Kinetics Question (Dependant motion, gravity, pulleys)

[dontdisturbmycircles]

I am in second year engineering and am trying very hard in this course. I just started doing problems regarding simple kinetics this morning and I am getting a lot of wrong answers. Originally I just claimed to myself that I had made simple math errors but understood the concepts. The math in this question is simple enough, I have checked my math over many times with no success. I am getting kind of discouraged and was wondering if someone would be so kind to make sure I am setting up my equations correctly.

The first observation in this problem is that both T1 and T2 are unknowns since the weights are accelerating. Noting that the rope is taken to be inextensible, we get the eq's of constraint I have written below which allow for a relation between Aa and Ab to be derived as well as for Ab and Ac. I believe these to be correct as they are fairly simple.

Anyways if I solve the system at the end using a scrap piece of paper OR my calulator (tried both ways to make sure) I get Ab = -4.6ft/s^2, and according to my arbitrary selection of direction for Ab, this means 4.6ft/s^2 downward. Anyways, the solution in the book is 2.48ft/s^2 UPWARDS. I have spent a long long time checking my math, so I suppose I will admit that there must be a flaw in my technique unless the answer in the back is wrong.

I would appreciate it dearly if anyone would help me with this problem!

Homework Statement

http://img227.imageshack.us/img227/5333/3491219pm6.jpg

Specifically question 12.19

Homework Equations

F=mA Ma=Wa/g

The Attempt at a Solution

http://img228.imageshack.us/img228/4917/349prob004yc2.jpg
http://img227.imageshack.us/img227/9090/349prob005bc6.jpg

 

[Doc Al]

The book's answer is correct.

I believe you are messing up your signs. I suggest that when finding \Sigma F_y you always use the same sign convention. (I'd use up = +.)

When deciding upon the signs of the accelerations, just pick an arbitrary guess for the direction of a_B. I'd just assume that it is upwards with a magnitude of a_B. (If that assumption proves wrong, the answer will be negative.) Then you can use your constraint equations to find the other accelerations.

 

[dontdisturbmycircles]

Okay, I will try adopting a more consistent sign convention. I suppose there is no harm in always assuming that accelerations are upward and that upwards is positive. Because yea, its really discouraging to keep getting wrong answers. Thankyou very much for verifying the answer in the back of the book, as well as giving out the tips regarding these problems. I appreciate it. :-D

 

[Doc Al]

I suppose there is no harm in always assuming that accelerations are upward and that upwards is positive.

Picking one of the accelerations as upward is just an arbitrary assumption so you can write the equations consistently. (As you know, not all the accelerations can be upward, since the masses are constrained.) Choosing upwards as positive is a convention.