In our example, knowing Valentina's weight on the moon and the Earth/moon gravity ratio allows us to solve for her Earth weight.
This calculation utilizes the concept of direct variation, where one variable changes directly as another does. Since we've established Earth's gravity is six times stronger, we multiply Valentina's moon weight of 54 pounds by the ratio of 6 to find her Earth weight: \[ 54 ext{ pounds} \times 6 = 324 ext{ pounds}. \]

• Direct variation and ratios simplify weight calculations.
• Understanding these calculations is essential for designing equipment that can both reach space and function correctly on the surface of celestial bodies.
• Such calculations are vital in various scientific and practical applications, confirming the necessity of grasping these mathematical principles.