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 magnitude 27N and 30N, use vector addition and the Pythagorean theorem to find the magnitude of the net force. Then, use the cosine rule to calculate the angle between the forces. The angle is approximately 25.3 degrees.

Step-by-step explanation:

To find the angle between two forces of magnitude 27N and 30N, we need to use the concept of vector addition. The magnitude of the resultant of the two force is 8N. We can use the Pythagorean theorem to find the magnitude of the net force: Fnet = √((27N)2 + (30N)2) = 39N

To find the angle between the two forces, we can use the cosine rule: cos(θ) = ((27N)2 + (39N)2 - (30N)2) / (2 × 27N × 39N)
Using a calculator, we can find that the angle between the two forces is approximately 25.3 degrees.

Answer 2

The angle between two forces is 165 degrees.

Step-by-step explanation:

We have,

Force 1,
`F_1=27\ N`

Force 2,
`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 formula as follows :

`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.