A ball of mass m100 g is attached to a central pole by two...

A ball of mass m=100 g is attached to a central pole by two wires, as shown in the diagram below. The ball is moving in a circle around the pole with an angular velocity of ω=5 revolutions per second. a)Calculate the magnitude of the tension in the lower wire. b) calculate the magnitude of the tension in the lower wire. c) Is there any non-zero mass of the ball for which the tension in the lower wire would be 0 N? d) Without changing the geometry of the wires, are there any other variables that you could change that would result in a zero tension in the lower wire, but a non-zero tension in the upper wire? Picture: A pole split in half with 0.50m length for each section (1.0m total) with two wires coming off of the top and bottom of the pole connected to the ball (modeled as a point where they connect). The length of both of the wires are 1.0 m each.

Transcript

00:01 So, in this question, they have given that we have four pulleys and three objects that is hanging from the strings.

00:06 So we have to find the acceleration of block c.

00:09 Now, what we have to do in order to find the acceleration of block c, first assume the tension of these strings.

00:17 So let's say that this pulley, this string has tension t, this pulley has tension t.

00:24 So according to this, this rob will have a tension of 2t.

00:27 Now again this have t this have 2 t this have again t this have this have t now how can we find the acceleration we have know that due to gravity the masses of these blocks is given is equal to m mass of each block is given in this question each block that is equal to m so due to the gravity there will be a downward force i can say m g there is again a downward force that is again m g and here again that will be equal to mg now if i write the equations from the c block so for block c if i write the equation so i can write that let's say that the acceleration is in the downward direction i'm just assuming that the acceleration of block c is in the downward direction so i can say that this is a so let's say that block he has a acceleration a a block b has acceleration a b and block c has acceleration a c that i'm representing in downward direction so if i write the equations now so what i can write that m g minus 2 t that will be equal to m a now how can i write this according to the newton's law of motion that f is equal to m a where f is equal to total force now according to the constant equation now what i can write that acceleration of a plus two times acceleration of b because it is attached with two strengths plus two time acceleration of c that will be equal to zero because the algebra sum of total acceleration will be equal to zero because it is in opposite direction and some acceleration will be in downward direction and some acceleration will be in upward direction so eventually they will cancel each other now we know that acceleration of b is equal to acceleration of c because these two acceleration is attached these two blocks are attached with two strings having same tension and the mass of these two blocks are also same so according to this what i can say that the acceleration of block a will be equal to minus four times acceleration of block c i can write like this now this negative sign is representing that we take the direction wrong.

02:58 So we took that the acceleration of block c will be in downward direction, but in reality this block will go in upward direction, right? now this same acceleration, if i put in this equation, let's say this is equation one.

03:12 So if i put acceleration in equation one, so how can i write that mg minus 2t that will be equal to m multiplied by acceleration of block or i can say in this equation i need to find acceleration of block c so i can write acceleration of block c now we just have to solve for acceleration of block c so i can write that mg minus 2 multiply by mass into acceleration of block a because t is equal to m into acceleration of block a so 2 t will be equal to 2 multiply by acceleration of block a...

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