Two forces act at a point in the plane. The angle between the two forces is given. Find the magnitude of the resultant force. forces of 232

Question

Two forces act at a point in the plane. The angle between the two forces is given. Find the magnitude of the resultant force. forces of 232 and 194 ​newtons, forming an angle of 67

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Gerda 6 months 2021-08-13T02:09:15+00:00 1 Answers 6 views 0

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    2021-08-13T02:10:45+00:00

    Answer:

    408N at 89.89°

    Explanation:

    This problem requires that we resolve the force vectors into

    x- and y

    -componentsOnce this is done, we can add the components easily, as the one 2-dimensional problem will be two 1-dimensional problems.

    Finally, we will convert the resultant force into standard form and find the equilibrant.

    Resolve into components:

    F1x =F1cos 180°= 232(−1)=−232N

    F1y=F1sin180°=0N

    F2x=F2cos(−140°)=194(−0.766)=−148.6N

    F1y=F1sin(−140°)=232(−0.643)=−149.17N

    Note the change of the angle used to give the direction of

    F2. Standard angles (rotation from thex

    -axis; counterclockwise is +) should be used to avoid sign errors in the results.

    Now, we add the components:

    Fx=F1x+F2x=−380.6N

    Fy=F1y+F1y=−148.17N

    Technically, this is the resultant force. However, it should be changed back into standard form. Here’s how:

    F=√(Fx)2(Fy)2=√(−380.6)^2(−148.17)^2=408N

    θ=tan−1(−148.17−380.6)

    =89.89°

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