Help needed with a Statics Question: Load is supported by a Pulley and Cables

In summary, the discussion revolves around a statics problem involving a load supported by a pulley system and cables. Participants seek assistance in analyzing the forces acting on the system, ensuring equilibrium, and calculating tension in the cables while considering factors such as weight, angles, and the configuration of the pulley.
  • #1
MecEngPterois
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Thread moved from the technical forums to the schoolwork forums
What I did was split the problem into two seperate summations based on x & y coordinates:

Tcos(25) - Tcos(55) - Px = 0
Tsin(25+Tsin(55) +Py - Q = 0,

Where Q = 1860

I initially got an answer of 2391N, but it keeps marking me wrong for said answer.

This is the free body diagram, (the previous question asked me to construct) that I am basing my work off of:

Screenshot 2023-09-07 132413.png
Here is the question.
Screenshot 2023-09-07 132108.png
 
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  • #2
Welcome, @MecEngPterois !

Could you show us your work in detail?

Think of the principle behind a bow and an arrow.
Is it easier for the hand to initiate the pulling of the cord than directly bending the bow?
 
  • #3
The horizontal and vertical force balances on the pulley F should read:
$$T\cos{25}-(T+P)\cos{55}=0$$. $$T\sin{25}+(T+P)\sin{55}-Q=0$$
 
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Likes Lnewqban
  • #4

FAQ: Help needed with a Statics Question: Load is supported by a Pulley and Cables

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What is the first step in solving a statics problem involving a pulley and cables?

The first step is to draw a free-body diagram (FBD) of the system. This involves sketching the pulley, cables, and the load, and then indicating all the forces acting on each component. This helps in visualizing the problem and identifying the forces and their directions.

How do you calculate the tension in the cables supporting a load through a pulley system?

To calculate the tension in the cables, you need to apply the principles of equilibrium. For a system in static equilibrium, the sum of all forces and moments must be zero. You can set up equations based on these principles and solve for the unknown tensions. Typically, this involves resolving forces into their components and ensuring that the sum of forces in each direction equals zero.

What assumptions are typically made in a statics problem involving pulleys and cables?

Common assumptions include that the pulley is frictionless and massless, the cables are inextensible and massless, and the system is in static equilibrium. These simplifications help to make the problem more tractable by focusing on the primary forces and interactions.

How do you account for the angle of the cables in your calculations?

The angle of the cables affects the direction and magnitude of the tension forces. You need to resolve the tension forces into their horizontal and vertical components using trigonometric functions (sine and cosine). These components are then used in the equilibrium equations to solve for the unknowns.

What if there are multiple pulleys in the system? How does this affect the analysis?

When multiple pulleys are involved, the analysis becomes more complex as each pulley changes the direction of the cable tension. You need to consider the tension in each segment of the cable separately and apply the equilibrium conditions to each pulley. This often results in a system of equations that must be solved simultaneously.

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