Three masses with mass M, 2M and 3M (with M=1kg) are set up asshown in the gure,

Question

Three masses with mass M, 2M and 3M (with M=1kg) are set up asshown in the gure, with the mass 2M on a surface with kinetic coecient offriction k = 0:25. The pulleys have moment of inertia I = 0:05kgm2 and radius r =5cm. The mass 2M is initially at rest at the center of the table, 5m long.(a) What's the tension on each of the strings pulling on the 2M mass? (b) How longafter the system is released from rest does the mass 2M reach the edge of thetable? (c) What's the system's kinetic energy at the same time? (d) How dierentwould be your answers

Explanation / Answer

This is an incredibly long sum, so i'm not going to do thecalculations, but i will tell you how to go about solving it. for body 1: vertical forces: weight (mg) and tension Tension causes it to move upwards so use T1-mg=ma you get your first equation for body 2: we have friction and T1 acting towards the left and T2 actingtowards the right. Subtract and equate to ma. this should give you your second equation for body 3: same as 1, except it will be mg-T2=ma this gives you the third equation. So far you should have the value of T1 or T2 (after solvingsimultaneously) for the pulley, we know that the Tension provides the torque. So =I (where is angular acceleration) That is tension*radius =I * and a=r so should be able to calculate a. Sorry, but thats all i can help..

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