Pulley & Tension: Solving for Acceleration and Tension

[whitehorsey]

1. See Attachment

2. F = ma


3. For the block on the incline plane, I know it has Fnormal, Fweight, and Ftension. While the one hanging has Ftension and Fweight.

Fn = 6gcos30
ƩFx = 6gcos30 - T = 6a
6gsin30 - (2g +2a) = 6a
6gsin30 -2g = 8a
2g(3sin30 - 1) = 8a
a = 1.225

T = 6gsin30 - 6a
= 22.05N

Is this correct? And when do I use negative acceleration versus positive acceleration?

 

[Simon Bridge]

As a matter of policy, I don't like telling people whether a specific answer is correct or not.
At some stage you will have to deal with problems where nobody knows the answer and you need to get used to this. Besides, I can make mistakes as easily as you - why should you trust my answer any more than your own?
Instead I'll try to show you how to have confidence in your results.

One of the ways to have confidence in your working is to draw th pictures - in this case, two free body diagrams. Did you do this? It's OK that you didn't post them - but you should do them. The fbds should give you three equations that are coupled together - but you are only interested in two of them. Is your working consistent with the free-body diagrams? i.e. you have written that Fx=Fn-T = Ma (using M for the big mass and m is the little mass - cute eh? Note: it is best to do the algebra first) - does this make sense from your fbd for M?

Another way is to comment your working as you go - in words.
eg. what are you defining as the "x" component? which way is "positive"? you need to be clear on this point.

Related to this is doing the algebra first, avoid subscripts, encode directions explicitly with the + or - sign, and put the numbers in only at the end. This makes it easier to troubleshoot your working.

In your equations, you want the letters to represent magnitudes and put the + or - sign in for direction.
If the magnitude turns out to be negative, when you done the math, then it just means the direction should have been opposite.

To your question: a negative acceleration is a slowing-down in the positive direction and a speeding-up in the negative direction. This is why it is important to define your directions on the fbd. All you need to know is the direction of the net force on either mass.

BTW: 30deg is a very nice angle - sin(30)=0.5