Question

You are in a helicopter towing a 129-kg laser detector that is mapping out the thickness of the Brunt Ice Shelf along the coast of Antarctica. The original cable used to suspend the detector was damaged and replaced by a lighter one with a maximum tension rating of 313 pounds, not much more than the weight of the detector. The replacement cable would work without question in the case that the detector and helicopter were not accelerating. However, some acceleration of the helicopter is inevitable. In order to monitor the tension force on the cable to make sure the maximum is not exceeded (and therefore to not lose the very expensive detector) you calculate the maximum angle the cable can make with the vertical without the cable exceeding the tension limit. (a) Assuming straight and level flight of the helicopter, what is that maximum angle? (b) What is the corresponding acceleration? (c) Your colleague wants to add a 7.00-kg infrared camera to the detector. What is the maximum allowable angle now?

Answer 1

So the laser detector which is suspended has mass, , while the maximum tension rating of the string with which the detector is suspended is, (where, is the gravitational acceleration). So, the diagram says:

is the acceleration of the helicopter H.

So, from the figure, in the maximum scenario:

So, the maximum angle is given by (from eq 1):

And, the corresponding maximum acceleration is given by (from eq 2):

Now, when the infrared camera of mass 7 kg is added, then the total mass,

So the maximum allowed angle will decrease, and the same equation applies with in place of :

So,

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