A 12.0-kg monkey hangs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 185 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)?
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This is Giancoli Answers with Mr. Dychko. Here's a free-body diagram of the monkey; there's a string exerting a force upwards and there's gravity down and we'll take up to be the positive direction, in which case, we can write Newton's second law as the string force up minus the gravity force down equals mass times acceleration. And we'll solve for acceleration by dividing both sides by m and this equation is true just before the string breaks. After the string breaks, there is zero string force and then monkey is just in free-fall. So we'll substitute the numbers here; we have 185 newtons is the maximum force the string could have exerted minus 12 kilograms times 9.8 meters per second squared, all divided by 12 kilograms. That gives 5.62 meters per second squared upwards; must have been the acceleration of the elevator. It's up because it turns out to be positive and we chose up to be the positive direction.
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