Answer:
2538.72 N
Explanation:
Given data:
There are some missing values, so, I will assume them, and then you affix them. It's basically just substitution....
m₁ = mass of crate = 193.5 kg
m₂ = mass of the boom = 91.7 kg
g = acceleration by gravity = 9.81 m/s²
L = length of the boom
θ = angle of the boom to the horizontal
φ = angle of the cable to horizontal
Solution:
I'm assuming that
tan (θ) = 6/12 = 0.5
This then makes
θ = arctan(0.5)= 26.57°
The second and last assumption I'm making is that
tan(φ) = 3/12 = 0.25
This also makes
φ = arctan(0.25) = 14.04°
Now, since the system is in equilibrium, the magnitude of clockwise torque has to be equal to anticlockwise torque. This means that
m₁ * g * cos(θ) *L/2 + m₂ * g *cos(θ) * L = T * sin(θ+φ) * L
(m₁/2 + m₂) * g * cos(θ) = T * sin(θ+φ), making T subject of formula, we have
T = (m₁/2 + m₂) * g * cos(θ) / sin(θ + φ)
T = [(193.5)/2 + (91.7)] * (9.81) * cos(26.57°) / sin(26.7°) + (14.04°))
T = [(96.75 + 91.7) * 9.81 * 0.894] / 0.651
T = 188.45 * 8.77 / 0.651
T = 1652.7065 / 0.651
T = 2538.72 N
