Question
Two force 10N and 20N are inclined at angle 60degree to each other. Find the magnitude and direction of the resultant
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We can use vector addition to find the magnitude and direction of the resultant force:
- Draw a diagram representing the two forces as vectors. Label one force as F1 = 10N and the other as F2 = 20N. The angle between them is 60 degrees.
- Use trigonometry to find the components of each force in the x and y directions. For F1, the x-component is 10cos(60) = 5N and the y-component is 10sin(60) = 8.66N. For F2, the x-component is 20cos(120) = -10N and the y-component is 20sin(120) = 17.32N (note the negative sign for the x-component due to the angle being greater than 90 degrees).
- Add the x-components and y-components separately to find the components of the resultant force. Rx = 5N - 10N = -5N and Ry = 8.66N + 17.32N = 25.98N.
- Use the Pythagorean theorem to find the magnitude of the resultant force: R = sqrt((-5)^2 + (25.98)^2) = 26.87N.
- Use trigonometry again to find the angle that the resultant force makes with the x-axis. tan(theta) = Ry/Rx = -25.98/5, so theta = -80.54 degrees (note the negative sign due to the resultant vector being in the third quadrant). Therefore, the direction of the resultant force is 80.54 degrees below the negative x-axis.
- Draw a diagram representing the two forces as vectors. Label one force as F1 = 10N and the other as F2 = 20N. The angle between them is 60 degrees.
- Use trigonometry to find the components of each force in the x and y directions. For F1, the x-component is 10cos(60) = 5N and the y-component is 10sin(60) = 8.66N. For F2, the x-component is 20cos(120) = -10N and the y-component is 20sin(120) = 17.32N (note the negative sign for the x-component due to the angle being greater than 90 degrees).
- Add the x-components and y-components separately to find the components of the resultant force. Rx = 5N - 10N = -5N and Ry = 8.66N + 17.32N = 25.98N.
- Use the Pythagorean theorem to find the magnitude of the resultant force: R = sqrt((-5)^2 + (25.98)^2) = 26.87N.
- Use trigonometry again to find the angle that the resultant force makes with the x-axis. tan(theta) = Ry/Rx = -25.98/5, so theta = -80.54 degrees (note the negative sign due to the resultant vector being in the third quadrant). Therefore, the direction of the resultant force is 80.54 degrees below the negative x-axis.