At the surface of Jupiter's moon Io, the acceleration due to gravity is g = 1.81 m/s2. A watermelon weighs 44.0 N at the surface of the earth. (b) What would be its mass and weight on the surface of Io?

Verified step by step guidance

1. First, determine the mass of the watermelon on Earth. Use the formula for weight: \( W = m \cdot g \), where \( W \) is the weight, \( m \) is the mass, and \( g \) is the acceleration due to gravity on Earth (\( 9.81 \text{ m/s}^2 \)). Rearrange the formula to solve for mass: \( m = \frac{W}{g} \). Substitute \( W = 44.0 \text{ N} \) and \( g = 9.81 \text{ m/s}^2 \) to find the mass.
2. Next, use the mass calculated from the previous step to find the weight of the watermelon on Io. The weight on Io can be calculated using the formula \( W_{\text{Io}} = m \cdot g_{\text{Io}} \), where \( g_{\text{Io}} = 1.81 \text{ m/s}^2 \) is the acceleration due to gravity on Io.
3. Substitute the mass obtained from the first step and \( g_{\text{Io}} = 1.81 \text{ m/s}^2 \) into the formula \( W_{\text{Io}} = m \cdot g_{\text{Io}} \) to calculate the weight of the watermelon on Io.
4. Verify the units in your calculations to ensure they are consistent. The mass should be in kilograms (kg) and the weight should be in newtons (N).
5. Review the calculations to ensure accuracy and consistency with the physical principles involved, such as the relationship between mass, weight, and gravitational acceleration.

Key Concepts

Weight and Mass Relationship

Weight is the force exerted by gravity on an object, calculated as the product of mass and gravitational acceleration (W = mg). Mass is a measure of the amount of matter in an object and remains constant regardless of location, while weight varies with the gravitational field strength.

Gravitational Acceleration

Gravitational acceleration is the rate at which an object accelerates due to the force of gravity. It varies depending on the celestial body, with Earth's average being 9.81 m/s² and Io's being 1.81 m/s². This difference affects the weight of objects on different planets or moons.

Conversion of Weight to Mass

To find the mass of an object from its weight, use the formula mass = weight / gravitational acceleration. On Earth, a watermelon weighing 44.0 N has a mass of 44.0 N / 9.81 m/s². This mass remains constant when calculating its weight on Io using Io's gravitational acceleration.