Part A) Consider four vectors ~ F1, ~ F2, ~ F3, and ~ F4 with magnitudes F1 = 38

Question

Part A) Consider four vectors ~ F1, ~ F2, ~ F3, and ~ F4 with
magnitudes F1 = 38 N, F2 = 39 N, F3 = 21 N,
and F4 = 43 N, ?1 = 150 ?, ?2 = -140 ?,
?3 = 17?, and ?4 = -74?, measured from the
positive x axis with counterclockwise positive.
What is the magnitude of the resultant vec-
tor ~F = ~ F1 + ~ F2 + ~ F3 + ~ F4?
Answer in units of N.
Part B)What is the direction of this resultant vec-
tor ~F , within the limits of -180? and 180? as
measured from the positive x axis with coun-
terclockwise positive ?
Answer in units of ?.

Explanation / Answer

Use the component method.
Fx=Fcos with being made between the vector and the positive horizontal axis measured counterclockwise.

Fx=F1cos(150)+F2cos(220)+F3cos(17)+F4cos(286)=-30.85 N

Fy=F1sin(150)+F2sin(220)+F3sin(17)+F4sin(286)=-41.26 N

R=(Fx2+Fy2)= 51.52 N

Direction:

using the tangent function and being made with the negative y axis,

tan=(Fx/Fy)

= 36.79 degrees from the negative y axis which makes =-126.79 degrees so that it lies between ±180 degrees. Counterclockwise from the positive x axis it is =233.21 degrees.

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