thanks for everyone helping me i am really greatful ,and the explations are makiing understand more thank you ...i need help in this homework too ,and i need answers for all please..there is another part continued.
regards
1. Vector sum of forces:
$\displaystyle
\bold{V} = (2\bold{i} + \bold{j}) + (3\bold{i} - 2\bold{j}) + (-\bold{i} -3\bold{j}) = (2+3-1) \bold{i} +(1-2-3)\bold{j} = 4 \bold{i} -4\bold{j} \mbox{ N}
$
The the acceleration $\displaystyle \bold{a} = \bold{V}/m$
2. let the tension be $\displaystyle \bold{T}$ then the total force on the first particel, and hence the acceleration is:
$\displaystyle
\bold{T}-m_1\bold{g} = m_1 \bold{a_1}
$
and for the second particle:
$\displaystyle
\bold{T}-m_2\bold{g} = m_2 \bold{a_2}
$
but $\displaystyle \bold{a_2} = -\bold{a_1}$ so:
$\displaystyle
\bold{T}/m_2-\bold{g} = -[\bold{T}/m_1-\bold{g}]
$
which can then b solved for $\displaystyle \bold{T}$
RonL
Start by drawing a Free-Body-Diagram for the ball.
I have a +x axis to the right and a +y axis upward. There is a weight (w) acting straight downward, a tension (T) acting at 50 degrees above the -x axis, and an applied force (F) of 50 N acting in the +x direction.
Since the ball is in equilibrium we know that
$\displaystyle \sum F_x = 0$
$\displaystyle \sum F_y = 0$
So:
$\displaystyle \sum F_x = -Tcos(50) + F = 0$
which implies
$\displaystyle T = \frac{F}{cos(50)} = \frac{50 \, N}{cos(50)} = 77.7862 \, N$
and
$\displaystyle \sum F_y = Tsin(50) - w = 0$
which implies
$\displaystyle w = Tsin(50) = \frac{F}{cos(50)} \cdot sin(50) = F tan(50)$
$\displaystyle = (50 \, N)tan(50) = 59.5877 \, N$
-Dan