a meter stick of wight 0.8 n is pivoted at 40 cm mark at which mark 1n load should be located to balence the sticke
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Since the stick by itself is unbalanced with the fulcrum off center, the weight must be placed on the short (40 cm) side. Let x be the distance of the 1 N weight from the fulcrum, measured toward the short end, in cm. The stick's weight acts at the center of mass at x = -10 cm
0.8*(-10) + 1*x = 0 at equilbrium
x = 8 cm
0.8*40-1x=0
x=32cm
To balance the meter stick, you need to determine the position where a 1 N load should be placed. Let's break down the process step by step:
1. Understand the situation: You have a meter stick, which is a long straight rod, weighing 0.8 N. It is pivoted at the 40 cm mark, which means that it can rotate around that point.
2. Set up the equilibrium condition: In order to balance the meter stick, the clockwise and counterclockwise moments acting on it must be equal. A moment is the turning effect produced by a force about a pivot point. So, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments.
3. Calculate clockwise moments: The weight of the meter stick (0.8 N) acts vertically downwards from its center of mass. The distance between the pivot point (40 cm mark) and the center of mass of the meter stick can be assumed to be located at the center (50 cm mark). Therefore, the clockwise moment caused by the weight is given by: Moment = Weight x Distance = 0.8 N x 10 cm = 8 N.cm
4. Determine the counterclockwise moment: The counterclockwise moment is produced by the 1 N load. Let's denote the distance from the pivot point to the position where the 1 N load should be placed as 'x'. The counterclockwise moment caused by the 1 N load is given by: Moment = Load x Distance = 1 N x x cm
5. Set up the equilibrium equation: As mentioned earlier, the sum of the clockwise moments equals the sum of the counterclockwise moments. So, we can equate the clockwise moment (8 N.cm) to the counterclockwise moment (1 N x cm), and solve for 'x': 8 N.cm = 1 N x cm.
6. Solve for 'x': Multiply both sides of the equation by 1 cm to isolate 'x'. This results in: 8 N.cm = x
7. Finalize the answer: From the equation in step 6, we can deduce that 'x' should be equal to 8 cm. Therefore, a 1 N load should be placed at the 48 cm mark on the meter stick to balance it when the pivot point is at the 40 cm mark.
By following this step-by-step process, you can find the solution to the problem.