Question

view policies
current attempt in progress
a force vector \\(\vec{f_1}\\) points due east and has a magnitude of 180 newtons. a second force \\(\vec{f_2}\\) is added to \\(\vec{f_1}\\). the resultant of the two vectors has a magnitude of 430 newtons and points along the (a) east/ (b) west line. find the magnitude and direction of \\(\vec{f_2}\\). note that there are two answers.
(a) \quad number \quad newtons
(b) \quad number \quad newtons

Explanation:

Step1: Case (a) - Resultant east

Forces in same direction add. Let \( F_2 \) magnitude be \( F_{2a} \).
\( F_1 + F_{2a} = F_{resultant} \)
\( 180 + F_{2a} = 430 \)
\( F_{2a} = 430 - 180 = 250 \) N (direction: east)

Step2: Case (b) - Resultant west

Forces in opposite directions, \( F_2 \) must be west (larger magnitude). Let \( F_2 \) magnitude be \( F_{2b} \).
\( F_{2b} - F_1 = F_{resultant} \)
\( F_{2b} - 180 = 430 \)
\( F_{2b} = 430 + 180 = 610 \) N (direction: west)

Answer:

(a) Magnitude: \( 250 \) newtons, Direction: East
(b) Magnitude: \( 610 \) newtons, Direction: West