Three forces of 4N, 4N and 5N are acting at an angle of 0°, 30° and 150°. Find the resultant force.
Answers
The resultant force is
1.41 N
at
315
∘
.
Explanation:
The net force
(
F
net
)
is the resultant force
(
F
R
)
. Each force can be resolved into an
x
-component and a
y
-component.
Find the
x
-component of each force by multiplying the force by the cosine of the angle. Add them to get the resultant
x
-component.
Σ
(
F
x
)
=
(
3 N
⋅
cos
0
∘
)
+
(
4 N
⋅
cos
90
∘
)
+
(
5 N
⋅
cos
217
∘
)
=
−
1
N
Find the
y
-component of each force by multiplying each force by the sine of the angle. Add them to get the resultant
x
-component.
Σ
(
F
y
)
=
(
3 N
⋅
sin
0
∘
)
+
(
4 N
⋅
sin
90
∘
)
+
(
5 N
⋅
sin
217
∘
)
=
+
1
N
Use the Pythagorean to get the magnitude of the resultant force.
Σ
(
F
R
)
=
√
(
F
x
)
2
+
(
F
y
)
2
Σ
(
F
R
)
=
√
(
−
1
N
)
2
+
(
1
N
)
2
Σ
(
F
R
)
=
√
1 N
2
+
1 N
2
Σ
(
F
R
)
=
√
2 N
2
Σ
(
F
R
)
=
1.41 N
To find the direction of the resultant force, use the tangent:
tan
θ
=
F
y
F
x
=
1 N
−
1 N
tan
−
1
(
1
−
1
)
=
−
45
∘
Subtract
45
∘
from
360
∘
to get
315
∘
.
The resultant force is
1.41 N
at
315