Question

Consider the setup below. The masses are known as is the angle. The coefficients of static and kinetic friction are also known (Us, UK). The radius of the pulley is R (known) and it has a known mass Mo (i.e. it is not negligible). The system is released from rest. 12 MB -62 a) Calculate the accelerations of the blocks and the tensions in the cord. b) If, after the masses have moved a distance d (known) mass B lands on a spring of spring constant k (known), calculate the maximum compression of the spring.

Answer 1

スN. T2 ma magsina Let tension in Atring be T T ince radiu ully is R and maas pully disc hrafore is and Me moment ofdut neha is T MpR2. 2. 9.8 m/s and be Arichan het f

T-f-magsine ma A 11 uhere A acelerah on olo cks Siru larky Q2 T=m6 A we gut addng A- f+T-T M masing mat mh Gzoal aning torque about pulley we (T-R T d acceloratian where = angulax 1 (TT TA MpA R2 2. ng-esmag tes waing Me

/A 2. mat mb . ( inet M 2 matmay ma tmb (sinty ma) A Me YYh Ama+Mb 2. ma) g (mt -ain & +4ue3 Мо 2. + ma mb get we puting A dd distance Velocity 3after meving ue get 2 u 2 AS inihal velocity l= O final velecity JaAS 2(mb- (sn tes)ma ma t mh - MP

Now balanding enngy maases weget 2 xis the cempreasion of spring uhere mb cemes dewn and the distance kx2- 2 mg + 4kmbv 2mby t 2k. t 2 m k. cannot be negative 8ince 2(my - (sins t 64mag d Me/2 whore matmb