Question on Proportionate spheres (Help )

[aquirk]

Question on Proportionate spheres (Help!)

A spherical balloon is partially blown up and its surface area is measured. More air is then added, increasing the volume of the balloon. If the surface area of the balloon expands by a factor of 9.4 during this procedure, by what factor does the radius of the balloon change?

If the radius of a sphere is increased by 12 %, by what factor does its surface area increase?
- By what percentage does its surface area increase?
- By what factor does the sphere's volume increase?
- By what percentage does the sphere's volume increase?

The weight of an object at the surface of a planet is proportional to the planet's mass and inversely proportional to the square of the radius of the planet. Jupiter's radius is 11 times Earth's and its mass is 320 times Earth's. An apple weighs 1.0 N on Earth. How much would it weigh on Jupiter?

 

[LowlyPion]

A spherical balloon is partially blown up and its surface area is measured. More air is then added, increasing the volume of the balloon. If the surface area of the balloon expands by a factor of 9.4 during this procedure, by what factor does the radius of the balloon change?

If the radius of a sphere is increased by 12 %, by what factor does its surface area increase?
- By what percentage does its surface area increase?
- By what factor does the sphere's volume increase?
- By what percentage does the sphere's volume increase?

The weight of an object at the surface of a planet is proportional to the planet's mass and inversely proportional to the square of the radius of the planet. Jupiter's radius is 11 times Earth's and its mass is 320 times Earth's. An apple weighs 1.0 N on Earth. How much would it weigh on Jupiter?

What are your thoughts on a solution?

 

[aquirk]

I figured out the first few questions, I just have the one left about how much the object would weigh on Jupiter. I understand the proportional/inversely proportional aspects to the problem, I just don't get how you use them together to get the weight on Jupiter. I don't even get how they use the two to get the weight on Earth.

 

[LowlyPion]

I figured out the first few questions, I just have the one left about how much the object would weigh on Jupiter. I understand the proportional/inversely proportional aspects to the problem, I just don't get how you use them together to get the weight on Jupiter. I don't even get how they use the two to get the weight on Earth.

From the statement of the problem:

The weight of an object at the surface of a planet is proportional to the planet's mass and inversely proportional to the square of the radius of the planet. Jupiter's radius is 11 times Earth's and its mass is 320 times Earth's. An apple weighs 1.0 N on Earth. How much would it weigh on Jupiter?

It says the weight is proportional to the mass of the planet. That would mean the bigger the mass the greater the weight right?
Then it says that the weight is also inversely proportional to the square of the radius of the planet.

So if you put that in a formula it would look like:

$$Weight \propto \frac{Planet Mass}{Radius^2}$$

So if your weight on Earth is 1N and the Planet Mass is 320 times greater and the Radius is 11 times greater then the apple will be ______ times greater?

 

[tiny-tim]

Welcome to PF!

I understand the proportional/inversely proportional aspects to the problem, I just don't get how you use them together to get the weight on Jupiter. I don't even get how they use the two to get the weight on Earth.

Hi aquirk! Welcome to PF!

That's the beauty of this dimension method …

you don't need to know how they use the two to get the weight on Earth! …

just follow LowlyPion's advice … take the figure they've given you for Earth, and plug it into the dimension equation.

 

[Mussidae]

an apple wieghs 1.0 N on Earth. set it up so you are multipling 320 by Earths planet mass divided by Earths Radius^2 multiplied by 11. the Earth Data cancels to 1.0 N so 320/11 is roughly 29.0 multiplied by 1.0 N we get that an apple wieghs 29.0 N on Jupiter.