  ToughSTEM  ToughSTEM
A question answer community on a mission
to share Solutions for all STEM major Problems.
Cant find a problem on ToughSTEM?
0
Lifting boom

A crate with a mass of 189.5 kg is suspended from the end of a uniform boom with a mass of 84.5 kg. The upper end of the boom is supported by a cable attached to the wall and the lower end by a pivot (marked X) on the same wall. Calculate the tension in the cable.   Edit
Added Sun, 05 Jul '15 Community
1
Comment  Solutions
0
m? = mass of the crate = 189.5 kg
m? = mass of the boom = 84.5 kg
g = acceleration by gravity = 9.81 m/s^2
L = length of the boom
? = angle of the boom to horizontal
? = angle of the cable to horizontal

From the image you can see that
tan(?) = 3/9
so
? = arctan(3/9) = 18.434 degrees

From the image you can see that
tan(?) = 4/9
so
? = arctan(4/9) =23.96 degrees

As the system is at equilibrium, you know that the clockwise torque (caused by the weight of the boom and crate) must be equal in magnitude to the counterclockwise torque (caused by the tension in the cable)
So:
m?*g*cos(?)*L/2 + m?*g*cos(?)*L = T*sin(? + ?)*L
(m?/2 + m?)*g*cos(?) = T*sin(? + ?)
T = (m?/2 + m?)*g*cos(?) / sin(? + ?)

T = [(189.5 kg)/2 + (84.5 kg)]*(9.81 m/s^2)*cos(18.434) / sin((18.434) + (23.962))
T = 2474.17 N  < - - - - - - - answer  Edit
Added Sun, 05 Jul '15 Community
1
Comment  Close Choose An Image
or
Get image from URL
GO
Close Back
Close
What URL would you like to link?
GO             α
β
γ
δ
ϵ
ε
η
ϑ
λ
μ
π
ρ
σ
τ
φ
ψ
ω
Γ
Δ
Θ
Λ
Π
Σ
Φ
Ω
Copied to Clipboard

to interact with the community. (That's part of how we ensure only good content gets on ToughSTEM)
OR      OR
ToughSTEM is completely free, and its staying that way. Students pay way too much already.
Almost done! Welcome to the Club!
Choose a new Display Name
Only letters, numbers, spaces, dashes, and underscores, are allowed. Can not be blank.
Great! You're all set, . A question answer community on a mission
to share Solutions for all STEM major Problems.
Why
The Purpose
How
The Community
Give Feedback Tell us suggestions, ideas, and any bugs you find. Help make ToughSTEM even better.