To find the tension in the rope, we need to analyze the forces acting on the system.
In this scenario, there are two forces at play:
1. The weight of the heavier bucket pulling downward with a force of 110 N.
2. The tension in the rope pulling upward.
Since the rope is ideal, it is assumed to be massless and frictionless. This means that the tension in the rope is the same throughout its length.
Now, let's break down the forces:
- The weight of the heavier bucket is 110 N, pulling downward.
- The tension in the rope pulls upward.
Since the heavier bucket is descending, it means that the force of tension in the rope must be greater than 110 N to overcome the weight of the bucket.
Let's assume that the tension in the rope is T N. Since the lighter bucket weighs 65 N, the net force pulling up must be equal to the difference in weights (110 N - 65 N) to achieve equilibrium.
So, we have the equation: T - 65 N = 110 N
Simplifying the equation: T = 110 N + 65 N
T = 175 N
Therefore, the tension in the rope is 175 N.