Question

does changing length of a spring also change radius of a bodys circular path?

Answer 1

can somebody explain me this?

Answer 2

If you are swirling the object around in a circular path at the end of the spring, then the spring will length and the radius increase, until the force,

F = - k r equals the centripetal force, F=- m v^2/r

If you know k, m, and v, you can equate these forces and find r.

Answer 3

what is k? I am familiar with F = -mv^2/r
is it force constant?

Answer 4

also why does it chance period? is that because of gravity?

Answer 5

k is the spring constant, often written as F = - k x,
where x is displacement from its equilibrium position.
The equation I gave you probably should have been F = -k(r - r0),
where r0 is the unstretched length of the spring, another constant that you would have had to be supplied with. I used r to connect it with the centripetal force term.

Answer 6

thank you so much!! can i ask if i also was correct with my guess of why it effects period too?

Answer 7

The period T will be determined by T = 2 pi r / v
another expression can be obtained for it by using F = -m r w^2, where w (omega) is the angular velocity w=2 pi /T