THE MASS OF VENUS IS 81.5% OF THE EARTH AND ITS RADIUS IS 94.9% THAT OF THE EARTH. A)COMPUTE THE ACCELERATION DUE TO GRAVITY ON THE SURFACE OF VENUS FROM THESE DATA.B)IF A ROCK WEIGHS 75.0N ON EARTH,WHAT WOULD IT WEIGH ON THE SURFACE OF VENUS?
a. g is proportional to Mass/radius^2
gvenus=9.8*.815/.949^2= you do it.
b. weight=75*gvenus above.
A) To compute the acceleration due to gravity on the surface of Venus, we can use the formula:
acceleration due to gravity (g) = G * (mass of Venus) / (radius of Venus)²
Where G represents the gravitational constant, which is approximately 6.67430 x 10^-11 N(m/kg)².
Given that the mass of Venus is 81.5% of the Earth's mass and the radius of Venus is 94.9% of the Earth's radius, we can use the following values:
mass of Venus = 0.815 * (mass of Earth)
radius of Venus = 0.949 * (radius of Earth)
Now we can substitute these values into the formula to calculate the acceleration due to gravity on the surface of Venus.
acceleration due to gravity (g) = (6.67430 x 10^-11 N(m/kg)²) * (0.815 * (mass of Earth)) / (0.949 * (radius of Earth))²
(Assuming the mass of Earth is 5.972 x 10^24 kg and the radius of Earth is 6.371 x 10^6 m)
B) To determine the weight of a rock on the surface of Venus, we can use the formula:
weight on Venus = weight on Earth * (acceleration due to gravity on Venus / acceleration due to gravity on Earth)
Given that the weight of the rock on Earth is 75.0 N, and we have already calculated the acceleration due to gravity on Venus, we can substitute these values into the formula to find the weight of the rock on the surface of Venus.
weight on Venus = 75.0 N * (acceleration due to gravity on Venus / acceleration due to gravity on Earth)
Now let's calculate these values step by step.
1. Calculate the mass of Venus:
mass of Venus = 0.815 * (mass of Earth)
mass of Venus = 0.815 * (5.972 x 10^24 kg)
2. Calculate the radius of Venus:
radius of Venus = 0.949 * (radius of Earth)
radius of Venus = 0.949 * (6.371 x 10^6 m)
3. Calculate the acceleration due to gravity on the surface of Venus:
acceleration due to gravity (g) = (6.67430 x 10^-11 N(m/kg)²) * (mass of Venus) / (radius of Venus)²
4. Calculate the weight of the rock on the surface of Venus:
weight on Venus = 75.0 N * (acceleration due to gravity on Venus / acceleration due to gravity on Earth)
To compute the acceleration due to gravity on the surface of Venus, we can use the formula for the acceleration due to gravity:
g = (G * M) / R^2
where:
g is the acceleration due to gravity,
G is the universal gravitational constant (approximately 6.67430 × 10^-11 m^3⋅kg^-1⋅s^-2),
M is the mass of the celestial object (in this case, Venus),
and R is the radius of the celestial object (in this case, Venus).
A) Compute the acceleration due to gravity on the surface of Venus:
Given that the mass of Venus is 81.5% of the Earth's mass and the radius is 94.9% of the Earth's radius, we need to find the actual values of the mass and radius of Venus.
Let's assume the mass of Earth to be Me and the radius of Earth to be Re.
Mass of Venus (Mv) = 81.5% of Me = (81.5/100) * Me
Radius of Venus (Rv) = 94.9% of Re = (94.9/100) * Re
Substituting these values into the equation, we get:
g = (G * Mv) / Rv^2
B) To find the weight of the rock on the surface of Venus, we need to use the formula for weight:
weight = mass * acceleration due to gravity
Given that the weight of the rock on Earth is 75.0N, let's assume the mass of the rock to be m.
Weight of rock on Earth = mass * acceleration due to gravity on Earth = m * g(e)
Weight of rock on Venus = mass * acceleration due to gravity on Venus = m * g(v)
Substituting the values into the equation, we have:
Weight of rock on Earth / Weight of rock on Venus = g(e) / g(v)
So, to find the weight of the rock on the surface of Venus, we can use the above equation and the known weight of the rock on Earth.