gravitational and elastic potential energy....

[Cyber]

Hi sup guys i need you help...

 

What are the relationships between the gravitational potential energy of a suspended mass and elastic potential energy in a stretched spring?

 

the answer to this...

 

The gravitational potential energy of a suspended mass is inversely proportional to the elastic potential energy in a stretched spring

 

is this answer correct...

 

thanks in advance

[swansont]

Since an answer can be right for the wrong reason, you need to explain why you think that. Show your work.

[Severian]

The gravitational potential energy of a suspended mass is inversely proportional to the elastic potential energy in a stretched spring

 

This looks wrong to me.

 

The elastic potential energy is [math]E_E = \frac{1}{2}kx^2[/math] where k is the spring constant, and x is the extension of the spring beyond its natural length.

 

Usually one would write the gravitational potential energy of an object is [math]E_G = mgh[/math] where m is its mass, g is the acceleration due to gravity and h is the height from some arbitrary ground level.

 

Then, taking the zero of the gravitational potential at the height of natural extension of the string, [math]E_G = -mgx[/math] which is clearly not inversely proportional to [math]E_E = \frac{1}{2}kx^2[/math].

 

However, this gravitational potential is just an approximation, so maybe they want you to use [math]E_G = -G\frac{Mm}{r}[/math], where M and m are the mass of the Earth and object respectively, r is its distance from the centre of the Earth and G is the gravitational constant. (This reduces to the previous example for small deviations form the zero point.) But again, this isn't inversely proportional to the elastic case.