Q.1 Two identical rollers, each of weight 600 N are supported by an inclined plane and a vertical wall as shown in figure. If the system is in equilibrium, assuming smooth surfaces find the reactions induced at point of supports A, B and C
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The resultant of any number of concurrent forces can be found by resolving each force into its rectangular components and then adding the components algebraically. Remember, the sum of Fx = 0 and Fy = 0. The resulting numbers will be the compontents of the resultant.
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Answer: Since there are many unknowns, we can not solve the sum by using one F.B.D. Since the system is in equilibrium, we can break it as shown below:-
Applying static conditions of equilibrium,
∴ΣMC≅0(+ve)∴R3×r+500cos30×r+500sin30×r+R5×r=0∴R3×r=500cos30+500sin30+R5∴ΣFx(→+ve)=0∴R5+500sin30=0∴R5=−500sin30∴R5=−250N∴R5=250N(→)∴R3=500cos30+500sin30−500sin30=500cos30∴R3=433.013NΣFx=0∴R1−500sin30−R5=0∴R1−250−250=0∴R1=500NΣFy=0∴R2−500cos30=0∴R2=500cos30=433.013N
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