Math Problem Statement

A bag of sugar weighs 1.00 lb on Earth. What would it weigh in Newtons on the Moon, where the free-fall acceleration is one-sixth that on Earth?

Solution

To find the weight of the sugar bag in Newtons on the Moon, we can go through the following steps:

Step 1: Convert Weight on Earth from Pounds to Newtons

  1. A weight of 1.00 lb on Earth is equivalent to a force in Newtons, since weight is the force of gravity acting on an object.

    To convert from pounds to Newtons: 1 lb=4.448 N1 \text{ lb} = 4.448 \text{ N} So, the weight of the sugar bag on Earth is: 1.00lb×4.448N/lb=4.448N1.00 \, \text{lb} \times 4.448 \, \text{N/lb} = 4.448 \, \text{N}

Step 2: Calculate the Weight on the Moon

  1. On the Moon, the gravitational acceleration is one-sixth of that on Earth. Therefore, the weight of the sugar bag on the Moon is also one-sixth of its weight on Earth.

    Weight on Moon=4.448N6=0.7413N\text{Weight on Moon} = \frac{4.448 \, \text{N}}{6} = 0.7413 \, \text{N}

Answer

The weight of the 1.00 lb sugar bag on the Moon would be approximately: 0.741N0.741 \, \text{N}

Would you like additional details or have any questions?

Related Questions

  1. How would the weight change if the gravitational acceleration were one-fourth that of Earth?
  2. What would the sugar bag’s weight be on a planet with twice the Moon’s gravitational acceleration?
  3. How do we calculate weight on a celestial body with unknown gravitational force?
  4. What would the sugar bag's mass be in kilograms?
  5. How do other planets’ gravity affect weights similarly?

Tip

Weight varies depending on the gravitational field strength, but mass stays constant regardless of location.

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Math Problem Analysis

Mathematical Concepts

Weight Conversion
Gravitational Acceleration

Formulas

Weight (N) = Mass (kg) × Gravitational Acceleration (m/s^2)
1 lb = 4.448 N

Theorems

Weight varies with gravitational field strength

Suitable Grade Level

Grades 9-12