1. The problem statement, all variables and given/known data A double pulley consists of two separate pieces that are welded together; a hoop of radius 10.0 cm and a disk of radius 25.0 cm. The moment of inertia of the pulley is 0.160 kg-m^2. A 15.0 kg block (m1), on a 35.0° incline, is attached to the outer pulley by a massless cable and a 24.0 kg block (m2) is hanging from the inner pulley by a massless cable. The incline has a kinetic coefficient of friction of 0.250. At the instant shown in the diagram, the two blocks are at a height of 1.50 m and are moving in the appropriate direction with m2 having a speed of 0.240 m/s. The motion is considered complete when either m 1 reaches the bottom of the incline or just before m2 hits the ground. Use force methods to answer the following questions. a) What direction are the blocks moving and why? b) How far will each block travel in their respective directions? c) Find the angular acceleration of the pulley? d) Find the acceleration of block m1. e) Find the acceleration of block m2. f) Find the tension in cable 1. g) Find the tension in cable 2. 2. Relevant equations 3. The attempt at a solution So far I think I have found the acceleration of m2, which would indicate that it is moving downward and thus pulling m1 up the ramp. Using this formula, and also factoring in friction, I got 3.1 for the acceleration. a = ( m2*g - m1*g*sin(θ) - μk*m1*g*cos(θ) ) / ( m1 + m2 ) a = ((24.0*9.81)-(15.0*9.81*sin(35°))-(0.25*15*9.81*cos(35°)))/39.0 a= 3.1 But does that actually mean m2 is pulling m1? Does the double pulley affect this at all? Overall I am pretty confused how the double pulley plays into this. The only problem I could find that was remotely similar to this was this one, but I still don't understand the difference between a regular pulley and double pulley here. As for b), I think the final position of m1 would be calculated with: xf = (2/k)[m2g - m1*g*sin(θ) - μk*m1*g*cos(θ)] So I could take xf - xi and find the distance traveled. But if I understand correctly that would be using energy, and I need to solve this with force methods. I also imagine the radii will affect the distance traveled, though I don't what equation to use. Guidance on double pulleys and determining distance-traveled greatly appreciated!