Two forces 3kg & 5kg weight act at point making an angle 60° with each other find the magnitude & direction of the resultant

3 kg weighs 3*9.8 = 29.4 Newtons

5 kg weighs 5*9.8 = 49 Newtons

say the 49 N force is in the x axis direction
tthe 29.4 N force is 60 degrees toward the Y axis

Sum of x forces= 49+29.4cos 60 = 63.7 N
Sum of y forces = 29.4 sin 60 = 25.5 N

magnitude = sqrt(25.5^2 + 63.7^2)
= 68.6 N or weight of mass of 7 kg on earth

direction = tan^-1(25.5/63.7) = 21.8 degrees

To find the magnitude and direction of the resultant force, we can use the concept of vector addition.

Step 1: Resolve the forces into their x and y components.
The force of 3 kg weight can be split into x and y components as follows:
Fx1 = F1 * cos(60°) = 3 kg * cos(60°) = 1.5 kg
Fy1 = F1 * sin(60°) = 3 kg * sin(60°) = 2.598 kg

The force of 5 kg weight can be split into x and y components as follows:
Fx2 = F2 * cos(60°) = 5 kg * cos(60°) = 2.5 kg
Fy2 = F2 * sin(60°) = 5 kg * sin(60°) = 4.33 kg

Step 2: Add the x and y components separately.
Rx = Fx1 + Fx2 = 1.5 kg + 2.5 kg = 4 kg
Ry = Fy1 + Fy2 = 2.598 kg + 4.33 kg = 6.928 kg

Step 3: Use the Pythagorean theorem to find the magnitude of the resultant force.
R = sqrt(Rx^2 + Ry^2) = sqrt((4 kg)^2 + (6.928 kg)^2) = sqrt(16 kg^2 + 48 kg^2) = sqrt(64 kg^2) = 8 kg

Step 4: Use trigonometry to find the angle of the resultant force.
θ = atan(Ry / Rx) = atan(6.928 kg / 4 kg) = atan(1.732) = 59.99° (approximately 60°)

Therefore, the magnitude of the resultant force is 8 kg and its direction is approximately 60°.

To find the magnitude and direction of the resultant force, we can use the concept of vector addition. We need to break down the given forces into their respective horizontal and vertical components, and then add them up.

Step 1: Resolve the Forces
Resolve each force into its vertical and horizontal components. We can use trigonometry to find the components:
- The horizontal component of a force is given by: F * cos(theta), where F is the magnitude of the force and theta is the angle it makes with the horizontal axis.
- The vertical component of a force is given by: F * sin(theta).

For the 3kg force (F1 = 3kg):
- Horizontal component: F1x = 3kg * cos(60°)
- Vertical component: F1y = 3kg * sin(60°)

For the 5kg force (F2 = 5kg):
- Horizontal component: F2x = 5kg * cos(180° - 60°)
- Vertical component: F2y = 5kg * sin(180° - 60°)

Step 2: Add the Components
Add up the horizontal components and the vertical components:

Horizontal component of the resultant force (Rx):
Rx = F1x + F2x

Vertical component of the resultant force (Ry):
Ry = F1y + F2y

Step 3: Find the Magnitude and Direction
The magnitude of the resultant force (R) can be found using the Pythagorean theorem:
R = sqrt(Rx^2 + Ry^2)

The direction of the resultant force can be found using trigonometry:
angle = arctan(Ry/Rx)

Now, let's calculate the values.

Horizontal component of F1:
F1x = 3kg * cos(60°) = 1.5 kg
Vertical component of F1:
F1y = 3kg * sin(60°) = 2.598 kg

Horizontal component of F2:
F2x = 5kg * cos(180° - 60°) = -2.5 kg
Vertical component of F2:
F2y = 5kg * sin(180° - 60°) = -4.33 kg

Adding the horizontal components:
Rx = F1x + F2x = 1.5 kg + (-2.5 kg) = -1 kg

Adding the vertical components:
Ry = F1y + F2y = 2.598 kg + (-4.33 kg) = -1.732 kg

Calculating the magnitude of the resultant force:
R = sqrt((-1 kg)^2 + (-1.732 kg)^2) = 2 kg

Calculating the direction of the resultant force:
angle = arctan((-1.732 kg) / (-1 kg)) ≈ 120° (rounded to the nearest degree)

Therefore, the magnitude of the resultant force is 2 kg and the direction is approximately 120° with respect to the horizontal axis.