Four forces and a couple are applied to a block as shown in the figure 1. a. Rep

Question

Four forces and a couple are applied to a block as shown in the figure 1. a. Replace the four forces and the couple by a FORCE-COUPLE SYSTEM at C. b. Express the resultant FORCE as a single force making sure to give angle (s) to determine where the line of action of the force is. c. Express the resultant MOMENT in Cartesian vector form. d. Determine the moment that the resultant force produces about line AB, and give your answer as a scalar. e. Express the moment about line AB using Cartesian notation (i.e. Express the moment as a vector)

Explanation / Answer

From the diagram
let i,j, k be unit vectors along x,y and z axis

Net force at C = F = 110j + 400(-i) + 100(-j) + 500i = 100i + 10 j N
Net moment abbout C = 500j + 100*5 i + 500*5 j = 500i + 3000 j Nm

hence resultant force at C should be 100i + 10j N = sqroot(100^2 + 10^2) = 100.49 N at an angle = arctan(10/100) = 5.710 deg anticlockwise from +x axis in xy plane
moment at C should be 500i + 3000j Nm = sqroot(500^2 + 3000^2) = 3041.381 Nm in direction = arctan(3000/500) = 80.53 deg ccw from +x axis in xy plane

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