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

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

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.