A turtle is pulling two stacked boxes as shown in the above figure. The string attached to the bottom box is parallel to the ground. The mass of the bottom box is mb and that of the top box is ma. The tension in the string is T. The coefficient of static friction between the bottom box and the ground is μb and that between the two boxes is μa.
[Figure: Shows turtle pulling two stacked boxes with string parallel to ground]
Find the range of T with sufficient justification and mathematical reasoning when:
a) two boxes are static
b) the bottom box is moving relative to the ground with the box on top resting on it
c) the bottom box is moving relative to the ground but there is also relative motion between the top and the bottom box