where must a 1200n weight be hung on a uniform, 200N pole so that a boy at one end supports one-third as much as a man at the other end?
To determine where the 1200N weight must be hung on the uniform 200N pole, and ensure that the boy supports one-third of the weight compared to the man, we need to apply the principle of moments or torque.
Moments or torques can be calculated by multiplying the force applied by the distance from the pivot point. In this case, the pivot point is the point where the pole is being held.
Let's define the following variables:
- F1: Force applied by the boy (to be determined).
- F2: Force applied by the man (to be determined).
- D1: Distance from the pivot point to the boy.
- D2: Distance from the pivot point to the man.
- D3: Distance from the pivot point to where the 1200N weight is hung.
According to the problem, we know the following conditions:
1. F1 + F2 = 200N (since the total force on the pole is 200N).
2. F1 = (1/3) * F2 (since the boy supports one-third of the weight compared to the man).
To find the solution, we need to solve the system of equations formed by the conditions above.
First, substitute F1 in terms of F2 from equation (2) into equation (1):
(1/3) * F2 + F2 = 200N
(4/3) * F2 = 200N
F2 = (3/4) * 200N
F2 = 150N
Now, substitute this value of F2 into equation (2) to find F1:
F1 = (1/3) * 150N
F1 = 50N
From the calculations above, we have determined that the force applied by the boy (F1) is 50N, and the force applied by the man (F2) is 150N.
Finally, to determine the position where the 1200N weight must be hung, we can use the principle of moments. The sum of the clockwise moments (taking clockwise direction as positive) must be equal to the sum of the anticlockwise moments.
Considering the distances D1, D2, and D3, we can set up the following equation based on the principle of moments:
F1 * D1 + F2 * D2 = 1200N * D3
Substituting the known values:
50N * D1 + 150N * D2 = 1200N * D3
To calculate the unknown distances D1, D2, and D3, we need additional information or measurements provided in the problem statement. Without these values, it is not possible to determine the exact positions where the weights should be hung.