An aluminum block of mass m1 = 3.15 kg and a copper block of mass m2 = 7.40 kg a

Question

An aluminum block of mass m1 = 3.15 kg and a copper block of mass m2 = 7.40 kg are connected by a light string over a frictionless pulley. They sit on a steel surface as shown in the figure below, where theta = 31.5degree. (See the table below for the appropriate coefficients of friction). (a) When they are released from rest, will they start to move (yes or no ) ? (b) If the blocks move, determine the magnitude of their acceleration. (If the blocks do not move, enter 0.) (c) If the blocks move, determine the magnitude of the tension in the string. (If the blocks do not move, enter 0.) N (d) If the blocks do not move, determine the sum of the magnitudes of the forces of friction acting on the blocks. (If the blocks move, enter 0.)

Explanation / Answer

m1 = 3.15 Kg m2 = 7.40 Kg = 31.50 (a) Yes (b) Coefficient of kinetic friction between Aluminum block (m1) and steel 1 = 0.47 Coefficient of kinetic friction between copper (m2) and steel 2 = 0.36 Let a be the acceleration of the blocks and T be the tension along the string. From Netons law of motion : For m1,     T - 1m1g = m1a         ------------(1) For m2,     m2g sin - T - 2 m2g cos = m2 a       -----------(2)        On adding (1) & (2) , we get                   m2g sin - 2 m2g cos  - 1m1g = (m1 + m2) a                   37.89 - 22.26 - 14.5 = 10.55 a                                            1.13 = 10.55 a                             Acceleration a = 1.13/10.55                                                    = 0.107 m/s^2   (c) Tension along the string T = m1a + 1 m1 g                                        = 0.3373 + 14.508                                        = 14.84 N (d) 0 (d) 0

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