0
$\begingroup$

enter image description here

The point O is where the small mass is attached. I'm trying to find out the minimum velocity that should be given to the mass so that it can complete a full circle but if the fixed point is accelerating, how will it affect the answer? What force will act on the particle?

$\endgroup$
  • $\begingroup$ Can't you just apply the equivalence principle? $\endgroup$ – João Vítor G. Lima Feb 28 '19 at 14:41
  • $\begingroup$ Uh what is that? I haven't really covered relativity so I don't know how to... $\endgroup$ – Sameer Thakur Feb 28 '19 at 16:03
  • $\begingroup$ Just consider that the acceleration $a$ becomes a pseudo force field in the opposite direction and you're done. $\endgroup$ – João Vítor G. Lima Feb 28 '19 at 16:38
0
$\begingroup$

The pseudo force acts in the vertically downward direction if the acceleration is vertically up. If the acceleration is given in vector form as xi+yj then the pseudo force is m(-xi-yj). Where m is the mass of body.

To find minimum velocity, we must assume that the tension in the string is 0 at the highest point, hence only the force due to gravity and force due to pseudo force would contribute to the net centripetal force ($\frac{mv^2}{r}$). Where v is the velocity at the highest point . In this way the acceleration affects the minimum velocity.

$\endgroup$
  • $\begingroup$ Please have a look at my answer and confirm whether it's the right way. $\endgroup$ – Sameer Thakur Feb 28 '19 at 19:00
  • $\begingroup$ Also in that case if the point accelerates only in the x-direction, will it have no effect on the value of the minimum velocity required to complete the circle because at the topmost point the pseudo force won't be acting along the y-axis? $\endgroup$ – Sameer Thakur Feb 28 '19 at 19:05
0
$\begingroup$

So I took a special case when a=g/3 and there's a downward pseudo force and got this answer. Can someone confirm this?

enter image description here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.