A 500 g mass is connected to a spring that has an uncompressed length of.2 m and has a spring constant of 10 n/m. The other end of the spring is held overhead, and the mass is spun around in a circle so that the spring makes an angle of 15 with respect to the horizontal. Given this how could i find the speed of the mass?
Answers
Answer:
Anything kept on a table with a spring attached to it does not start to move on its own. So you have to give it an initial push perpendicular to the radius vector. That would elongate the spring and the spring will try to pull it back with a force. Hence the actual length of the spring would be (r+x)(r+x) and not (r−x)(r−x) as you have stated.
Also, there should be no tangential force because you state that the motion is uniform, hence its speed should not change.
And I think that the expression would be
Kx=mv2r+xKx=mv2r+x
Where r is the length of the spring and x is the extension in the spring.
You see, if xx remains constant, the centripetal force will be constant and you can imagine the spring to be a string, as in string the tension remains constant for uniform circular motion and it happens in real life and thus is not vague. So similar stuff can also happen with springs!
( I hope you wont get this wrong next time in your exam :-P )