How would Fg vs. r look on a graphical diagram?Fg on y-axis, r on

[saan100]

how would Fg vs. r look on a graphical diagram?
Fg on y-axis, r on x-axis (from 1re to 6re)

re (radius of the Earth)

If a cannon ball is fired from the top of Everest parallel to the Earth's surface fast enough (ignoring air resistance and assuming that it doesn't bump into anything), it will "orbit" the Earth and hit the back of the cannon that it was fired from. Find the speed required to do this.

 

[JaredJames]

As this is homework, you'll need to show an attempt first.

The relationship for the first part is what? Linear? Squared? Cubic? Inverse-Square?

The second part, what equations do you know?

 

[saan100]

for the first part, it would linear .
for the second part, i would use v=2pi*r divided by T

 

[JaredJames]

for the first part, it would linear

Really? What's the equation for gravitational force?

for the second part, i would use v=2pi*r divided by T

I'm going to refer you here: http://en.wikipedia.org/wiki/Orbital_speed

You'd be better off using v = sqrt(GM/r) as you know all the numbers for that quite easily.

Where v = velocity, G = gravitational constant, M = mass of earth, r = radius of Earth plus height of everest.

If you don't know the speed, you won't know T from your above equation.

 

[saan100]

- the equation for Fg = G*m1*m2/r^2

-for second part, I'm confused over the formula you provided. Would you kindly explain it?

 

[JaredJames]

- the equation for Fg = G*m1*m2/r^2

Ok, so what does that tell you about the Fg and r relationship?

-for second part, I'm confused over the formula you provided. Would you kindly explain it?

Have a read through the link I provided, it's really short.

v = \sqrt {\frac {GM}r}

If you plug in the numbers as per my previous post, you will get the required orbital velocity for the height of everest. In other words, the speed you need the canon ball to travel at. That's all there is to it.

 

[saan100]

The relationship - The greater the radius, the lesser the gravitation force

 

[JaredJames]

The relationship - The greater the radius, the lesser the gravitation force

Of course, but what does the equation tell you?

Gravitational force decreases...

a) linearly to radius.
b) proportional to the square of the radius.
c) proportional to the cube of the radius.
d) inversely proportional to the square of the radius.

Look at it a bit simpler, the relationship is g = a/r².

Where a = Gm₁m₂

 

[saan100]

a) linearly to radius.

- for the second part question, in the equation r = re + h , how do u get the height of the everest

 

[JaredJames]

a) linearly to radius.

No, ok I'll give it to you. Gravity is inversely proportional to the square of the radius.

for the second part question, in the equation r = re + h , how do u get the height of the everest

Google.

 

[saan100]

thanks for the help !

 

[JaredJames]

thanks for the help !

Do you understand the first bit regarding the relationship though? Could you explain it with reference to the equation?