Mass hanging from a 2-pulley system

[a1234]

Homework Statement

I have a question about the pulley problem in the attachment.

Homework Equations

This question can be answered using equilibrium of forces, namely Fx = 0 and Fy = 0.

The Attempt at a Solution

The answer key states that for the sum of the x-components, we should use the equation FsinΘ - FsinΘ = 0, and similarly for y, 2FcosΘ - 150(9.8) = 0.

In this solution, why is the portion of the cord on the right side of the image (which makes a 45 degree angle) ignored? Is it because this portion does not apply a force on the 15-kg mass?

In general, how do we approach such problems, which have multiple pulleys at different angles?

 

[Doc Al]

In this solution, why is the portion of the cord on the right side of the image (which makes a 45 degree angle) ignored? Is it because this portion does not apply a force on the 15-kg mass?

The equations represent the sum of forces acting on the first pulley, which must sum to zero. The pulled rope exerts its tension twice (in different directions) and the vertical rope that attaches to the mass exerts its tension downward.

In general, how do we approach such problems, which have multiple pulleys at different angles?

Often it's useful to analyze forces acting on the pulleys involved, as done here.

 

[CWatters]

Read up on free body diagrams (FBD). Typically they contain one body and the forces acting on it. Sometimes you need to draw two or more FBDs to represent a system (example: for a car towing a caravan) and write and solve simultaneous equations.

In your case you only need one FBD for the left hand pulley because the tension in the rope is the same everywhere (the rope isn't accelerating). There is no "unknown variable in the middle" (such as the tension in the tow hitch).