The 2.5-kg wieght is released from rest -- Determine the spring constant k

[Alexanddros81]

Homework Statement

14.27 The 2.5-kg weight is released from rest in position A, where the two springs
of stiffness k each are undeformed. Determine the largest k for which the weight
would reach position B

Homework Equations

The Attempt at a Solution

Hi. Can you check if I am going at the right direction?
Also for $Wy_B$ and $Wy_A$ am I replacing with 2.5(0.45) and 2.5(0.3) respectively?

 

[kuruman]

So far so good except for the gravitational potential energy.

 

[Alexanddros81]

Do I replace $Wy_A$ and $Wy_B$ with 2.5(0.3) and 2.5(0.45) respectively?

 

[kuruman]

Do I replace $Wy_A$ and $Wy_B$ with 2.5(0.3) and 2.5(0.45) respectively?

Almost but not quite. Something is missing. The problem talks about a 2.5-kg weight. Is weight measured in kilograms?

 

[Alexanddros81]

A yes but ofcourse W = mg where mass is m=2.5kg.
But I don't understant why the Potential Energy of W is mg(0.3) at position A and mg(0.45) at position B.
I mean I don't understant it in relation to the Figure.
Can you explain to me a bit more?
At Which point do I say that the potential energy of W is zero? (in the figure)

 

[kuruman]

At Which point do I say that the potential energy of W is zero? (in the figure)

Any point you like. The zero of potential energy is irrelevant. Consider this, when a mass moves from point A to B, mechanical energy conservation says
T_A + U_A = T_B + U_B
or
T_B - T_A + U_B - U_A = 0
or
ΔT + ΔU = 0.
It's the difference that matters, not where you put the zero of energy because it drops out.

 

[Alexanddros81]

By the way do I post problem questions from
'Orbital Mechanics for Engineering Students' by Curtis
in this forum (Introductory Physics Homework)?

 

[kuruman]

By the way do I post problem questions form Orbital Mechanics for Engineers by Curtis
in this forum (Introductory Physics Homework)?

I am not familiar with the textbook. I looked at its table of contents and I think "Advanced Physics Homework" would be more appropriate. Try that and if I am wrong, a mentor will move it to its rightful place, perhaps in "Engineering."

 

[Alexanddros81]

Ok so here is my solution:

 

[kuruman]

I didn't run the numbers, but the method is correct.