Two 10-kilogram boxes are connected by a massless string thatpasses over a massl

Question

Two 10-kilogram boxes are connected by a massless string thatpasses over a massless frictionless pulley as shown above. Theboxes remain at rest, with the one on the right hanging verticallyand the one on the left 2 meters from the bottom of an inclinedplane that makes an angle of 60 degrees with the horizontal. Thecoefficients of kinetic friction and static friction between theleft-box and the plane are 0.15 and 0.30, respectively. You may useg=10m/s^2, sin 60=0.87 and cos 60=0.50. a. What is the tension T in the string? b.Determine the magnitude of the frictional force acting onthe box on the plane. The string is then cut and left-hand box slides down theinclined plane. c.Determine the amount of mechanical energy that is convertedinto thermal energy during the slide to the bottom. d.Determine the kinetic energy of the left-hand box when itreaches the bottom of the plane.  

Explanation / Answer

(a)   For right hand box T = mg                                    T =10 kg *9.8m/s2                                       =98 N                                       =98 N (b) For left hand box FN=mg cos                                     =10kg*9.8m/s2*cos60                                     =49 N Frictional force acting on the boxFs=sFN                                                    where coefficient of static friction s=0.30                                                           Fs=0.30*49                                                                 =14.7N (d) For left hand box ,           fromequation of motion                                                v2-u2 =2as                                                  v2 -0=2*9.8*2                                                     v2 =39.2m/s    Kinetic energy of left hand box=(1/2)mv2                                                   = (1/2)*10*39.2                                                  =196 j                                                   = (1/2)*10*39.2                                                  =196 j

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