HW: Newton's Second Law and Angles

AI Thread Summary
The discussion centers on understanding how the angle (theta) of a thread supporting a mass relates to the acceleration of a system, as described by Newton's Second Law. The user initially struggled with drawing a free body diagram to analyze the forces acting on the system, particularly the tension in the string. After further exploration and reviewing similar problems, they derived equations for the forces in both the x and y directions, leading to a relationship between theta and acceleration. The user confirmed their solution after the relevant diagram was approved for viewing. The thread concludes with the user feeling satisfied that they have solved the problem.
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[SOLVED] HW: Newton's Second Law and Angles

Homework Statement


The system shown in the figure can be used to measure the acceleration of the system. An observer riding on the platform measures the angle (theta) that the thread supporting the light all makes with the vertical. There is no friction anywhere.

How is (theta) related to the acceleration of the system? (Mathematical/with an equation)

Homework Equations


F=ma

The Attempt at a Solution



Well, after working on this for at least an hour, I'm thinking that to figure out what the angle has to be I have to use the idea of drawing a free body diagram of the ball/angle part of the diagram or something. I'm really having some serious trouble doing this so any help would be awesome. Thanks!

Edit: I just figured out that if I do draw the whole free body diagram, it looks like i may be able to find how the angle is related. However, in order to do so, I need to know what the tension force of the string that the ball is on would be, and that's where I'm getting stuck.
 

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So I just read a couple of other threads about similar problems as this, and I think I figured out the right answer, but I'd like someone to check it if they can...

Pretty much, I found the forces on the hanging ball in terms of x and y (like the forces in the x direct and the forces in the y direction), and then solved for theta... if this is right, then

Ax=gcos(theta)
Ay=g-gsin(theta)
 
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Hey guys, I don't mean to be pesky, and I know this probably wasn't the best time to post this, but this thing is due in the morning and i just want to see if it's correct or not... thanks :)
 
Hard to say, while your attachment is still pending approval and we can't see it. Can you try and describe the system in words?
 
ohh ok sry about that. Pretty much, there are 2 masses. One is hanging off of a pully and the other is on a horizontal surface with no friction attached by that same string on the same pully. On the second mass (the one on the horizontal surface), there is a pole with a massless ball hanging. The angle that this ball is at is supposed to be related to the acceleration of the system.

Update: The picture looks like it just got approved, so that should be a lot more helpful.
 
Last edited:
Well, I think I figured it out, so i'll leave this as solved.
 
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