Question

find the angle between two forces of magnitude 27N and 30N if the magnitude of the resultant of the two force is 8N​

Answer 1

To find the angle between two forces of magnitudes 27N and 30N with a resultant of 8N, the Law of Cosines is used, where the inverse cosine of the calculated value from the equation gives the angle.

Step-by-step explanation:

To find the angle between two forces of magnitude 27N and 30N with a resultant force magnitude of 8N, we can use the Law of Cosines, which in this context relates the magnitudes of the two forces and the resultant force with the angle between the forces. The Law of Cosines states:

c² = a² + b² - 2ab×cos(θ)

Where c is the magnitude of the resultant force, and a and b are the magnitudes of the individual forces while θ is the angle between them. In our case:

8² = 27² + 30² - 2×27×30×cos(θ)

Next, we solve for cos(θ) and then use a calculator to find θ. Remember to take the inverse cosine to find the angle. This method enables us to determine the angle without knowing the actual direction of each force, just their magnitudes and the magnitude of the resultant.

Answer 2

`\theta=165^(\circ)`

Step-by-step explanation:

`F_1=27\ N`

`F_2=30\ N`

Resultant of two forces, F = 8 N

It is required to find the angle between two forces. The resultant of two force is given by the :

`F=√(F_1^2+F_2^2+2F_1F_2\cos\theta)`

`\theta` is the angle between F₁ and F₂

So,

`F^2=F_1^2+F_2^2+2F_1F_2\cos\theta\\\\\cos\theta=(F^2-F_1^2-F_2^2)/(2F_1F_2)\\\\\cos\theta=((8)^2-(27)^2-(30)^2)/(2* 27* 30)\\\\\cos\theta=-0.966\\\\\theta=\cos^(-1)\left(-0.966\right)=165^(\circ)`

So, the angle between two forces is 165 degrees.