Problem 33 - Algebra 1

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 equipment?

Step-by-Step Solution

Answer

Valentina V. Tereshkova would weigh 324 pounds on Earth with her equipment.

Step 1: Determine the constant of variation

Find the constant of variation (k) using the information on Buzz Aldrin. This task can be achieved by dividing the weight on Earth by the weight on the Moon for Buzz Aldrin. So, \( k = \frac{Weight_{Earth, Buzz}}{Weight_{Moon, Buzz}} = \frac{360 lbs}{60 lbs} = 6 \)

Step 2: Use the constant of variation to find the weight on Earth for Valentina

Using the constant from step 1, multiply Valentina's weight on the moon to find her weight on Earth. So, \( Weight_{Earth, Valentina} = Weight_{Moon, Valentina} \times k = 54 lbs \times 6 = 324 lbs \)

Step 3: Interpret the result

The result indicates that Valentina V. Tereshkova would have weighed 324 pounds on Earth with her equipment.

Key Concepts

Gravity

Gravity is a fundamental force that attracts objects with mass towards each other. On Earth, gravity gives us our weight by pulling us towards the center of the planet. The force of gravity is why objects fall to the ground when dropped. Gravity on Earth is approximately 9.8 meters per second squared (m/s²). It is important to understand that gravity is not the same everywhere. For example, the Moon has weaker gravity due to its smaller size compared to Earth. This difference in gravity affects how much you weigh on each celestial body.

Weight Calculation

Weight is the force exerted by gravity on an object's mass. It can be calculated using the formula: \( Weight = Mass \times Gravity \). On Earth, this means multiplying your mass by Earth's gravitational force. This formula helps determine how much an object weighs. So, if you know the mass of an object and the gravity of the location, you can calculate the weight.

• On Earth, the gravity is 9.8 m/s². You multiply this by the mass to find the weight in newtons.
• On the Moon, gravity is about 1.6 m/s², so the weight of the same object would be less.

Constant of Variation

Direct variation with gravity means that weight changes proportionally with gravity. The constant of variation, often denoted by \( k \), shows the relationship between weights on different celestial bodies. In mathematical terms, \( k \) is calculated by dividing the weight on Earth by the weight on another body. For Buzz Aldrin, the constant was determined by \( k = \frac{360 \text{ lbs}}{60 \text{ lbs}} = 6 \). This constant helps calculate weights on Earth and the Moon by scaling the weight by \( k \). It provides a simple and reliable method to relate weights across different gravities.

Earth and Moon Weight Comparison

Comparing weights between Earth and the Moon involves understanding the difference in gravity. Because the Moon's gravity is weaker, objects weigh less than they do on Earth. This difference is quantified through the constant of variation. By knowing Buzz Aldrin's weight reduction, the constant of 6 was found, highlighting how much less an object weights on the Moon.

• Valentina V. Tereshkova weighed 54 pounds on the Moon.
• By applying the constant of variation, we discovered she would weigh 324 pounds on Earth.

This comparison highlights how gravity significantly affects weight, an essential concept in studying different planetary bodies.