Question

12.
If the four forces as shown are in equilibrium, Express F1 and F2 in unit vector form.
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Answer 1

it can be solved easily with help of vector form.

write 15N in vector form

i.e., -15cos37° i + 15sin37° j

= -15 × 4/5 i + 15 × 3/5 j

= -12 i + 9 j

similarly, write 10N in vector form,

i.e., 10cos30° i + 10sin30° j

= 5√3 i + 5 j

vector form of F2 $F_2sin30^{\circ}\hat{i}+F_2cos30^{\circ}\hat{j}$

now, at equilibrium,

Fnet = 0

or, (-12i + 9j) + (5√3i + 5j) + ($-F_1\hat{j}$) + $(F_2sin30^{\circ}\hat{i}+F_2cos30^{\circ}\hat{j})$ = 0

or, (-12 + 5√3 + F2sin30°)i + (9 + 5 - F1 + F2cos30°)j = 0

so, (-12 + 5√3 + F2sin30°) = 0 or, (9 + 5 - F1 + F2cos30°) = 0

(-12 + 5√3 + F2sin30°) = 0

or, F2sin30° = -12 + 5√3

or, F2 = (-24 + 10√3)N =

and (9 + 5 - F1 + F2cos30°) = 0

or, 14 - F1 + (-24 + 10√3) × √3/2 = 0

or, 14 - F1 + (-12√3 + 15) = 0

or, 14 - 12√3 + 15 = F1

or, F1 = (29 - 12√3) N