A block and spool are each pulled by a string across a frictionless surface. The string is wound around the spool such that it may unwind as it is pulled, the string attached to the block is at the center of mass. The block and spool have the same mass and the strings (massless) pull each with the same constant force.
Is the magnitude of the acceleration of the block greater than, less than, or equal to that of the spool? Explain.
Do the block and spool cross the finish line at the same time?
The Attempt at a Solution
net torque = Fnet*r = I*α = T*r
^(foregoing sin(theta) because not applicable)
I=(1/2)Mr^2 <-- for solid cylinder
a_tangential = (2T/M)
Fnet= ma= T
I think I might be using the equations wrong because this conclusion doesn't add up to the conceptual answer?
Things I understand:
The work of the hand for the spool is greater than that for the block because it has to apply the force over a longer distance, which follows KE= 0.5mv^2 + 0.5I(ω)^2 for the spool.
Things that are tripping me up:
Shouldn't the center of mass of the spool and the center of mass of the block have the same acceleration because they have the same mass and the same net force?
Conceptually, I'm thinking that they cross at the same time, but my math doesn't add up?