Question

calculate the net force when each set of forces acts on the same object. draw an fbd for each object. k/u c
(a) 5.5 n w, 3.4 n w, 4.2 n e ans: 4.7 n w
(b) 92 n up, 35 n down, 24 n down ans: 33 n up
(c) 15 n up, 15 n down, 35 n e, 12 n w ans: 23 n e

Explanation:

Step1: Define directions

Let's assume West (W) and Up as positive directions. East (E) and Down will be negative.

Step2: Calculate net force for (a)

Forces: \(F_1 = 5.5\space N\), \(F_2=3.4\space N\) (both W), \(F_3=- 4.2\space N\) (E).
Net force \(F_{net}=F_1 + F_2+F_3=(5.5 + 3.4-4.2)\space N = 4.7\space N\) [W]

Step3: Calculate net force for (b)

Forces: \(F_1 = 92\space N\) (up), \(F_2=-35\space N\) (down), \(F_3=-24\space N\) (down)
Net force \(F_{net}=F_1+F_2 + F_3=(92-35 - 24)\space N=33\space N\) [up]

Step4: Calculate net force for (c)

Forces: \(F_1 = 15\space N\) (up), \(F_2=-15\space N\) (down), \(F_3 = 35\space N\) (E), \(F_4=-12\space N\) (W)
Vertical forces: \(F_{1}+F_{2}=(15 - 15)\space N=0\space N\)
Horizontal forces: \(F_{3}+F_{4}=(35-12)\space N = 23\space N\) [E]

Answer:

(a) \(4.7\space N\) [W]
(b) \(33\space N\) [up]
(c) \(23\space N\) [E]