ToughSTEM
Sign Up
Log In
ToughSTEM
A question answer community on a mission
to share Solutions for all STEM major Problems.
Cant find a problem on ToughSTEM?
0
A uniform 26 kg door that is 2.5 m high by 0.80 m wide is hung from two hinges that are 20 cm from the top and 20 cm from the bottom. If each hinge supports half the weight of the door, find the magnitude and direction of the horizontal components of the forces exerted by the two hinges on the door. 

(Take the direction of forcing the door away from the hinges to be positive and the direction of forcing the door toward the hinges to be negative.)
Edit
Added Mon, 08 Jun '15
Community
1
Comment
Add a Comment
Solutions
0
What are our Givens?
m = 26-kg
H = 2.5-m
W = 0.80-m
d = 0.20-m = distance of a hinge from its closest edge
Free Body Diagram of the Two Hinged Door System
What's it asking?
What is the horizontal force the two hinges exert.
H_t = ? (top hinge horizontal force)
H_b = ? (bottom hinge horizontal force)

Use the fact the Net Torque = 0 and one of the hinges as a reference point to find the Horizontal force of one of the hinges.

We're going to use the bottom hinge as the reference point.
Tq = H_t * (H - 2d) - m * g * W / 2 = 0
H_t = m * g * W / 2 * / (H-2d)

Plug in the variables to solve for H_t

H_t = 26-kg * 9.81-m/s^2 * 0.8-m / 2 / (2.5-m - 2*0.2-m)
H_t = 48.59-kg*m/s^2 = 48.59-N

Because the directions specified that the force going towards the hinges (to the left) is negative, H_t is a negative value.

H_t = -48.95-N

Now we have to find H_b.
Because the system is in static equilibrium and we know one of the two forces acting in the y direction, expressing the forces in the y direction will enable us to solve for H_b.

Fy = H_t + H_b = 0
>> H_b = -H_t
H_b = 48.95-N
Edit
Added Mon, 08 Jun '15
Community
1
Comment
Add a Comment
Add Your Solution!
Close

Click here to
Choose An Image
or
Get image from URL
GO
Close
Back
Add Image
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

Add Your Solution
Sign Up
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!
Please check your email to finish creating your account!
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.