Question

Consider two masses, M = 3.0 kg and M2 = 2.5 kg, connected by a strong cord of negligible mass that extends over a frictionless pulley. Mass M is placed on a surface that makes an angle of 30° with respect to the horizontal, while mass M, is hanging freely. The coefficient of kinetic friction between the surface and the mass is ilk = 0.25. a) Draw Free Body diagrams for the two masses b) Write the equations for the two masses in the direction of motion ( both x and y direction) c) Find acceleration of the system. d) Find the tension in the string connecting the two blocks. M-3.0 kg M = 0.25 M - 2.5 kg 30°

Answer 1

The solution is given below.

I Tersion in the string gn acceleration due to pravima - 3kg AT - 9-8 m/s2 I' 1 M2=2.5kg migsind Mgth, gusto R- Normal reaction Migcoso mag F' frictional force aux R if'aak mi gcoso equation of motion for mass Mais Mag-T= и, а a= acceleration of the system equation of motion for mass M is -f't T-migsino = h, a T- Migrino - MK Mi gcoso = m, a 3 T m, a from equation 1 und ② eliminate T- Mag- Mga from a from Mag-maa mig sino - Me mig coso = wso Ma gom, g sino-heig Methn 3x9.84 sin 30° -0.25x 3x9. 8x68530 3+ 2.5 a 0.624 mygr acceleration of the systems 0.624 myse a = 2:58 98 - Answer i from equation o TE Mag- Maa (gra) Mq 2.5 9.8- 01624) "T - 22.94 N Answer Tension in the strong = 22.94 N

Thank you.