Astudent in mec 101 class designs a rack and pinion based mechanism to convert rotary motion of the shaft of a dc motor to a linear motion. the rack is meant to push on a box to move it. the box weighs 1 kg and the coefficient of static and kinetic friction between the box and the floor is 0.3. if the box has to be moved at a speed of 1 cm/s, then what should be the torque applied by the motor in g. cm and the nominal speed of the motor in revolutions per min? the motor is directly attached to the gear. assume that the rack is supported on frictionless railings, and module of the rack is 1 mm/tooth and the gear has 20 teeth on it. note: although the units of torque in the s. i. system are n. m, very often catalogues and datasheet for motors would give torque ratings in kg. cm or g. cm. in that case, converting the torque to n. m would require you to multiply by gravitational acceleration (g) to convert from kg. cm to n. m. the rationale for asking the torque here in g. cm is so that you can readily compare it to the commonly reported torque in g. cm.