the two forces act an angle 120.the bigger the force is 40 and resultant is perpendicular to the smaller one find the smaller force
30
To find the smaller force, we can use vector addition and trigonometry. Here's how:
1. Start by drawing a diagram to visualize the problem. Draw two vectors to represent the forces acting at an angle of 120 degrees. Let the bigger force be called F1, and the smaller force be called F2.
2. Since the resultant R is perpendicular to the smaller force F2, draw R as a horizontal line at a right angle to F2.
3. Notice that the triangle formed by F1, F2, and R is a right triangle. The angle between F1 and the resultant R is therefore 90 degrees.
4. Use trigonometry to solve for the smaller force F2. Since the angle between F1 and F2 is 120 degrees, we can use the cosine rule:
F1^2 = F2^2 + R^2 - 2 * F2 * R * cos(angle)
Since F1 = 40, R = F2 (due to being perpendicular), and angle = 90 degrees, we can substitute these values into the equation:
40^2 = F2^2 + F2^2 - 2 * F2 * F2 * cos(120)
5. Simplify the equation:
1600 = 2 * F2^2 - 2 * F2^2 * (-0.5)
1600 = 2 * F2^2 + F2^2
1600 = 3 * F2^2
6. Solve for F2:
F2^2 = 1600 / 3
F2 = sqrt(1600 / 3)
F2 ≈ 25.82 (rounded to two decimal places)
Therefore, the smaller force is approximately 25.82.