A shop sign weighing 200 N hangs from the end of a uniform 180 -N beam as shown

Question

A shop sign weighing 200 N hangs from the end of a uniform 180 -N beam as shown in (Figure 1)

Part A

Find the tension in the supporting wire (at 35.0 ).

Express your answer to three significant figures and include the appropriate units.

Part B

Find the horizontal force exerted by the hinge on the beam at the wall.

Express your answer to three significant figures and include the appropriate units. Enter positive value if the direction of the force is to the right and negative value if the direction of the force is to the left.

Part C

Find the vertical force exerted by the hinge on the beam at the wall.

Express your answer to three significant figures and include the appropriate units. Enter positive value if the force is upward and negative value if the force is downward.

Explanation / Answer

Forces on the beam are as under
1. Tension T due to wire at an angle 35 deg
2. Weight of bar W at distance 0.85m from the wall
3. Weight of board, H at distance 1.7 m from the wall
4. Horizontal force of reaction, R due to the support
5. Vertical force due to the hinge = R'

Force balance

200 + 180 = Tsin(35) + R'
Tcos(35) = R

moment balance about the hinge

200*0.85 + 180*1.7 = Tsin(35)*1.35

a. T = 614.726 N
b. R = Tcos(35) = 503.554 N
c. R' = 380 - Tsin(35) = 27.407 N

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