Two buckets of sand hang from opposite ends of a rope that passes over an ideal pulley. One bucket is full and weighs 110 N ; the other bucket is only partly filled and weighs 65 N .

You release the lighter bucket and the heavier one descends. What is the tension in the rope?

sum forces: Wheavy-Wlight=(SumMasses)acceleration.

Now consider the tension to move the lighter upward
tension=Wlight+MassLight*acceleration
now consider the tension to keep the heavier from free falling
tension=Wheavy-Massheavy*acceleration

guess what? if you solve either of these, you get the same tension.

To find the tension in the rope, we need to consider the forces acting on each bucket.

Let's assume the tension in the rope is T.

For the heavier bucket (110 N), there are two forces acting on it: the weight of the bucket (110 N) acting downward and the tension in the rope (T) acting upward.

For the lighter bucket (65 N), there are also two forces acting on it: the weight of the bucket (65 N) acting downward and the tension in the rope (T) acting upward.

Since the buckets are connected by a rope passing over an ideal pulley, the tension in the rope is the same on both sides.

Now let's write the equations for the forces on each bucket:

For the heavier bucket:
Tension in the rope = Weight of the bucket
T = 110 N

For the lighter bucket:
Tension in the rope = Weight of the bucket
T = 65 N

Since the tension in the rope is the same for both buckets, we can equate the two equations:

110 N = 65 N

Therefore, the tension in the rope is 65 N.

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.