two forces 20N each are inclined at 100 degree to each other.find the single force that will; replace the given force system balance the given force system
α =(360⁰ - 2•100⁰)/2=80⁰
F12=sqrt{F1²+F2²-2•F1•F2•cosα}=
=sqrt{400+400-2•20•20•cos80⁰}=25.71 N
Direction:
F1 is directed along the positive X-axis ,and F2 is 100⁰ measured from
the positive X- axis with the counter-clockwise, F is 230⁰measured from
the positive X- axis with the counter-clockwise
Well, when two forces are inclined to each other, we can use the parallelogram law to find the resultant force.
To replace the given force system, we need to find the resultant force. Using the parallelogram law, we can create a parallelogram with the two forces as adjacent sides. The diagonal of the parallelogram represents the resultant force.
To balance the given force system, we need to find the third force that will cancel out the effect of the two forces. This force should have the same magnitude as the resultant force, but in the opposite direction.
But let's be honest, with these numbers and angles, it's like trying to find a needle in a haystack or a clown in a serious business meeting. It's not gonna be easy!
To find the single force that will replace the given force system, we can use the concept of vector addition.
Step 1: Draw a diagram to represent the two forces.
Let's represent the first force as F1 and the second force as F2.
Step 2: Resolve the forces into their horizontal and vertical components.
F1 can be resolved into its horizontal component F1x and vertical component F1y. Similarly, F2 can be resolved into its horizontal component F2x and vertical component F2y.
Step 3: Calculate the horizontal and vertical components.
Since we are given the forces and the angle between them, we can use trigonometric formulas to calculate the horizontal and vertical components.
F1x = F1 * cos(theta1)
F1y = F1 * sin(theta1)
F2x = F2 * cos(theta2)
F2y = F2 * sin(theta2)
Where theta1 and theta2 are the angles made by forces F1 and F2 with the horizontal axis.
Step 4: Add the horizontal and vertical components separately.
Add the horizontal components and vertical components of the forces to get the resultant horizontal force (Rx) and resultant vertical force (Ry).
Rx = F1x + F2x
Ry = F1y + F2y
Step 5: Calculate the magnitude and direction of the resultant force.
Using the Pythagorean theorem, we can calculate the magnitude (R) of the resultant force:
R = sqrt(Rx^2 + Ry^2)
The direction of the resultant force (thetaR) can be calculated using the inverse tangent function:
thetaR = arctan(Ry / Rx)
To balance the given force system, we need to have a single force with the same magnitude as the resultant force but in the opposite direction. Therefore, the single force that balances the given force system would have a magnitude of R and a direction opposite to thetaR.
To find the single force that will replace the given force system, we can resolve the forces into their horizontal and vertical components.
1. Replace the given force system:
To replace the given force system, we need to find the resultant force. Since the two forces are inclined at an angle of 100 degrees to each other, we can use the parallelogram law of vector addition.
Step 1: Resolve the forces into their horizontal and vertical components.
The horizontal component of each force can be found using trigonometry:
Horizontal component = force x cos(angle)
Force 1 horizontal component = 20 N x cos(100°)
Force 2 horizontal component = 20 N x cos(100°)
The vertical component of each force can also be found using trigonometry:
Vertical component = force x sin(angle)
Force 1 vertical component = 20 N x sin(100°)
Force 2 vertical component = 20 N x sin(100°)
Step 2: Add the horizontal and vertical components separately to find the resultant force:
Resultant horizontal component = Force 1 horizontal component + Force 2 horizontal component
Resultant vertical component = Force 1 vertical component + Force 2 vertical component
Step 3: Use the Pythagorean theorem to find the magnitude of the resultant force:
Resultant force = sqrt((Resultant horizontal component)^2 + (Resultant vertical component)^2)
Calculate the values to get the resultant force.
2. Balance the given force system:
To balance the given force system, we need to find the equilibrant force, which is equal in magnitude but opposite in direction to the resultant force. In this case, the equilibrant force will cancel out the effects of the given forces.
Follow the steps mentioned above to find the resultant force. The magnitude of the equilibrant force is the same as the magnitude of the resultant force, but the direction is opposite.
Keep in mind that if the forces are acting on an object in equilibrium, the net force on the object should be zero. Hence, the resultant and equilibrant forces will have the same magnitude but opposite directions to achieve a balanced force system.