# Statics Pulley FBD: Man's Weight on Cable and Pulley System

• papasmurf
In summary, a Simple Statics Pulley FBD is a visual representation of a pulley system used to analyze forces and motion. To create one, all external forces must be identified and labeled on a simple diagram. The purpose is to better understand how the system works and interactions between forces. Common assumptions include massless and frictionless ropes, and neglecting rope weight. Real-life applications include engineering and physics for analyzing pulley systems, as well as everyday uses such as flagpole or bike pulley systems.
papasmurf

## Homework Statement

A man having a weight of 150 lb supports himself by means of the cable and
pulley shown in the figure. If the seat has a weight of 15 lb, determine the force that must
be exerted on cable at A, and the normal force the man exerts on the seat.

Answers provided by the teacher:
TA=110 lb.
NS=40 lb.

ƩFy=0

## The Attempt at a Solution

I have attached my rude attempt at a free body diagram. Sorry, this was my only option.
Basically, I am asking someone to check my free body diagram. Any help would be greatly appreciated!

#### Attachments

• PULLEYFBD.gif
11.3 KB · Views: 1,155
The forces are wrong at location D. The person sitting on the seat is pulling down at A. Therefore the tension at D is not 165 lbs.

At D, going off the FBD I attached, would I... replace the two 165 lb. forces with Tc and Tc? And Tc = 165/2? I don't think that is right, but I'm not sure what else could possibly be going on?

Edit: Are you trying to say that his pull causes a force at D as well that I have not included?

Last edited:
"Edit: Are you trying to say that his pull causes a force at D as well that I have not included?"

Yes. Because he is pulling down at A, he is exerting less normal force on the seat at E. This force is unknown. Therefore the tension at E must be less than 165 lbs.

Not sure if this is right...
I left my free body diagram for C as it is in my attachment.
I changed the free body diagram for D... I now have Ta going up, and 2Tc going down with 165/2 going down?

What is the tension at E? I am looking for an algebraic expression. You are implying that it is 165/2. That is incorrect.

Provide me with an algebraic expression for the tension at E.

Hint: You are standing on a bathroom scale. Next to the scale is a rope dangling from the ceiling. You pull on the rope. What happens to the scale reading? Relate the scale reading (tension at E) of the scale to the pulling force on the rope.

Ok algebraic expression for tension at E... Te + Ns - 150 - 15 = 0?

Edit: Not trying to be rude or pushy, thank you for your help, but, if this isn't right, could you just supply me with the correct free body diagram? I have to leave for class at 3:40 EST at the latest, I'd be very grateful for that.

Last edited:
OK good.

TE = 165 + Ns
where Ns is the force that you are pulling down on pulley C at A . You have two unknowns, namely TE and Ns.

Now looking at pulley C, do you see any mechanical advantage to the arrangement? Can you algebraically relate Ns to TE thereby getting a second equation. Once you have that you can solve your problem.

is the second equation Ns = 2Te?

No time to draw but here is your solution.

At E

Te = 165 - Fa
where Te is tension at E. Fa is force person pulls down with.

At A

Fa = 2 * Te
due to mechancial advantage.

Solving: Te = 55 lbs; Fa = 2 * Te = 110 lbs.

Seat force = 150 - 110 = 40 lbs

Yes thank you so much! Just in time to get to class on time too! Thanks again

Edit: Not important for class, but how did you figure Te to be 55 lbs. Just from solving the equations?

Yes, just solved equations.

## 1. What is a Simple Statics Pulley FBD?

A Simple Statics Pulley FBD (Free Body Diagram) is a visual representation of a pulley system that allows for the analysis of forces and motion. It includes all the external forces acting on the pulley system, such as tension, weight, and friction.

## 2. How do you create a Simple Statics Pulley FBD?

To create a Simple Statics Pulley FBD, you must first identify all the external forces acting on the system. This includes the weight of the object being lifted, the tension in the ropes, and any frictional forces. Then, draw the pulley system as a simple diagram, with the object being lifted as a box and the ropes as lines. Finally, label each force with its direction and magnitude.

## 3. What is the purpose of a Simple Statics Pulley FBD?

The purpose of a Simple Statics Pulley FBD is to analyze the forces and motion of a pulley system. By creating a visual representation of the system and labeling all the external forces, it allows for a better understanding of how the system works and how the forces interact with each other.

## 4. What are some common assumptions made in a Simple Statics Pulley FBD?

Some common assumptions in a Simple Statics Pulley FBD include assuming the ropes and pulleys are massless and frictionless, and neglecting the weight of the ropes. These assumptions are made to simplify the analysis and make the calculations more manageable.

## 5. What are some real-life applications of a Simple Statics Pulley FBD?

Simple Statics Pulley FBDs are commonly used in engineering and physics to analyze the forces and motion of pulley systems, such as elevators, cranes, and weightlifting machines. They are also used in everyday life, such as in the design of a flagpole pulley or a bike pulley system for hanging storage.

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