The mass of Venus is 81.5% that of the earth, and its radius is 94.9% that of the earth. (b) If a rock weighs 75.0 N on earth, what would it weigh at the surface of Venus?

Verified step by step guidance

1. Calculate the mass of Venus by multiplying the mass of Earth by 81.5%. Use the formula: \( M_{Venus} = 0.815 \times M_{Earth} \).
2. Calculate the radius of Venus by multiplying the radius of Earth by 94.9%. Use the formula: \( R_{Venus} = 0.949 \times R_{Earth} \).
3. Use the gravitational force formula to find the weight on Venus. The formula is \( F = G \frac{M_{Venus} \times m}{R_{Venus}^2} \), where \( G \) is the gravitational constant, \( M_{Venus} \) is the mass of Venus, \( m \) is the mass of the object, and \( R_{Venus} \) is the radius of Venus.
4. Calculate the mass of the rock from its weight on Earth using the formula \( m = \frac{W_{Earth}}{g_{Earth}} \), where \( W_{Earth} \) is the weight of the rock on Earth and \( g_{Earth} \) is the acceleration due to gravity on Earth.
5. Substitute the values of \( M_{Venus} \), \( R_{Venus} \), and \( m \) into the gravitational force formula to find the weight of the rock on Venus.

Key Concepts

Weight and Gravitational Force

Weight is the force exerted by gravity on an object, calculated as the product of mass and gravitational acceleration (W = mg). On different celestial bodies, the gravitational acceleration varies due to differences in mass and radius, affecting the weight of objects. Understanding how to calculate weight in different gravitational fields is essential for solving problems involving weight on other planets.

Gravitational Acceleration

Gravitational acceleration (g) is the acceleration experienced by an object due to the gravitational pull of a planet. It can be calculated using the formula g = G(M/r²), where G is the gravitational constant, M is the mass of the planet, and r is its radius. For Venus, knowing its mass and radius relative to Earth allows us to determine its gravitational acceleration and subsequently the weight of objects on its surface.

Proportional Relationships

Proportional relationships are used to compare quantities that change in relation to one another. In this context, the weight of an object on Venus can be determined by establishing a ratio based on the gravitational accelerations of Earth and Venus. By understanding how the mass and radius of Venus affect its gravity, we can apply these ratios to find the new weight of the rock when transferred from Earth to Venus.