A block of mass is attached to a spring and kept in horizontal position in a vertical plane. When the block is allowed to then, find the maximum extension in the spring.
1) Spring's constant=
2) Natural length of spring=
I was trying to make a problem using some concepts of Work Energy and Circular motion and I came up with this. Here is my approach, please tell me if I am right or not.
First of all, the extension in the spring will be maximum when radial velocity () will be zero. Now the work is only done by conservative forces in this situation so we can conserve energy.
The extension will be maximum when . So this does not implies that the velocity of the block is zero at the lower most position. Also we can see that only a component of is acting in the tangential direction which is responsible for tangential velocity and tangential acceleration. So is not going to be zero at the lower most position.
If we consider torque about point then
I got this equation. There is a term of in the equation that has to related with or to solve the problem.
Although the motion is not circular but if consider the motion of the block for a very small interval of time then we can assume that it's a circular motion so . Can we do so?
Using this we can express in term of angular velocity. But still there is term containing there. How can this be solved?
Am I overlooking some thing very obvious? Because using calculus in spring problem often gets very complicated.