hm it's been a week since the PSAT. A friend at church said the PSAT on Saturday was "pathetically easy" . . . hm we'll see how our scores compare.
Today in Physics lab some people weren't there (either dropped the class or something else idk) so we had to shuffle the groups a bit and I ended up in a group of 3. hm but we finished earlier than like everyone so gg
, acceleration and I derped it up like 3 times before finally getting it. Those darn
signs. Here's the derivation:
Two weights (one heavier than the other) suspended by a pulley (weight on either side, string goes over pulley and comes around 180 degrees back down toward the ground -sorry too lazy to get diagram) have several forces acting on them.
Let the lighter weight have a mass of
and the heavier have a mass of
.
We know that the heavier one goes downward while the lighter one goes up toward the pulley. With free-body diagrams we can see the forces in the y direction (up/down) acting upon the two weights. (We can assume it does not move sideways at all)
- Weight 1 has 2 forces: (1) it's own weight,
, (where g is gravity) and (2) the tension pulling it up which we will simply represent as T.
- Weight 2 also has 2 forces: (1) it's own weight,
and (2) the tension pulling it up (which will also be T).
We find an equation by which we can find acceleration so we can compare our measured values with an accepted/correct value.
Derive an expression for acceleration from the masses:
We can write the forces by the vector sums:
$\sum F_1_y=m_1g-T = -m_1 a $
The T is subtracted because it's going in the opposite direction (up). The force=mass (acceleration) part is negative because the whole weight is going up.
$\sum F_2_y = m_2 g - T= m_2 a $
(LaTeX put in quotes for easier reading)
We can combine the two equations because of the common T terms:
hm Special is(was) on FTW right now.
[21:33] EpicSkills32: woah
[21:33] EpicSkills32: special
[21:33] Special: HI
[21:33] EpicSkills32: dam
[21:33] Special: xd sup
[21:33] Special: havent been on forever
[21:33] EpicSkills32: yea ikr
[21:33] EpicSkills32: stupid hacker pengu beat your record
[21:34] Special: lol isnt he banned
[21:34] EpicSkills32: um idk probably
[21:34] Special: ah
[21:35] thatmathgeek: hi epic
[21:35] thatmathgeek: back!
[21:35] thatmathgeek: wb wb
[21:35] EpicSkills32: hey
[21:35] EpicSkills32: look it'
[21:35] EpicSkills32: s Speical
[21:36] EpicSkills32: Special*
[21:36] [To: Special] <private stuff to make sure I've correctly identified him in real life>
[21:37] [Special] yeah
[21:37] thatmathgeek: hi Special
[21:37] Special: hey be back later sorry
[21:37] thatmathgeek: ..
[21:37] thatmathgeek: .
I heard this song a long time ago, but I never remembered to look for it until a few days ago. This is the version I think of when I think of this song.
by EpicSkills32, Oct 23, 2014, 5:56 AM ![$\ [\text{Blog Post 135}] $](http://latex.artofproblemsolving.com/4/6/0/4601e4acde56ccb0bdcbef3be2693772d00c7956.png)
, acceleration and I derped it up like 3 times before finally getting it. Those darn 
signs. Here's the derivation:
and the heavier have a mass of 
.
,
and (2) the tension pulling it up (which will also be T).![\[ T = m_1 g + m_1 a \]](http://latex.artofproblemsolving.com/6/d/3/6d325df0a5fcd43181727c2a90d1db0545fab331.png)
![\[ T = m_2 g - m_2 a \]](http://latex.artofproblemsolving.com/d/f/f/dff25bf3b07abe4b4fcd6d9977f357712655bf81.png)
![\[ \implies \, m_1g+m_1 a = m_2 g - m_2 a \]](http://latex.artofproblemsolving.com/c/0/e/c0e8c4e3de99beea96be9489e101e5bcdf1a1725.png)
![\[ m_1 a + m_2 a = m_2 g - m_1 g \]](http://latex.artofproblemsolving.com/0/5/6/0560fefa7a915076fe08ddc1e8236a769329bb9d.png)
![\[ a \left(m_1 + m_2 \right) = g\left(m_2 - m_1 \right) \, \therefore \, a = \boxed{ \dfrac{g\left(m_2-m_1\right)}{m_1 +m_2}} \]](http://latex.artofproblemsolving.com/1/1/d/11d431b216aa52fc4a2f672a0223407bc066b8c9.png)
He ended up not coming back on
September 2024
June 2024