Step-by-step explanation:
Let
= mass of the painter
= mass of the scaffold
= mass of the equipment
= tension in the cables
In order for this scaffold to remain in equilibrium, the net force and torque on it must be zero. The net force acting on the scaffold can be written as
![3T = (m_p + m_s + m_e)g\:\:\:\:\:\:\:(1)](https://tex.z-dn.net/?f=3T%20%3D%20%28m_p%20%2B%20m_s%20%2B%20m_e%29g%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%281%29)
Set this aside and let's look at the net torque on the scaffold. Assume the counterclockwise direction to be the positive direction for the rotation. The pivot point is chosen so that one of the unknown quantities is eliminated. Let's choose our pivot point to be the location of
. The net torque on the scaffold is then
![T(1.4\:\text{m}) + m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m}) - 2T(5.2\:\text{m}) = 0](https://tex.z-dn.net/?f=T%281.4%5C%3A%5Ctext%7Bm%7D%29%20%2B%20m_sg%281.9%5C%3A%5Ctext%7Bm%7D%29%20%2B%20m_pg%284.2%5C%3A%5Ctext%7Bm%7D%29%20-%202T%285.2%5C%3A%5Ctext%7Bm%7D%29%20%3D%200)
Solving for T,
![9T = m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m})](https://tex.z-dn.net/?f=9T%20%3D%20m_sg%281.9%5C%3A%5Ctext%7Bm%7D%29%20%2B%20m_pg%284.2%5C%3A%5Ctext%7Bm%7D%29)
or
![T = \frac{1}{9}[m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m})]](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B1%7D%7B9%7D%5Bm_sg%281.9%5C%3A%5Ctext%7Bm%7D%29%20%2B%20m_pg%284.2%5C%3A%5Ctext%7Bm%7D%29%5D)
![\:\:\:\:= 423.3\:\text{N}](https://tex.z-dn.net/?f=%5C%3A%5C%3A%5C%3A%5C%3A%3D%20423.3%5C%3A%5Ctext%7BN%7D)
To solve for the the mass of the equipment
, use the value for T into Eqn(1):
![m_e = \dfrac{3T - (m_p + m_s)g}{g} = 14.6\:\text{kg}](https://tex.z-dn.net/?f=m_e%20%3D%20%5Cdfrac%7B3T%20-%20%28m_p%20%2B%20m_s%29g%7D%7Bg%7D%20%3D%2014.6%5C%3A%5Ctext%7Bkg%7D)
Answer:
Step-by-step explanation:
Jack's method is equivalent because of the "law of commutative property", which means that multiplication problems have the same result no matter the order.
2x5 is the same as 5x2
Answer: (this is solving for m)
m= −4
/7
n + −8
/7
Step-by-step explanation:
7m + 4n + 8+ −4n =0 + −4n
7m + 8= −4n
7m + 8 + −8 = −4n + −8
7m = −4n − 8
7m
/7 = (−4n − 8 )
/7
m= −4
/7
n + −8
/7
Answer:
1000=450 (1+ 0.06) y
4
Step-by-step explanation:
In the paranthesis where it says 0.06 and then 4 at the bottom its supposed to be a fraction btw
Answer:
![209.43 \: \: {units}^{3}](https://tex.z-dn.net/?f=209.43%20%20%5C%3A%20%20%5C%3A%20%7Bunits%7D%5E%7B3%7D%20)
Step-by-step explanation:
![v = \pi {r}^{2} \frac{h}{3} \\ = \pi \times {5}^{2} \times \frac{8}{3} \\ = 209.439](https://tex.z-dn.net/?f=v%20%3D%20%5Cpi%20%7Br%7D%5E%7B2%7D%20%20%5Cfrac%7Bh%7D%7B3%7D%20%20%5C%5C%20%20%3D%20%5Cpi%20%5Ctimes%20%20%7B5%7D%5E%7B2%7D%20%20%5Ctimes%20%20%5Cfrac%7B8%7D%7B3%7D%20%20%5C%5C%20%20%3D%20209.439)