A 18.6 kg monkey hangs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 202 N and breaks as the elevator accelerates. What was the elevator's minimum acceleration?
(in m/s^2)
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To determine the elevator's minimum acceleration, we need to consider the forces acting on the monkey when the cord breaks.
1. First, let's identify the forces involved:
- Weight force (mg): This is the force acting on the monkey due to its weight, where m is the mass of the monkey and g is the acceleration due to gravity (9.8 m/s^2).
- Tension force (T): This is the force exerted by the cord on the monkey.
2. Since the monkey is hanging motionless, the upward tension force in the cord must balance the downward weight force:
T = mg
3. When the cord breaks, the only force acting on the monkey is its weight force:
mg = ma
4. Rearranging the equation, we can find the minimum acceleration (a):
a = g
Therefore, the minimum acceleration of the elevator is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2.