Two vectors 10N and 20N are inclined at 60degrees to each other find the resultant force
To find the resultant force of two vectors inclined at an angle, we can use the vector addition method.
Step 1: Resolve the vectors into their horizontal and vertical components.
- The first vector of 10N can be resolved into its horizontal and vertical components as follows:
- Horizontal component: 10N * cos(60°) = 5N
- Vertical component: 10N * sin(60°) = 8.66N (approximately)
- The second vector of 20N can be resolved into its horizontal and vertical components as follows:
- Horizontal component: 20N * cos(60°) = 10N
- Vertical component: 20N * sin(60°) = 17.32N (approximately)
Step 2: Add the horizontal and vertical components separately.
- Horizontal component: 5N + 10N = 15N
- Vertical component: 8.66N + 17.32N = 25.98N (approximately)
Step 3: Use the horizontal and vertical components to find the magnitude and direction of the resultant force.
- Magnitude of the resultant force can be found using the Pythagorean theorem:
- Resultant force (F) = sqrt[(horizontal component)^2 + (vertical component)^2]
- F = sqrt[(15N)^2 + (25.98N)^2] ≈ 30.27N
- To find the direction of the resultant force, use trigonometry:
- Tan(θ) = vertical component / horizontal component
- θ = Tan^(-1)(25.98N / 15N) ≈ 59.04°
Therefore, the resultant force is approximately 30.27N and is inclined at an angle of approximately 59.04° to the horizontal.
To find the resultant force of two vectors inclined at an angle to each other, you can use vector addition.
You can break down the given vectors into their x and y components using basic trigonometry. Let's assume the 10N vector is vector A and the 20N vector is vector B.
Vector A can be broken down into its x and y components as follows:
Ax = 10N * cos(60°)
Ay = 10N * sin(60°)
Vector B can be broken down into its x and y components as follows:
Bx = 20N * cos(0°) (Since vector B is along the x-axis)
By = 20N * sin(0°) (Since vector B is along the x-axis)
Now, you can add the x components and y components separately to find the resultant components:
Rx = Ax + Bx
Ry = Ay + By
Using these resultant components, you can find the magnitude and direction of the resultant force.
The magnitude of the resultant force can be found using the Pythagorean theorem:
Resultant magnitude (R) = sqrt(Rx^2 + Ry^2)
The direction of the resultant force can be found using trigonometry:
Resultant direction (θ) = tan^(-1)(Ry / Rx)
Plugging in the values, we have:
Rx = 10N * cos(60°) + 20N * cos(0°)
Ry = 10N * sin(60°) + 20N * sin(0°)
Rx = 10N * 0.5 + 20N * 1
Ry = 10N * √3/2 + 20N * 0
Rx = 5N + 20N = 25N
Ry = 10N * √3/2 + 0 = 10N * √3/2 = 5N√3
Therefore:
Resultant magnitude (R) = sqrt((25N)^2 + (5N√3)^2) = sqrt(625N^2 + 75N^2) = sqrt(700N^2) = 10√7 N (approximately 26.457 N)
Resultant direction (θ) = tan^(-1)((5N√3) / 25N) = tan^(-1)(√3/5) ≈ 59.04°
Hence, the resultant force is approximately 26.457 N at an angle of 59.04 degrees to the x-axis.
To find the resultant force, we can use the law of cosines.
Letting the vectors be A = 10N and B = 20N, and the angle between them be 60 degrees, we have:
Resultant force^2 = A^2 + B^2 - 2AB * cos(angle)
Resultant force^2 = (10N)^2 + (20N)^2 - 2(10N)(20N) * cos(60 degrees)
Calculating this expression gives us:
Resultant force^2 = 100N^2 + 400N^2 - 2(10N)(20N) * 0.5
Resultant force^2 = 100N^2 + 400N^2 - 200N^2
Resultant force^2 = 300N^2
Taking the square root of both sides gives us the magnitude of the resultant force:
Resultant force = sqrt(300N^2) = 17.32N
Therefore, the magnitude of the resultant force is approximately 17.32N.