Problem 5.32 Determine the magnitude of force at the pin A and in the cable BC n

Question

Problem 5.32 Determine the magnitude of force at the pin A and in the cable BC needed to support the 500-lb load. Neglect the weight of the boom AB. 8 ft 15 Part A Determine the magnitude of force at the pin A Express your answer to three significant figures and include the appropriate units. FA Value Units Submit My Answers Give Up Part B Determine the force in the cable BC Express your answer to three significant figures and include the appropriate units FacValue Units Submit My Answers Give Up

Explanation / Answer

Part A:

Let us consider the free body diagram of AB. at point B,the forces acting are 500 lb(vertically downwards),and tension in the cable BC acting along BC

From moment equilibrium of AB about support A,we get

500*8cos35=Tcos22*8sin35 - Tsin22*8cos35

T=1820.7 lb

Vertical force at pin A=500+1820.7sin22=1182.0 lb(vertically upwards)

Horizontal force at pin A=1820.7cos22=1688.1 lb(towards right)

magnitude of force at pin A=sqrt(11822+1688.12)=2060.8 lb

Part B:

tension in cable BC = T=1820.7lb

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