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

Verified step by step guidance

1. First, understand that weight is the force exerted by gravity on an object. It is calculated using the formula: $W=mg$, where $W$ is the weight, $m$ is the mass of the object, and $g$ is the acceleration due to gravity.
2. Next, calculate the gravitational acceleration on Venus using the formula: $g=\frac{GM}{R^2}$, where $G$ is the gravitational constant, $M$ is the mass of Venus, and $R$ is the radius of Venus.
3. Since the mass of Venus is 81.5% that of Earth, express this as $M=0.815M$_e, where $M$_e is the mass of Earth.
4. Similarly, the radius of Venus is 94.9% that of Earth, expressed as $R=0.949R$_e, where $R$_e is the radius of Earth.
5. Finally, substitute these values into the gravitational acceleration formula to find $g$ for Venus, and then use the weight formula $W=mg$ to calculate the weight of the rock on Venus, knowing its mass from its weight on Earth.

Key Concepts

Gravitational Force

Gravitational force is the attractive force between two masses. On a planetary surface, it is calculated using the formula F = mg, where F is the force (weight), m is the mass of the object, and g is the acceleration due to gravity. The weight of an object varies depending on the gravitational pull of the planet it is on.

Acceleration Due to Gravity

The acceleration due to gravity (g) on a planet's surface is determined by the planet's mass and radius. It is calculated using the formula g = G * (M/R^2), where G is the gravitational constant, M is the planet's mass, and R is its radius. This value affects how much an object weighs on that planet.

Proportionality and Ratios

Proportionality and ratios are mathematical tools used to compare quantities. In this context, they help determine how changes in mass and radius affect gravitational force. By comparing Venus's mass and radius to Earth's, we can calculate the change in gravitational acceleration and thus the weight of an object on Venus.