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

here,

weight , w = 200 N

weight of beam , wb = 180 N

A)

let the tension in the wire be t

taking moment of force about the hinge

t * sin(35) * 1.35 - wb * 1.7/2 - w * 1.7 = 0

t * sin(35) * 1.35 - 180 * 1.7/2 - 200 * 1.7 = 0

t = 636.68 N

the tension in the wire is 636.68 N

B)

let the horizontal force exerted by the hinge on the beam at the wall be Fx

Fx - t * cos(35) = 0

Fx = 636.68 * cos(35)

Fx = 521.54 N

the horizontal force exerted by the hinge on the beam at the wall is 521.54 N

C)

let the vertical force be Fy

equating the moment of forces about tension point

(1.35 - 1.7/2) * wb - fy * 1.35 - w * ( 1.7 - 1.35) = 0

(1.35 - 1.7/2) * 180 - fy * 1.35 - 200 * ( 1.7 - 1.35) = 0

fy = 14.81 N

the vertical force exerted by the hinge on the beam at the wall is 14.81 N

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