Two forces acting on point A, one force 10N and the other 12N in the direction of N, 30°E. What is the magnitude and direction of the resultant force
To find the magnitude and direction of the resultant force, we can use vector addition.
1. Start by drawing a diagram. Draw a line segment to represent the first force, 10N, in the direction of N. Then draw another line segment to represent the second force, 12N, at a 30° angle to the east of north.
2. Convert the 12N force into its x (east) and y (north) components. To do this, we can use trigonometry. The x-component can be found by multiplying the magnitude (12N) by the cosine of the angle (30°). Likewise, the y-component can be found by multiplying the magnitude (12N) by the sine of the angle (30°).
x-component: 12N * cos(30°) = 12N * √3/2 = 6√3 N (east)
y-component: 12N * sin(30°) = 12N * 1/2 = 6N (north)
3. Add the x-components and y-components of the two forces separately.
x-component: 0N (since the first force is in the north direction and has no east component)
y-component: 10N + 6N = 16N (north)
4. Use the Pythagorean theorem to find the magnitude of the resultant force. The magnitude is the square root of the sum of the squares of the x-component and y-component.
magnitude = √(0^2 + 16N^2) = √(0 + 256N^2) = 16N
5. Finally, determine the direction of the resultant force. To do this, use inverse trigonometry to find the angle that the resultant force makes with the north direction.
direction = arctan(y-component / x-component)
= arctan(16N / 0) = undefined (There is no x-component, so the angle is undefined.)
Therefore, the magnitude of the resultant force is 16N, and the direction is undefined.