A slab is subjected to two forces F 1 and F 2 of same magnitude F as shown in the figure. Force F 2 is in XY- plane while force F 1 acts along z -axis at the point ( 2 i + 3 j ) . The

Question

A slab is subjected to two forces F 1 ​ ​ and F 2 ​ ​ of same magnitude F as shown in the figure. Force F 2 ​ ​ is in XY- plane while force F 1 ​ acts along z -axis at the point ( 2 i + 3 j ​ ) . The moment of these forces about point O will be:

TestHub · Accepted Answer

Given, F 1 ​ = 2 F ​ ( − i ^ ) + 2 F 3 ​ ​ ( − j ^ ​ ) r 1 ​ = 0 i ^ + 6 j ^ ​ Torque due to F 1 ​ force τ F 1 ​ ​ = r 1 ​ × F 1 ​ = 6 j ^ ​ × ( 2 F ​ ( − i ^ ) + 2 F 3 ​ ​ ( − j ^ ​ ) ) = 3 F ( k ^ ) Torque due to F 2 ​ force τ F 2 ​ ​ = ( 2 i ^ + 3 j ^ ​ ) × τ net ​ = τ F 1 ​ ​ + τ F 2 ​ ​ ​ F k ^ = 3 F i ^ + 2 F ( − j ^ ​ ) = 3 Fi + 2 F ( − j ^ ​ ) + 3 F ( k ^ ) = ( 3 i ^ − 2 j ^ ​ + 3 k ^ ) F ​

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