Question

Please solve & explain

VECTORS & FORCES COMPONENTS PRACTICE INSTRUCTIONS: Find the indicated quantity. F3 I Fi l=0.750 N F. 0-2277" 9-60 F Net 1F2 1=1.000 N FNet -1.753 N

Answer 1

Suppose given that Force is F and it makes angle A with +x-axis, then it's components are given by:

Fx = |F|*cos A

Fy = |F|*sin A

Using above rule:

F1 = magnitude of 0.750 N at 0 deg with +x-axis

F1x = |F1|*cos 0 deg = 0.750*cos 0 deg = 0.750 N

F1y = |F1|*sin 0 deg = 0.750*sin 0 deg = 0 N

F2 = magnitude of 1.000 N at 30 deg with +ve x-axis (for components we use angle of vector with +x-axis)

F2x = 1.000*cos 30 deg = 0.866 N

F2y = 1.000*sin 30 deg = 0.500 N

F3 = magnitude of |F3| at 270 deg with +x-axis

F3x = |F3|*cos 270 deg = 0 N

F3y = |F3|*sin 270 deg = -|F3| N

Also,

Fnet = magnitude of 1.753 N at -22.77 deg with +x-axis

Fnet_x = 1.753*cos (-22.77 deg) = 1.616 N

Fnet_y = 1.753*sin (-22.77 deg) = -0.678 N

Now Using net force balance

Fnet = F1 + F2 + F3

Using component forms

(Fnet_x i + Fnet_y j) = F1x i + F1y j + F2x i + F2y j + F3x i + F3y j

(F3x i + F3y j) = (Fnet_x - F1x - F2x) i + (Fnet_y - F1y - F2y) j

Using above values:

0 i - |F3| j = |(1.616 - 0.750 - 0.866)| i + (-0.678 - 0 - 0.500) j

0 i - |F3| j = 0 i - 1.178 j

Compare both sides

-|F3| = -1.178

|F3| = 1.178 N

Please Upvote.

Comment below if you have any query.