Two Forces 10N and 20N are Inclined at angle 60degree to each other. Find the resultant force
53.13
draw one force vector
connect the second to it, tail-to-tip
connect the two ends. That is the resultant.
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To find the resultant force, we can use the concept of vector addition. Since the forces are inclined at an angle to each other, we need to determine both the horizontal and vertical components of each force.
Let's analyze the horizontal components first:
- The horizontal component of the 10N force can be calculated by multiplying the force magnitude by the cosine of the angle between the force and the horizontal axis: 10N * cos(60°) = 10N * 0.5 = 5N.
- The horizontal component of the 20N force can be calculated in the same way: 20N * cos(60°) = 20N * 0.5 = 10N.
Now let's find the vertical components:
- The vertical component of the 10N force can be calculated by multiplying the force magnitude by the sine of the angle: 10N * sin(60°) = 10N * (√3 / 2) ≈ 8.66N.
- The vertical component of the 20N force can be calculated in the same way: 20N * sin(60°) = 20N * (√3 / 2) ≈ 17.32N.
Now that we have the horizontal and vertical components for both forces, we can add them separately to find the resultant force components:
- The horizontal component of the resultant force is obtained by adding the horizontal components of the two forces: 5N + 10N = 15N.
- The vertical component of the resultant force is obtained by adding the vertical components of the two forces: 8.66N + 17.32N ≈ 25.98N.
Finally, we can find the magnitude and direction of the resultant force using the Pythagorean theorem and trigonometry:
- The magnitude of the resultant force can be calculated using the formula: magnitude = √(horizontal component^2 + vertical component^2) = √(15N^2 + 25.98N^2) = √(225N^2 + 675N^2) = √900N^2 ≈ 30N.
- The direction of the resultant force can be found by calculating the arctangent of the vertical component divided by the horizontal component: arctan(25.98N / 15N) ≈ 60°.
Therefore, the resultant force is approximately 30N, inclined at an angle of 60° with the horizontal axis.