Find the resultant nd direction of two forcrs 10N and 20N inclined at an angle 60 degree to each othet
Please I don't understand
To find the resultant force and direction of two forces, we can use vector addition. Let's name the two forces as force A (10N) and force B (20N).
Step 1: Resolve the forces into their horizontal and vertical components.
Force A:
- The horizontal component of force A is given by Acosθ, where θ is the angle between force A and the horizontal axis.
- The vertical component of force A is given by Asinθ.
Using trigonometry, we can calculate these components:
Horizontal component of force A = 10N * cos(60°) = 5N
Vertical component of force A = 10N * sin(60°) = 8.66N (approximately)
Force B:
- The horizontal component of force B is given by Bcosθ, where θ is the angle between force B and the horizontal axis.
- The vertical component of force B is given by Bsinθ.
Using trigonometry again, we can calculate these components:
Horizontal component of force B = 20N * cos(60°) = 10N
Vertical component of force B = 20N * sin(60°) = 17.32N (approximately)
Step 2: Add the horizontal and vertical components separately to find the resultant.
Horizontal component of the resultant force = 5N + 10N = 15N
Vertical component of the resultant force = 8.66N + 17.32N = 25.98N (approximately)
Step 3: Use Pythagorean theorem to find the magnitude of the resultant force.
Magnitude of the resultant force = √((15N)^2 + (25.98N)^2)
Magnitude of the resultant force = √(225 + 675.0404)
Magnitude of the resultant force ≈ √900.0404
Magnitude of the resultant force ≈ 30N
Step 4: Use inverse tangent to find the direction of the resultant force.
Direction of the resultant force = tan^(-1)((Vertical component of the resultant force) / (Horizontal component of the resultant force))
Direction of the resultant force = tan^(-1)(25.98N / 15N)
Direction of the resultant force ≈ 58.4° (approximately)
Therefore, the resultant force of the two forces (10N and 20N at 60°) is approximately 30N, and the direction is approximately 58.4°.
To find the resultant for two forces, we can use the concept of vector addition. Here's how you can find the resultant force and its direction:
1. Draw a diagram: Start by drawing a diagram representing the forces. Label one force as 10N and the other as 20N. In this case, the forces are inclined at an angle of 60 degrees to each other.
2. Decompose the forces: Now, you need to resolve each force into its horizontal and vertical components. To do this, use trigonometry. For the 10N force, the horizontal component is 10N * cos(60°), and the vertical component is 10N * sin(60°). Similarly, for the 20N force, the horizontal component is 20N * cos(60°), and the vertical component is 20N * sin(60°).
3. Add the horizontal and vertical components separately: Add the horizontal components of both forces together. Then, add the vertical components of both forces together.
4. Find the resultant magnitude: Use the Pythagorean theorem to find the magnitude of the resultant force. The resultant force magnitude (R) can be calculated as R = sqrt((Sum of horizontal components)^2 + (Sum of vertical components)^2).
5. Find the resultant direction: The direction of the resultant force can be found using the tangent function. The angle (θ) can be calculated as θ = atan((Sum of vertical components) / (Sum of horizontal components)).
6. Substitute the values: Plug in the values obtained in steps 3, 4, and 5 into the respective formulas to find the resultant force magnitude and its direction.
By following the above steps, you can find the resultant force magnitude and direction for the given forces.
F = 10N.[0°] + 20[60°] = 10 + 20*Cos60 +
i20*sin60 = 10 + 10 + 17.3i = 20 + 17.3i
= 26.5N.[40.9°].