To determine which prediction Shari could make regarding her weight on Venus in comparison to her weight on Earth, we need to carefully examine the provided data and understand the factors that influence weight.
Weight is determined by the force of gravity acting on a person's mass, and this force is given by the equation:
[tex]\[ \text{Weight} = \text{mass} \times \text{gravitational acceleration} \][/tex]
Looking at the provided data:
- The gravitational acceleration on Venus is [tex]\(8.9 \, m/s^2\)[/tex].
- The gravitational acceleration on Earth is [tex]\(9.8 \, m/s^2\)[/tex].
Since weight depends directly on the gravitational acceleration, we can immediately see that gravitational acceleration on Venus is lower than on Earth. Consequently, given the same mass, a person’s weight would indeed be lower on Venus because the gravitational force is weaker.
Next, let's evaluate the statements one by one to see which is the best prediction:
1. "Her weight is greater on Venus because Venus has less mass."
- This statement is incorrect. The weight of an object is not directly influenced solely by the mass of the planet; it is dependent on the gravitational acceleration of the planet.
2. "Her weight is lower on Venus because the acceleration due to gravity is lower."
- This statement is correct. Since the gravitational acceleration on Venus [tex]\( (8.9 \, m/s^2) \)[/tex] is lower than that on Earth [tex]\( (9.8 \, m/s^2) \)[/tex], a person will weigh less on Venus.
3. "Her weight is lower on Earth because it is farther from the Sun."
- This statement is unrelated to the weight of a person. The distance from the Sun does not affect a person's weight on the planet.
4. "Her weight is greater on Venus because Venus has a smaller diameter."
- This statement is incorrect. While the diameter can influence surface gravity when considering the mass and radius of a planet, it is not a direct factor in determining weight without considering gravitational acceleration. Since gravitational acceleration on Venus is already provided and is less than on Earth, the smaller diameter does not lead to greater weight on Venus.
Based on this analysis, the best prediction Shari could make is:
Her weight is lower on Venus because the acceleration due to gravity is lower.
