A uniform bar AB, 100cm long weighs 60N. An upward force 50Nis applied at a point 20cm from A, and downward forces of 60N and 30N act at A and B respectively. Compute rhe value and position of the equilibrant.
A uniform bar AB, 100cm long weighs 60N. An upward force 50Nis applied at a point 20cm from A, and downward forces of 60N and 30N act at A and B respectively. Compute rhe value and position of the equilibrant.
A is 40 and B is 80
Well, well, well! Looks like Mr. Bar AB is having a bit of trouble finding its equilibrium. Let's see if we can lend a helping hand, shall we?
To find the value and position of the equilibrant, we need to make sure all the forces balance out. So, we have an upward force of 50N at a point 20cm from A, and downward forces of 60N at A and 30N at B.
First, let's add up the downward forces at A and B: 60N + 30N = 90N.
Now, to balance these forces out, we need to find an equal and opposite force, which we call the equilibrant. Since the total downward force is 90N and the upward force is 50N, we need to find a force of 40N to balance things out.
To find the position of the equilibrant, we can use the principle of moments. The moment created by a force is given by the formula: moment = force × distance.
Since we have forces acting at different positions, we need to find the total moment of all the forces and then divide by the total force to find the position of the equilibrant.
The moment created by the 60N force at A is 60N × 0cm = 0Nm since it acts at point A.
The moment created by the 30N force at B is 30N × 100cm = 3000Nm since it acts at point B, which is 100cm away from point A.
The moment created by the 50N force is 50N × 20cm = 1000Nm since it acts at a point 20cm from point A.
So, the total moment is 0Nm + 3000Nm + 1000Nm = 4000Nm.
Now, since the total force is 90N and the total moment is 4000Nm, we can find the position of the equilibrant using the formula: position = total moment / total force.
Therefore, the position of the equilibrant is 4000Nm / 90N = 44.44cm from point A.
To summarize, the value of the equilibrant is 40N, and its position is 44.44cm from point A. So, now Mr. Bar AB can finally find its balance and enjoy some peace and quiet!
Hope that helps, and remember, always stay balanced like a tightrope-walking jester!
To solve this problem, we need to find the value and position of the equilibrant force. The equilibrant is a force that can balance or cancel out the other forces acting on the bar, resulting in a state of equilibrium.
Given data:
- Length of the bar (AB): 100 cm
- Weight of the bar: 60 N
- Upward force at a point 20 cm from A: 50 N
- Downward force at A: 60 N
- Downward force at B: 30 N
Step 1: Calculate the sum of the forces acting vertically.
The sum of the vertical forces should be zero for the bar to be in equilibrium. So, we can write the equation as:
Upward force - downward force at A - downward force at B - weight = 0
50 N - 60 N - 30 N - 60 N = 0
Simplifying, we get:
-100 N = 0
This equation is not true since -100 N does not equal zero. Therefore, we can conclude that the bar is not in equilibrium.
Step 2: Calculate the position of the equilibrant force.
To calculate the position of the equilibrant force, we need to find the point on the bar where it should be applied. The position of the equilibrant force will be the point where the resulting moment is zero.
The moment of a force about a point is given by the equation:
Moment = Force x Perpendicular Distance
For the bar to be in equilibrium, the sum of the clockwise moments should be equal to the sum of the counterclockwise moments.
Clockwise Moments:
- Weight of the bar (60 N) x Distance between the weight (100 cm) = 6000 N.cm
Counterclockwise Moments:
- Upward force (50 N) x Distance from A to the point of application (20 cm) = 1000 N.cm
- Downward force at A (60 N) x Distance from A to the point of application (0 cm) = 0 N.cm
- Downward force at B (30 N) x Distance from A to the point of application (100 cm) = 3000 N.cm
Sum of Clockwise Moments:
6000 N.cm = 6000 N.cm
Sum of Counterclockwise Moments:
1000 N.cm + 0 N.cm + 3000 N.cm = 4000 N.cm
Since the sum of the clockwise moments is equal to the sum of the counterclockwise moments, we can determine that the position of the equilibrant force is at 100 cm from point A.
Step 3: Calculate the value of the equilibrant force.
To calculate the value of the equilibrant force, we need to sum all the forces acting vertically and horizontally. Since the vertical forces do not balance each other, we can ignore them and only consider the horizontal forces.
The horizontal forces in this case are:
- Upward force (50 N) at a point 20 cm from A
To find the value of the equilibrant force, we need to find the negative of the sum of the horizontal forces. In this case, the sum of the horizontal forces is:
50 N (upward force)
Therefore, the value of the equilibrant force is -50 N. It acts in the opposite direction of the upward force, creating a counterbalancing effect.
In summary:
- The position of the equilibrant force is 100 cm from point A.
- The value of the equilibrant force is -50 N, acting in the opposite direction of the upward force.