body is at equilibrium under the action of three forces.one force is 10N acting due east and one is 5N in the direction 60¡ã northeast . what is the magnitude and direction of the third force
F1+F2 = 10 + 5[60].
F1+F2 = 10+5*Cos60 + i5*sin60,
F1+F2 = 12.5 + 4.33i. = 13.2N[19.1o]N. of E.
F3 is equal in magnitude to F1+F2 but 180o out of phase(opposite).
F3 = 13.2N[19.1+180] = 13.2N[199.1]CCW = 13.2N[19.1o] S. of W.
F1+F2+F3=0 (equilibrium)
10E+5cos60N+5Sin60E+F3=0
solve for F3
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To find the magnitude and direction of the third force, we need to use vector addition.
Step 1: Draw a diagram:
- Draw a circle to represent the body at equilibrium.
- Draw the first force of 10N due east as an arrow starting from the center of the circle.
- Draw the second force of 5N at an angle of 60 degrees northeast from the first force.
Step 2: Resolve the second force into its vertical and horizontal components:
- Draw a line parallel to the second force from the tip of the first force to represent the horizontal component.
- Draw a line perpendicular to the second force from the tip of the horizontal component to represent the vertical component.
Step 3: Add the horizontal components of the forces:
- The horizontal component of the first force is 10N since it acts due east.
- The horizontal component of the second force can be found using the cosine function:
Horizontal component = 5N * cos(60 degrees).
Step 4: Add the vertical components of the forces:
- The vertical component of the second force can be found using the sine function:
Vertical component = 5N * sin(60 degrees).
Step 5: Sum up the horizontal and vertical components separately:
- Sum up the horizontal components of the forces: 10N + (5N * cos(60 degrees)).
- Sum up the vertical components of the forces: (5N * sin(60 degrees)).
Step 6: Use the Pythagorean theorem to find the magnitude of the third force:
- Magnitude of the third force = √((Sum of horizontal components)^2 + (Sum of vertical components)^2).
Step 7: Use trigonometry to find the direction of the third force:
- Direction of the third force = arctan(Vertical component / Horizontal component).
By following these steps, you should now be able to find the magnitude and direction of the third force acting on the body at equilibrium.