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1. Homework Statement
3B. A uniform wooden sign of mass 4.0 kg hangs beside a building wall. The sign is 2.00 m
high and 4.00 m wide. It is supported by a hinge at P, that is midway up one
edge, and by a light rope that is attached exactly threequarters of the distance across the
upper edge. The rope makes an angle of 20.0 degrees with the horizontal.
(b) Write the conditions for static equilibrium of the sign and solve for the horizontal (H) and vertical (V) components of the force at P, and solve for the rope tension (T)
(c) Later, Prof. Fich of mass 90.0 kg climbs out of a window just below the sign, reaches up and grabs onto the bottom portion of the sign and, while hanging from the sign, begins to move away from the building. If the rope can only support a maximum tension of 1500 N, how far can Prof. Fich move away from the building ?
2. Homework Equations
net torque=0
Fnety=0
Fnetx=0
3. The Attempt at a Solution
I have the force equations set up.
Tsin20+Fpv4g=0
Tcos20=Fph
I am having trouble setting up the torque. For the moment arm, can you go through the sign? I cant get the moment arms and angles set up.
So far I have
Tsin38.4(sqroot10)=mg(2)
Is this right?
(The three lines I've drawn on the sign are what I think the 2 moment arms are, and also the vector for Fg)
3B. A uniform wooden sign of mass 4.0 kg hangs beside a building wall. The sign is 2.00 m
high and 4.00 m wide. It is supported by a hinge at P, that is midway up one
edge, and by a light rope that is attached exactly threequarters of the distance across the
upper edge. The rope makes an angle of 20.0 degrees with the horizontal.
(b) Write the conditions for static equilibrium of the sign and solve for the horizontal (H) and vertical (V) components of the force at P, and solve for the rope tension (T)
(c) Later, Prof. Fich of mass 90.0 kg climbs out of a window just below the sign, reaches up and grabs onto the bottom portion of the sign and, while hanging from the sign, begins to move away from the building. If the rope can only support a maximum tension of 1500 N, how far can Prof. Fich move away from the building ?
2. Homework Equations
net torque=0
Fnety=0
Fnetx=0
3. The Attempt at a Solution
I have the force equations set up.
Tsin20+Fpv4g=0
Tcos20=Fph
I am having trouble setting up the torque. For the moment arm, can you go through the sign? I cant get the moment arms and angles set up.
So far I have
Tsin38.4(sqroot10)=mg(2)
Is this right?
(The three lines I've drawn on the sign are what I think the 2 moment arms are, and also the vector for Fg)
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