Respuesta :
Answer:
Angle between the forces [tex]= 82.82[/tex] degrees
Explanation:
The resultant force value [tex]= 1.5[/tex] times of Force F
[tex]|R| = |F1| = |F2| =|F|[/tex]
Where R is the resultant force
[tex]R^2 = A^2 + B^2 + 2AB cos X\\(1.5F)^2 = F^2 + F^2 + 2F^2 cos X\\2.25F^2 = 2F^2 + 2F^2 cos X\\[/tex]
Cos X is the angle between the two forces.
On further simplifying the equation we get
[tex]2.25F^2 = 2F^2(1 + cos X)[/tex]
[tex](1 + cos X) = \frac{2.25F^2}{2F^2} \\(1 + cos X) = \frac{2.25}{2} \\(1 + cos X) = 1.125\\cos X = 1.125 - 1\\Cos X = 0.125\\X = Cos^{-1}0.125\\[/tex]
[tex]X = 82.82[/tex] degrees
Angle between the forces [tex]= 82.82[/tex] degrees
Answer:
The angle between the two forces will be "120°".
Explanation:
Given,
The resultant of force = 1.5F
Now,
By using formula for two resultant of two equal forces, we get
[tex]R^2=A^2+B^2+2ABCos\theta[/tex]
On putting the values, we get
⇒ [tex]1.5^2=1.5^2+1.5^2+2(1.5)(1.5)Cos\theta[/tex]
⇒ [tex]2.25=2.25+2.25+4.5Cos\theta[/tex]
⇒ [tex]2.25=4.5+4.5Cos\theta[/tex]
⇒ [tex]4.5Cos\theta=2.25-4.5[/tex]
⇒ [tex]4.5Cos\theta=-2.25[/tex]
⇒ [tex]Cos\theta=\frac{-2.25}{4.5}[/tex]
⇒ [tex]Cos\theta=-\frac{1}{2}[/tex]
⇒ [tex]\theta=120^{\circ}[/tex]
