# Energy of a system-a box moving in a circle

1. Jan 4, 2014

### haha1234

1. The problem statement, all variables and given/known data

A light spring has unstressed length 15.5cm.It is described by Hooke's law with spring constant 4.30N/m.One end of the horizontal spring is held on a fixed vertical axle,and the other end is attached to a punk of mass that can move without friction over a horizontal surface.The punk is set into motion in a circle with a period of 1.30s.
Find the extension of the spring x as it depends on m.

2. Relevant equations

3. The attempt at a solution

Firstly,I found the velocity of the punk.
1/2kx2=1/2mv2
v=[(4.3x2)/m]1/2
But I don't know what is the next step.

2. Jan 4, 2014

### Staff: Mentor

Let r be the radius of the circle. What is the radial acceleration of the mass? If the mass is traveling at this radius, how much is the spring stretched? What is the centripetal force that the spring must supply?

3. Jan 4, 2014

### Jilang

I don't think you are using the right equation here. Your equation is saying that the energy in the spring equals the kinetic energy of the punk - why would that be the case? Do you know any other equations that might apply?

4. Jan 4, 2014

### haha1234

I have used this approach is because the question has given the period of the circle,so I think I should find the velocity...

5. Jan 4, 2014

### Jilang

OK, do you know any other equations that have velocity in them?

6. Jan 4, 2014

### Staff: Mentor

What's the angular velocity ω?

7. Jan 4, 2014

### haha1234

ω=360°/1.3
=277?
andω=4.3/m?

Last edited: Jan 4, 2014
8. Jan 4, 2014

### Staff: Mentor

The angle has to be in radians, not degrees. After you get the angular velocity correct, express the radial acceleration in terms of ω and r.

Chet

9. Jan 5, 2014

### haha1234

I think I cannot get the correct radical acceleration.
The radical acceleration I have got is a=(4∏2/1.69)x

10. Jan 5, 2014

### Tanya Sharma

Correct...It would be better if you express it as a=(4∏2/1.69)(.155+x) where x is the extension in the spring .

11. Jan 6, 2014

### haha1234

Why the radius of the circle is 0.155+x?

12. Jan 6, 2014

### Tanya Sharma

What do you think radius would be ?