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Homework Statement
Calculate the net force acting on each object indicated in the following diagrams.
(diagrams attached)
Homework Equations
Sine Law: sin a/a = sin b/b = sin c/ c
Cosine Law: c^2 = a^2 + b^2 -2ab*cos(c)
SOHCAHTOA
The Attempt at a Solution
a) c2 = a2 + b2 – 2ab cos(c)
c2 = 222 + 382 – 2(22)(38) cos(55)
c2 = 968.980
c = 31.1 N
sinA/a= sinB/b= sinC/c
sin A/22 N= sin(55)/31.1 N
Sin A= 22 N sin(55)/31.1 N
A = 35.4 º
F net = 31.1 N [W35.4ºN]
b) I'm not sure how to do this one but I tried the following...
sin45=x/75
x = 12.02 N
8 Newtons + 10 Newtons = 18 Newtons
c=√a^2+b^2
=(18)^2+(12.02)^2
=√324+144
=√468
c=21.63N
And given this I can use the sin law to find cos (a)? I'm really unsure how to approach this one.
c)
32 degrees + 24 degrees = 56 degrees
c^2=a^2+b^2-2abCosC
=(15)^2 + (12)^2 -2(15)(12)Cos56
=√369-201.3
=12.94 N
Sin A / a = sin B/b = sin c/c
Sin (b) / 12 = sin (56) / 12.94
sin B = 0.7688
B = 50.2 degrees?
F net = 12.94 N [E 50.2 degrees N]
This is a concept I am not too confident with and I would greatly appreciate it if someone can look over my attempts and point out where I'm going wrong and steer me in the right direction. Thanks