# Newton’s Law of Motions: tension forces in a pulley

• Beth N
In summary, the problem involves a mass attached to a pulley with a force F applied and a frictional force f. The question is to find the acceleration of the mass in terms of F with and without friction. The answer is F/2m without friction and (F/2m)-(f/m) with friction. The tension of the rope attached to the mass is half of the force F due to the FBD of the rope, and with friction, the tension on the side attached to the box is lesser than the tension attached to the wall.

## 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.

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!

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Just draw a FBD of the rope alone. Since there is no friction between rope and pulley, the tension must be the same in each part of the rope - it is not diminished by a friction force. If the tension in the upper part of the rope and the lower part of the rope is identical, it must be ##F/2##.

Thank you ! That makes sense, I didn't think of making a FBD for the rope. To doublecheck my thinking: so if there is friction on the pulley, the tension force of the rope attached to the box would be lesser than the tension attached to the wall (because the friction force would point along the tension attached to the mass)?
My FBD is like this :

Thank you!

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stockzahn
Beth N said:
To doublecheck my thinking: so if there is friction on the pulley, the tension force of the rope attached to the box would be lesser than the tension attached to the wall (because the friction force would point along the tension attached to the mass)?

That's it. In many of these cases it helps to imagine an "extreme" situation. If for example the bearing of the pulley would be stuck and it doesen't rotate ...

I see. Thanks a lot, I'll have to try that tip!

## 1. What is Newton's Law of Motion?

Newton's Law of Motion states that an object at rest will stay at rest and an object in motion will stay in motion at a constant velocity unless acted upon by an external force.

## 2. How does tension force play a role in the pulley system?

In a pulley system, tension force is the force exerted by a rope or cable on an object. This force helps to keep the object in motion and allows for the transfer of energy through the system.

## 3. What are the three laws of motion according to Newton's Law?

The three laws of motion are: 1) The Law of Inertia, which states that an object will remain at rest or in motion unless acted upon by an external force. 2) The Law of Acceleration, which states that the acceleration of an object is directly proportional to the net force applied to it. 3) The Law of Action and Reaction, which states that for every action, there is an equal and opposite reaction.

## 4. How can tension force be calculated in a pulley system?

Tension force can be calculated by using the formula T = m * a, where T is the tension force, m is the mass of the object, and a is the acceleration of the object. This formula can be used for both single and multiple pulley systems.

## 5. What are some real-life applications of Newton's Law of Motion and tension forces in a pulley system?

Some real-life applications include elevators, cranes, and zip lines. In all of these systems, tension force and the principles of Newton's Law of Motion are used to lift and move objects with ease and efficiency.