if resultant of two forces when they act at an angle of 30 deg is 50N and when they act at 60 deg the resultant is 70N find magnitude of two forces

Question

if resultant of two forces when they act at an angle of 30 deg is 50N and when they act at 60 deg the resultant is 70N find magnitude of two forces

Answer 1

Four forces acting together 12N at 40°,10N at30°,15N at 60°and9N.find their resultant

Answer 2

To determine the magnitudes of the two forces, we can use the concept of vector addition. The resulting force can be calculated by adding the two forces using vector addition.

Let's assume the magnitudes of the two forces are F1 and F2. When the two forces act at an angle of 30 degrees, the resultant force is 50N. Mathematically, we can represent this as:

F1 + F2 = 50N ---(Equation 1)

When the forces act at an angle of 60 degrees, the resultant force is 70N. Mathematically, this can be expressed as:

F1 + F2 = 70N ---(Equation 2)

Now, we have a system of two equations (Equation 1 and Equation 2) with two unknowns (F1 and F2). We can solve this system of equations to find the magnitudes of the two forces.

To do this, we can use trigonometry and resolve the forces into their horizontal (x) and vertical (y) components.

Let's consider the forces F1 and F2 acting at an angle of 30 degrees. We can resolve these forces into their x and y components using trigonometry:

For Force F1:
Fx1 = F1 * cos(30) = F1 * √3/2
Fy1 = F1 * sin(30) = F1 * 1/2

For Force F2:
Fx2 = F2 * cos(30) = F2 * √3/2
Fy2 = F2 * sin(30) = F2 * 1/2

Using these components, we can rewrite Equation 1 and Equation 2:

(Fx1 + Fx2) + j(Fy1 + Fy2) = 50N ---(Equation 3)
(Fx1 + Fx2) + j(Fy1 + Fy2) = 70N ---(Equation 4)

where j represents the imaginary unit, which is included to indicate the vector addition operation.

Now, substitute the components:

(F1 * √3/2 + F2 * √3/2) + j(F1/2 + F2/2) = 50N ---(Equation 3)
(F1 * √3/2 + F2 * √3/2) + j(F1/2 + F2/2) = 70N ---(Equation 4)

Equating the real (x-component) and imaginary (y-component) parts of the equations separately:

Real parts:
F1 * √3/2 + F2 * √3/2 = 50 ---(Equation 5)
F1 * √3/2 + F2 * √3/2 = 70 ---(Equation 6)

Imaginary parts:
F1/2 + F2/2 = 50 ---(Equation 7)
F1/2 + F2/2 = 70 ---(Equation 8)

Now we have a new system of equations (Equation 5, Equation 6, Equation 7, and Equation 8) with two unknowns (F1 and F2).

Solving this system of equations will give us the values of F1 and F2, which represent the magnitudes of the two forces.

if resultant of two forces when they act at an angle of 30 deg is 50N and when they act at 60 deg the resultant is 70N find magnitude of two forces

876

Four forces acting together 12N at 40°,10N at30°,15N at 60°and9N.find their resultant

To determine the magnitudes of the two forces, we can use the concept of vector addition. The resulting force can be calculated by adding the two forces using vector addition.