fisica1-youn-e-freedman-exercicios-resolvidos

1.65: Let D r be the fourth force.
r r r r
A + B + C + D = 0,so
A
B
C
x
x
x
Then
D
= + Acos30.0
= −B
sin 30.0
= + C cos53.0
D
x
2 2
= D x
+ Dy
o
o
o
r
D = −
= + 86.6 N,
= −40.00 N, B
= −24.07 N,
r r r
( A + B + C )
A
y
y
C
= + Acos30.0
= + B cos30.0
−22.53
N, D = −87.34
N
=
y
= 90.2 N;
y
= −C
sin 53.0
o
o
= + 50.00 N
= + 69.28 N
o
= −31.90 N
tan α D y
/ D = 87.34/ 22.53
=
x
o
α = 75.54
o
o
φ = 180 + α = 256 , counterclockwise from + x - axis
1.66:
R
R
y
x
= A
= A
y
R =
x
+ B
+ B
R
y
2
x
x
= (170 km) sin 68
= (170 km) cos 68
+ R
2
y
=
tanθ
R
+ (230 km) cos 48
− (230 km) sin 48
2
( 311.5 km) + ( −107.2 km)
=
R
R
y
x
=
o
o
107.2 km
311.5 km
= 0.344
2
o
o
= 311.5 km
= −107.2 km
= 330 km
θ
R
= 19 o south of east