12 A box hangs from a balloon by means of a light inelastic string. The string is always vertical. The mass of the box is 15 kg .
Catherine initially models the situation by assuming that there is no air resistance to the motion of the box. Use Catherine's model to calculate the tension in the string if:
- the box is held at rest by the tension in the string,
- the box is instantaneously at rest and accelerating upwards at \(2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\),
- the box is moving downwards at \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and accelerating upwards at \(2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
Catherine now carries out an experiment to find the magnitude of the air resistance on the box when it is moving.
At a time when the box is accelerating downwards at \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\), she finds that the tension in the string is 140 N . - Calculate the magnitude of the air resistance at that time.
Give, with a reason, the direction of motion of the box.
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