12.
If the four forces as shown are in equilibrium, Express F1 and F2 in unit vector form.
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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
now, at equilibrium,
Fnet = 0
or, (-12i + 9j) + (5√3i + 5j) + () + = 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
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