PHYSICS QUESTION BEST ANSWER WILL BE CHOSEN NEED HELP ASAP?

Question

A shop sign weighing 215N 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∘). 

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

Answer 1

Draw the free body diagram

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a)

Calculate the tension in the wire.

Taking the moment about A.

∑ M_A = 0:   Anticlock wise is positive

-(W_B ) (0.85)+(T sin35^o)(1.35)-(W_S ) (1.7)=0

-(180) (0.85)+(T sin35^o)(1.35)-(215 ) (1.7)=0

T =518.5/1.35sin35^o

   = 669.6 N

Therefore, the tension in the wire is 669.6 N

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b)

Calculate the horizontal component of the hinge.

Consider equilibrium in horizontal direction:

∑ F_x = 0: Right side is positive

A_x -T cos35^o =0

A_x  =T cos35^o

       = 669.6 cos35^o

      = 548.5 N

Therefore, the horizontal force exerted by the hinge is 548.5 N

 

 

 

 

Comments

Free body diagram with all force components

Wb = Weight of beam = 180 N

Ws = Weight of sign board = 215 N

T = Tension in the supporting wire

 

Answer 2

c)

Calculate the vertical component of the hinge.

Consider equilibrium in vertical direction:

∑ F_y = 0: Upward side is positive

A_y +T sin35^o-W_B -W_S =0

A_x  =W_B +W_S-T sin35^o

       = 180+217-669.6 sin35^o

      = 12.92 N

Therefore, the vertical force exerted by the hinge is 12.92 N