Final answer:
The tension in the rope when the 90 kg box is at rest is 882 N.
Step-by-step explanation:
To find the tension in the rope when the 90 kg box is at rest, we need to consider the forces acting on the box. Since the box is on a frictionless surface, the only force acting on it is its weight, which is equal to its mass multiplied by the acceleration due to gravity. So, the tension in the rope must equal the weight of the box.
Using Newton's second law (F = ma), we can calculate the weight of the box by multiplying its mass by the acceleration due to gravity:
Weight = mass × acceleration due to gravity = 90 kg × 9.8 m/s² = 882 N
Therefore, the tension in the rope when the box is at rest is 882 N.