An atwood machine consists of a mass of 3.5 kg connected by a light string to a mass of 6.0 kg over a frictionless pulley with a moment of inertia of 0.0352 kg m2 and a radius of 12.5 cm. if the system is released from rest, what is the speed of the masses after they have moved through 1.25 m if the string does not slip on the pulley?
note: the professor has told us that the correct answer is 2.3 m/s. how does one arrive at this answer?

Explanation:

For the first mass we have , and for the second . The pulley has a moment of intertia and a radius .

We solve this with conservation of energy.  The initial and final states in this case, where no mechanical energy is lost, must comply that:

Where K is the kinetic energy and U the gravitational potential energy.

We can write this as:

Initially we depart from rest so , while in the final state we will have both masses moving at velocity v and the tangential velocity of the pully will be also v since it's all connected by the string, so we have:

where we have used the rotational kinetic energy formula and that

For the gravitational potential energy part we will have:

We don't know the final and initial heights of the masses, but since the heavier, , will go down and the lighter, , up, both by the same magnitude h=1.25m (since they are connected) we know that and , so we can write:

Putting all together we have:

Which means:

i dont think you are wrong for wanting to get even with someone who did you wrong.

(i'm an eye for an eye kind of person) but if this person hurt you in a sexual way, i dont suggest doing anything to him. he should be taken to the proper authorities, you could go to jail depending on what you do. if it was something small like your sibling took your spot on the couch, than yea, i would get even with him by taking one of his favorite snacks lol. but i dont suggest you doing anything illegal.

need to see circuit to get time constant