Final answer:
The maximum acceleration of the elevator so that a string does not break is 26.9 m/s².
Step-by-step explanation:
The maximum tension the strings can withstand is 75.4 N. In order to prevent a string from breaking, we need to make sure the tension in the string is below this maximum value. The acceleration of the elevator affects the tension in the string. If we assume the tension is at its maximum value, we can use the formula T = m(a+g), where T is the tension, m is the mass, a is the acceleration, and g is the acceleration due to gravity. In this case, we can rearrange the formula to find the maximum acceleration:
a = (T - m×g)/m
Plugging in the values, we have:
a = (75.4 N - 2.0 kg × 9.8 m/s²)/2.0 kg = 26.9 m/s²
Therefore, the maximum acceleration of the elevator so that a string does not break is 26.9 m/s².