Question:
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Step: 1
(a) Using parallelogram law determine the resultant force.
R=sqrt(P^2+Q^2+2PQcostheta
R=sqrt(10^2+15^2+2(10)(15)(cos75^circ)) R=20.0660338\ kN
The magnitude of resultant force is, R=20.0660338\ kN The angle made by resultant force with 15 kN force is, phi=sin^-1[(10sin75)/20.0660338]
phi=28.7751503^circ
The angle made by resultant force with the horizontal line, alpha=50^circ-phi
alpha=50^circ-28.7751503^circ alpha=21.22484969^circ
The angle made by resultant force with 10 kN force is, 21.22484969+25^circ=46.22484969^circ
The angle made by resultant force with the horizontal line, alpha=21.22484969^circ
Step: 2
(a) Using triangle rule determine the resultant force.
Use cosine law and find resultant force.
R=sqrt(10^2+15^2-2(10)(15)cos105^circ) R=20.0660338\ kN
Use sine law,
15/sin(alpha+25)=R/sin105
15/sin(alpha+25)=20.0660338/sin105 alpha+25=sin^-1(0.72206035)
alpha=21.22484969^circ
The angle made by resultant force with the horizontal line, alpha=21.22484969^circ
Final Answer
Answer is same with both method
The magnitude of resultant force is, R=20.0660338\ kN The angle made by resultant force with the horizontal line, alpha=21.22484969^circ
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