# Why does tension change from 15 N to 17 N when forces are replaced by weights?

I'm working on a problem involving a pulley system, and I’m confused about how the tension changes when forces are replaced by masses.

Initially, if I apply forces of 20 N and 15 N directly at the ends of a massless string (without any pulley or masses), the tension in the string is exactly 15 N, as expected.

However, when I introduce masses (which exert 20 N and 15 N due to gravity) and place them over a pulley, the tension comes out to be 17 N instead of 15 N. I understand how to solve this mathematically, but why does the tension increase to 17 N when masses are used, and why does the pulley play such a crucial role?

I tried working through the mechanics, but I can't quite grasp the intuition behind the change in tension. I've attached an image of my attempt to solve the problem, but I am struggling to understand why placing the system over the pulley makes this difference.

Please see the attached image.

## 2 answers

Initially, if I apply forces of 20 N and 15 N directly at the ends of a massless string (without any pulley or masses), the tension in the string is exactly 15 N, as expected.

No, it's not. You've got a problem without a solution, like dividing by 0. You can't apply 20 N to pull a string and then say the tension is 15 N. It is 20 N by definition of applying 20 N. Of course on the other end you have the same thing, resulting in 15 N. That's an impossible situation for a massless object. It simply can't be.

In the real world, there would be a net force of 5 N in one direction. That divided by the mass of the object would tell you its acceleration. In your case you have an impossible situation since the mass is 0.

why does the tension increase to 17 N when masses are used

Because of motion. The 1.5 kg mass is being accelerated, so more than just its weight of 15 N must be applied to it. This is of course assuming you are on earth where 1 kg weighs about 10 N.

#### 1 comment thread

The increase in tension from 15 N to 17 N happens because when you introduce masses and place them over a pulley, the dynamics of the system change. Without the pulley, forces directly oppose each other, and the tension matches the smaller force. However, adding masses introduces gravitational force, and the pulley allows for the redistribution of forces.

With the masses, the tension must balance both the weight of the masses and the gravitational pull. The pulley plays a crucial role because it changes the direction of the forces and allows the system to reach equilibrium at a new tension value. Essentially, the tension now has to counteract not just the direct forces, but also the effect of gravity on the masses, resulting in a higher tension value of 17 N.

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