The following three forces act on a particle: 30N at 30° with the x- axis, 50 N at 135° with the x-axis, and 20N along the negative x-axis. Find the fourth force on the particle which will keep it in equilibrium. Draw it's free-body diagram.
58.30N
To find the fourth force that will keep the particle in equilibrium, we need to add the three forces together and find the resultant force.
Step 1: Resolve the forces into their horizontal and vertical components.
Let's consider the x-axis as the horizontal direction and the y-axis as the vertical direction.
Force 1 (30N at 30° with the x-axis):
Horizontal component = 30N * cos(30°)
Vertical component = 30N * sin(30°)
Force 2 (50N at 135° with the x-axis):
Horizontal component = 50N * cos(135°)
Vertical component = 50N * sin(135°)
Force 3 (20N along the negative x-axis):
Horizontal component = -20N
Vertical component = 0N
Step 2: Add the horizontal and vertical components separately.
Horizontal component:
Sum of horizontal components = (30N * cos(30°)) + (50N * cos(135°)) - 20N
Vertical component:
Sum of vertical components = (30N * sin(30°)) + (50N * sin(135°)) + 0N
Step 3: Calculate the magnitude of the resultant force using the Pythagorean theorem.
Magnitude of the resultant force = sqrt((Sum of horizontal components)^2 + (Sum of vertical components)^2)
Step 4: Find the angle of the resultant force with the x-axis.
Angle of the resultant force = tan^(-1)((Sum of vertical components) / (Sum of horizontal components))
Step 5: Draw the free-body diagram.
The free-body diagram should include an arrow representing the resultant force, showing its direction and label its magnitude.
Note: The fourth force that will keep the particle in equilibrium will have the same magnitude as the resultant force but in the opposite direction.
By following these steps, you can find the magnitude and direction of the fourth force that will keep the particle in equilibrium and draw its free-body diagram.