Short Answer 
The answer outlines the application of Newton’s Second Law, explaining that the total weight of the monkey and cage (9 kg) results in a downward force of 90 N. For the system to remain in equilibrium, the upward force must match this weight, indicating a required force (F) of 90 N, unless specified by the problem context, which may suggest a different force, such as 40 N, due to additional factors like pulley mechanisms.
Step 1: Understand Newton’s Second Law
Newton’s second law states that the force acting on an object is equal to the mass of the object times its acceleration (F = m*a). To keep the monkey in equilibrium, the forces acting on the monkey and cage must balance out. Therefore, we need to consider only the relevant forces acting downward and the forces acting upward.
Step 2: Calculate the Weight of the System
Identify the total mass of the monkey and the cage. In this case, the total mass is 9 kg. The weight (the downward force due to gravity) can be calculated as follows:
- Weight = mass √ó g
- Weight = 9 kg × 10 m/s² = 90 N
This means the total downward force acting on the system is 90 N, which is crucial for understanding equilibrium.
Step 3: Determine the Force F for Equilibrium
In equilibrium, the upward force (tension in the rope or force F) must equal the weight acting downwards. This means:
- F = Weight
- F = 90 N
However, if the context of the problem suggests adjusting for pulley mechanisms, the corresponding force might be indicated as 40 N. It’s essential to review any specific assumptions about how tension is distributed in this system.