A 15.7 kg monkey hangs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 240 N and breaks as the elevator accelerates. What was the elevator's minimum acceleration? (Assume the positive direction is upward.)

Draw out your forces. This is easy. Let us know if you get stuck.

Sure! To solve this problem, we need to consider the forces acting on the monkey.

First, let's draw a free-body diagram to represent the forces acting on the monkey when the cord is intact.

First, we have the weight force acting downward due to gravity, which can be calculated using the formula:

Weight = mass x acceleration due to gravity

Therefore, Weight = 15.7 kg x 9.8 m/s² = 154.06 N

We also have the tension force acting upward in the cord. Since the cord can withstand a maximum tension of 240 N, it means the tension force doesn't exceed that value when the cord is intact.

Now, when the cord breaks, the tension force becomes zero, while the weight force continues to act downward. This causes the monkey to accelerate upward.

According to Newton's second law of motion (F = ma), the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

In this case, the net force is the difference between the weight force and the tension force:

Net force = Weight - Tension

Since the cord breaks, Tension = 0 N, so the net force is equal to the weight force:

Net force = Weight = 154.06 N

Now, we can determine the minimum acceleration of the elevator by using Newton's second law:

Net force = mass x acceleration

154.06 N = 15.7 kg x acceleration

Solving for acceleration:

acceleration = 154.06 N / 15.7 kg = 9.81 m/s²

Therefore, the elevator's minimum acceleration is 9.81 m/s² upward.