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## Homework Statement

Problem: 4.93[/B]

The pulley is assumed massless and frictionless. The mass of the object attached to the pulley is given in terms of m, the force applied to the pulley is F (refer to diagram), and frictional force is f.

Question: Find the acceleration of the mass m in terms of F if there is no friction between the surface and m. Repeat if the frictional force on m is f.

Answer key:

aceleration=F/2m. (without friction)

acceleration=(F/2m)-(f/m) (with friction)

Diagram:

## Homework Equations

F=ma (Newton's Second Law)

Fnet (horizontal)= -f+F (Calculating net force)

## The Attempt at a Solution

My initial answer was similar to the key, except that I forget that the tension of the string attached to the mass is half of the force F. I get that the tension is less than the force F because there are two separate strings doing the entire force F, but I don't know why each is exactly half of F; it seems simple but I could not understand its behavior physically.

**My question: how do we know T= F/2? Why wouldn’t the tension of the side attached to the wall be greater than the tension attached to the mass, because the mass is probably less heavy and is movable?**

Thank you!

Thank you!