Energy in circular path with spring

[edowuks]

We have a spring that has equilibrium at distance R. the spring is attached at horizontal distance R from circle (R is distance from edge of circle, distance from circles origo is 2R) that has radius R. Mass attached to spring can move freely in that circle path. In circle we have 3 points a=point where spring is at rest. B=at angle pi/2 C=opposite side of spring than the point a. (sorry I don't have picture and my english is bad).
A) calculate velocity at point a when spring is released from point b (at picture we have on paper we can see that at point b it has gravitational potential energy of mgR)
B) How hight should the spring constant be that mass never reachess point c

Ok I have banged my head to wall two days, I cannot figure what should I calculate here. Can I just calculate the A part by 'potential of spring'+mgR=½mv² (can potential of spring be calculated from length of pring-R). B-part I don't understand what should I calculate, but with my poor explanation I think no-one can give any hint?

I don't need anykind of solution just hint what I should be calculating, can't picture the problem in my head.

 

[LowlyPion]

We have a spring that has equilibrium at distance R. the spring is attached at horizontal distance R from circle (R is distance from edge of circle, distance from circles origo is 2R) that has radius R. Mass attached to spring can move freely in that circle path. In circle we have 3 points a=point where spring is at rest. B=at angle pi/2 C=opposite side of spring than the point a. (sorry I don't have picture and my english is bad).
A) calculate velocity at point a when spring is released from point b (at picture we have on paper we can see that at point b it has gravitational potential energy of mgR)
B) How hight should the spring constant be that mass never reachess point c

Ok I have banged my head to wall two days, I cannot figure what should I calculate here. Can I just calculate the A part by 'potential of spring'+mgR=½mv² (can potential of spring be calculated from length of pring-R). B-part I don't understand what should I calculate, but with my poor explanation I think no-one can give any hint?

I don't need anykind of solution just hint what I should be calculating, can't picture the problem in my head.

The potential in your spring is = ½*k*Δx² and as you point out that plus drop in height m*g*R will result in your ½*mv².

Your Δx here can be found by ordinary geometry.

For part 2 you know the KE at b so for the mass to make it to c, which by your description is at the same level as b then there is no need to account for any change in potential energy, so ½*k*(2R)² = the KE when it was at b.

 

[thomate1]

I would begin by breaking down the problem into smaller parts and identifying relevant equations and variables.

For part A, we are looking to calculate the velocity of the mass at point a when released from point b. We can use the conservation of energy principle, where the initial potential energy (gravitational potential energy mgR) is converted into kinetic energy (½mv²) at point a. So yes, your approach of setting the potential energy equal to the kinetic energy is correct. However, we also need to consider the potential energy of the spring, which can be calculated using Hooke's Law: potential energy of spring = ½kx², where k is the spring constant and x is the displacement of the spring from its equilibrium position. Since the spring is at rest at point a, the displacement x would be R. Therefore, our equation would be: mgR + ½kR² = ½mv². We can rearrange this to solve for v, which would give us the velocity at point a.

For part B, we need to determine the spring constant required for the mass to never reach point c. This means that at point c, the kinetic energy of the mass should be equal to the potential energy of the spring. So, we can set the kinetic energy at point c (½mv²) equal to the potential energy of the spring (½kx²), where x is now the distance between point c and the equilibrium position of the spring (which is 2R). Again, we can rearrange this equation to solve for k, which would give us the required spring constant.

It is important to note that these calculations assume ideal conditions, with no friction or other external forces acting on the system. In a real-world scenario, these factors would need to be taken into consideration. I hope this helps guide you in the right direction.