mohabitar said:
Ohhh ok I see I was supposed to put T from the 2nd equation into the first one. I missed that part. So speaking about this equation m2*g -T = m2*a, why does it work?
We see that the mass of the 2nd block x gravity minus the tension of the string = mass of 2nd block x acceleration. I don't understand the logic behind it. And we don't really use textbooks in this class, its all online and to find out the intuition behind a certain equation online is kind of hard, so any help here would be greatly appreciated.
The general idea is Newton's second law. There are a number of ways to phrase Newton's second law, but here is a common one*:
The mass
m of a given body times the acceleration
a of that body equals the sum of all forces acting on that particular body.
m \vec a = \sum_i \vec F_i
*(This version of the equation assumes constant mass.)
So what does all that really mean? Well, first draw a free body diagram. Draw all the force vectors onto the diagram. For a particular body, add up all the forces acting on that particular body (make sure you do a
vector sum). The result is equal to
that body's mass times its acceleration.
So let's look at block 2. There are two forces acting on it: The force of gravity
mg in the down direction and the tension
T in the up direction. If we define down as positive, then the sum of all forces acting on Block 2 is:
\sum_i \vec F_i = mg - T
Set that equal to
m2a.
m_2a = m_2g - T
Newton's second law in action! http://www.websmileys.com/sm/happy/535.gif Of course we don't know what
T is yet, but we'll come back to that.
There is only one force acting on Block 1, and that is the tension
T.
m_1a = T
Since the pulley is massless and frictionless, we know that the two tensions are equal. So combining our equations
m_1a = T = m_2g - m_2a
m_1a = m_2g - m_2a
and solving for
a,
m_1a + m_2a = m_2g
= a(m_1 + m_2) = m_2g
a = \frac{m_2g}{m_1 + m_2}
So now, minimize your web browser (you can come back to it later if you have to), take out your pencil and paper and repeat what I just did. But please don't try to look back and
memorize what I just did, that defeats the point. Instead just remember the following:
(1) Draw your free body diagram. Doing so is really useful.
(2) Newton's second law:
ma = sum of all the forces acting on that particular body.
(3) You might not be able to find the final answer for
a by analyzing just one body. But that's okay, move on to a different body and combine equations later.
Pencil, paper, go!
