Reactions with crate and pulley

[stinlin]

So I had an exam yesterday and ran into a problem like this. The crate was suspended in such a way that it's CG didn't seem to line up with the given measurements. Also, the tension in the cables around the pulleys are equal (nothing is said about the tension in the blue cable). There's a pin joint at the bottom area and a roller on that incline. How would you go about analyzing this system? Mainly my question is - if you sum moments about a, what do you do about the 150 lb crate and those pulleys? Thanks!

http://img507.imageshack.us/img507/9034/lamelh0.png

^^ Image

 

[radou]

Try looking at the crate separately. Which forces are acting on it? You should be able to find the force in the green string. Now, look at the system without the crate with the force in the green string acting on it. Write out the equations of equilibrium.

P.S. There is a neat graphical way to solve this. The force in the roller must be perpendicular to the direction of rolling. Further on, the force in the green string has a known direction, and the point of coincidence of the lines of these two forces is thereby known. Now, by drawing a line through that point and the point of the pin joint, you'll find the direction fo the force in the pin joint. Since you now have three forces, all of which directions are well known, and since you know the magnitude of one of them (the force in the green string), you can calculate your reactions graphically by simple vector addition and proper length and force scale selection.

 

[ravenprp]

for reference


Hi there! It sounds like you encountered a challenging problem on your exam. Let's break it down and see if we can figure out how to analyze this system.

First, it's important to remember that when dealing with pulleys, the tension in the cable is equal on both sides. This means that the tension in the blue cable is also equal to the tension in the red and green cables. This will be helpful in our analysis.

Next, we can use the fact that the crate is suspended by the cables to determine the forces acting on it. The weight of the crate, 150 lbs, is acting straight down. Since the crate is not moving, the tension in the cables must be equal to the weight of the crate. This means that each cable is supporting 50 lbs of the crate's weight.

Now, let's look at the pin joint at the bottom and the roller on the incline. These act as supports and can be treated as reaction forces. We can use the principles of static equilibrium to determine the forces acting at these points.

When you sum moments about point A, you will need to consider the forces acting on the crate and the forces acting at the pin joint and the roller. The weight of the crate will create a clockwise moment, while the reaction forces at the pin joint and the roller will create a counterclockwise moment. You will need to set these two moments equal to each other to solve for the unknown reaction forces.

I hope this helps! Remember to always draw a free body diagram and use the principles of static equilibrium to solve problems like this. Good luck with your exams!