A shop sign weighing 195 N hangs from the end of a uniform 170 - N beam a. Find

Question

A shop sign weighing 195N hangs from the end of a uniform 170-N beam

a. Find the tension in the supporting wire (at 35 degrees)

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

A shop sign weighing 195N hangs from the end of a uniform 170-N beam Find the tension in the supporting wire (at 35 degrees) Find the horizontal force exerted by the hinge on the beam at the wall. (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.) Find the vertical force exerted by the hinge on the beam at the wall. (Enter positive value if the force is upward and negative value if the force is downward.)

Explanation / Answer

The sign is acting by 195 N downward at 1.7 m from left
The beam is acting by 170 N downward at 0.85 m from left
The rope is acting by an inclined force (T N) at 1.35 m

Since the system is in equilibrium then the moment at any point is zero

Taking the moment at the left end of the beam so that the affect of the wall reaction is not regarded the we ca write the equation:

T*sin(theta)*1.35= 195*1.7 + 170*0.85

==> T= (195*1.7 + 170*0.85)/(sin(35 degrees)*1.35)=614.73 N

2) Horizontal force= T*cos(35 degrees)= 614.73*cos(35 degrees)= + 503.57 N

3) verticle force= T*sin(35 degrees) - 197-170= -14.4 N

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