A uniform of 100N pipe is use as a lever. When must the fulcrum (supported point) be placed if a 500N weight at one end to balance a 200N weight at the other end? How much load must support (S) hold?
To determine where the fulcrum (supported point) should be placed, we can use the principle of moments. The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments about any point must equal the sum of the anticlockwise moments about the same point.
Let's break down the problem:
1. The uniform pipe has a weight of 100N. We can consider this weight to act at the center of the pipe, which means its moment is zero.
2. On one end of the pipe, there is a 500N weight, and on the other end, there is a 200N weight. Let's denote the distance from the fulcrum to the 500N weight as x and the distance from the fulcrum to the 200N weight as y.
Now, let's calculate the moments about the fulcrum:
Clockwise moments:
500N * x
Anticlockwise moments:
200N * y
Since the system is in equilibrium (balanced), the sum of the clockwise moments must equal the sum of the anticlockwise moments:
500N * x = 200N * y
Now, we need to solve this equation to find the values of x and y. Since the uniform pipe has a weight of 100N and its moment is zero, it doesn't affect the equation.
Dividing both sides of the equation by 100N, we get:
5x = 2y
Now, we can choose any suitable values for x and y that satisfy this equation. For simplicity, let's choose x = 2 and y = 5. Substituting these values into the equation:
5 * 2 = 2 * 5
10 = 10
The equation is satisfied, which means x = 2 and y = 5 is a valid solution.
Therefore, the fulcrum should be placed at a distance of 2 units from the 500N weight and 5 units from the 200N weight for the lever to be balanced.
Now, let's calculate the load that the fulcrum must support (denoted as S):
Since the sum of the clockwise moments is equal to the sum of the anticlockwise moments, we can write:
(500N * x) = (200N * y) + S
Substituting the values of x and y we found earlier (x = 2, y = 5):
(500N * 2) = (200N * 5) + S
1000N = 1000N + S
To find the load S, we subtract 1000N from both sides of the equation:
1000N - 1000N = S
0 = S
Therefore, the load that the fulcrum must support (S) is 0N.