a string is wrapped tightly around the circumference of a wheel with a mass of 1
ID: 2202284 • Letter: A
Question
a string is wrapped tightly around the circumference of a wheel with a mass of 1.23kg and a radius of .324m. the string is attached to a block with a mass of 2.48kg which is .34m above the floor. when the mass is released the wheel rotates freely as the string unwinds without slipping. A. what is the initial energy of the system? B what is the moment of inertia of the wheel? C write the expression for the total energy of the system just before the block hits the floor? D what is the velocity of the block just before it hits the floor? E what is the angular velocity of the wheel just before the block hits the floor?Explanation / Answer
A) It is not stated clearly, but if you need the kinetic energy it's 0 (since the wheel and the block aren't moving at the beginning). B) The moment of interia of the wheel is calculated from this formula: I=(1/2)*M*r^2 Where M is the mass and r is the radius. C) The velocity and the acceleration of the molecules on the periphery of the wheel is the same as the velocity of the string, and therefore the block. So, about the velocity and the acceleration of the periphery, it is: V=w*r and a=A*r respectively, where "w" is the angular velocity and "A" is the angular acceleration of the wheel. We find all the forces in the system block-wheel. SEE THE ATTACHMENT IT CONTAINS A PICTURE WITH ALL THE FORCES T=T' (action-reaction) For the block: the resultant force is: SF= W-T, and SF=mass*acceleration (m*a) so we have: W-T=m*a. we only don't know T and a. For the wheel we have: the torque (t) is: t=T'*r and t=moment of inertia*angular acceleration (l*A) So we have: I*A=T'*r, and because T=T', we have I*A=T*r, but as we said, a=A*r A=a/r so we have: (I*a)/r=T*r I*a=T*r^2 we only don't know a and T. So far we have: W-T=m*a and I*a=T*r^2 It's a system of equations with two unknowns, you can easily solve this. D)You know the acceleration of the block, so you use h=(1/2)*a*t^2 (this time t=time) you find the time needed and then you use: Velocity=a*t E) We already said that V=w*r where V= velocity w=angular velocity. So w=V/r and we are finished!Related Questions
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