two forces of magnitudes 10N and 30N act upon a body in direction making angles of 30° and 40° with x-axis respectively. find the resultant force
Answers
Answer:
The resultant force is 29 N.
Answer:
The resultant of two forces are determined by the parallelogram rule as follows:
As the forces acting at different angle, so the resultant force will have magnitude related to the difference in the angle in which the incident forces were acted.
\text { Resultant }=\sqrt{F_{1}^{2}+F_{2}^{2}+2 F_{1} F_{2} \cos (\theta_{2}-\theta_{1})} Resultant =
F
1
2
+F
2
2
+2F
1
F
2
cos(θ
2
−θ
1
)
Here F1 and F2 are the two forces acting and their respective angles are given as and
So the resultant force will be
\text { Resultant force }=\sqrt{(10)^{2}+(20)^{2}+2 *(10 * 20) \cos (60-30)} Resultant force =
(10)
2
+(20)
2
+2∗(10∗20)cos(60−30)
\text { Resultant force }=\sqrt{100+400+400 \cos (30)} Resultant force =
100+400+400cos(30)
\text { Resultant force }=\sqrt{500+(400 * \frac{\sqrt{3}}{2})} Resultant force =
500+(400∗
2
3
)
\text { Resultant force }=\sqrt{500+(200 * 1.732)} Resultant force =
500+(200∗1.732)
\text { Resultant force }=\sqrt{846.4} Resultant force =
846.4
Thus, the resultant force is 29 N.