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. What would be its mass and weight on the surface of Io?

Verified step by step guidance

1. Step 1: Understand the relationship between weight, mass, and gravitational acceleration. Weight (W) is given by the formula: $W=mg$, where $m$ is the mass and $g$ is the gravitational acceleration.
2. Step 2: Calculate the mass of the watermelon using Earth's gravitational acceleration. On Earth, $g=9.8m/s^2$. Rearrange the formula to find mass: $m=W/g$. Substitute $W=44.0N$ and $g=9.8m/s^2$.
3. Step 3: Use the calculated mass to determine the weight of the watermelon on Io. The gravitational acceleration on Io is $g=1.81m/s^2$. Use the formula $W=mg$ and substitute the mass and Io's gravitational acceleration.
4. Step 4: Verify the units in your calculations. Ensure that the mass is in kilograms (kg) and the weight is in newtons (N). This is important for consistency and correctness in physics problems.
5. Step 5: Interpret the results. The mass of the watermelon remains constant regardless of location, as mass is an intrinsic property of matter. However, the weight changes depending on the gravitational acceleration of the celestial body.

Key Concepts

Weight and Mass

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. On different celestial bodies, the weight of an object changes due to variations in gravitational acceleration, while its mass remains the same.

Gravitational Acceleration

Gravitational acceleration is the acceleration experienced by an object due to the gravitational force of a celestial body. It varies depending on the mass and radius of the body. For example, Jupiter's moon Io has a gravitational acceleration of 1.81 m/s², which is significantly less than Earth's 9.81 m/s², affecting the weight of objects on its surface.

Calculating Weight on Different Celestial Bodies

To find the weight of an object on a different celestial body, you can use the formula W = mg, where 'm' is the mass of the object and 'g' is the gravitational acceleration of that body. By knowing the mass of the object (which can be derived from its weight on Earth) and the gravitational acceleration on Io, you can calculate the object's weight on that moon.