Question

Answer with process.....

Answer 1

CP7.Determine the acceleration of massM1relative to the ground in the following machine.All surfaces are frictionless and the pulley and rope are massless.Solution.Applying Newton’s second Law in thex-direction for all three masses and alsoin they-direction for mass 3 gives the following system of equations:T=M2a2,-N-T=M1a,N=M3a,T-M3g=M3a3(19)Where I have already invoked the constraint that the accelerations of masses 1 and 3 inthex-direction are the same, and I called their common accelerationa. I also abbreviateda2,x=a2anda3,y=a3. The termNrepresents the potential force of contact between masses1 and 3, and I have already invoked Newton’s Third Law by includingNin thex-equationfor mass 1 and-Nin thex-equation for mass 3 (we’re not certain ifNis positive or negativequite yet, but the equations will tell us in the end.)At this point we have a system of 4 equations and 5 unknownsT, a2, N, a, a3; we needanother equation. We have exhausted all dynamical information (namely information comingfrom the laws of motion), so there must be a constraint we’re missing. Indeed, there is such aconstraint, and it comes from the fact that the length of the rope is constant. This constraintcan be used to determine a constraint relating the accelerations, which turns out to bea=a2+a3(20)Now we have five equations and five unknowns, and we can solve (which I leave to you) togivea=-M2M3M1M2+M1M3+ 2M2M3+M23g(21)CP8.