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I don't care about the negligible tangential friction forces on the
string going over the pulley. I care about the much stronger forces
acting radially away from the pulley's center on the string. The
resultant of these forces has a horizontal component which is sufficient
to accelerate the cart horizontally (via its imposition of a horizontal
tension in the horizontal part of the tape) and has a vertical component
to provide the vertical tension in the vertical length of tape which
tends to retard the acceleration of the falling mass.