The sum of two forces inclined to each other at an angle is 18 kg wt and their resultant which is perpendicular to the smaller force is 12 kg wt Find the forces and the angle between them.
Answers
HEY MATE HOPE U ARE WELL..!
Explanation:
The second law of motion states that the force is a physical quantity which is defined as the rate of change of linear momentum with respect to the time and for a constant mass, it is the product of the mass and the acceleration.
Answer and Explanation:
F
1
+
F
2
=
18
N
(
F
1
+
F
2
)
2
=
324
F
2
1
+
F
2
2
=
324
−
2
F
1
F
2
Also, resultant is given by
R
=
√
F
2
1
+
F
2
2
+
2
F
1
F
2
cos
θ
144
=
324
−
2
F
1
F
2
cos
θ
+
2
F
1
F
2
cos
θ
2
F
1
F
2
(
1
−
cos
θ
)
=
180
Also,
tan
β
=
F
1
sin
θ
F
2
+
F
1
cos
θ
tan
90
∘
=
F
1
sin
θ
F
2
+
F
1
cos
θ
1
0
=
F
1
sin
θ
F
2
+
F
1
cos
θ
F
2
+
F
1
cos
θ
=
0
F
1
=
−
F
2
cos
θ
Substitute the value of
F
1
in equation (i),
F
2
=
√
90
cos
θ
(
cos
θ
−
1
)
Substituting
F
2
in the equation (i),
F
1
=
−
√
90
cos
θ
(
cos
θ
−
1
)