A block of mass m_1 = 8.0 kg sits on a frictionless table and is connected by a

Question

A block of mass m_1 = 8.0 kg sits on a frictionless table and is connected by a card [over a massless, frictionless pulley] to a second block of mass m_2 = 7.0 kg. hanging vertically. A force of 60.0N is applied to m_1 at an angle of 25 degree above the horizontal Draw the forces acting on each block. [Resole the forces where necessary] Determine the acceleration of the two blocks Determine the tension in the cord If the pulley [a solid disc] has o mass of M=2 70kg. and a radius of R = 0.11m. determine the acceleration of the system that now includes the pulley Use Newtons second law of rotation to determine the torque [T] exerted on the pulley by the two tensions.

Explanation / Answer

a) Here, 65 * cos25 - T = 8a

   and ,   T - 7 * 9.8 = 7a

b)   Solving equations

=> acceleration of blocks = 0.646 m/sec2

c)   Tension in cord =   64.078 N

d)   Here, - 65 * cos25 + T1 = 8a

   and ,   - T2 + 7 * 9.8 = 7a

=> (T2 - T1) = (Ma)/2

=>    68.6 - (2.7 *a)/2 - 58.91   =   15a

=>     acceleration , a = 0.592 m/sec2

=>   torque exerted = (64.456 - 63.64) * 0.11

                                 = 0.08976 N.m

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