In order to weight a boy in the laboratory a uniform plank of wood A B 3.0m long, having a mass of 8.0kg is pivoted about a point 0.5m from A .the boy stands 0.3m from A and mass is placed 0.5m from B in order to balanced the plank horizontal. Calculate the mass of the boy.
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To calculate the mass of the boy, we need to use the principle of moments. The principle of moments states that the sum of the clockwise moments about a point is equal to the sum of the anticlockwise moments. In this case, the pivot point is 0.5m from point A.
1. First, let's calculate the moment produced by the plank. The mass of the plank is given as 8.0kg and its length is 3.0m. The distance of the pivot point from the center of mass of the plank is 0.5m. So the moment produced by the plank is:
Moment of the plank = mass of the plank * gravitational acceleration * distance of pivot point from center of mass
= 8.0kg * 9.8 m/s² * 0.5m
2. Next, let's calculate the moment produced by the boy. The boy stands 0.3m from point A. We don't have the mass of the boy, so we'll represent it as M. The distance of the pivot point from the boy is 0.5m. So the moment produced by the boy is:
Moment of the boy = mass of the boy * gravitational acceleration * distance of pivot point from the boy
= M * 9.8 m/s² * (0.5m + 0.3m)
3. The mass is placed 0.5m from point B to balance the plank. Therefore, the moment produced by this mass is equal to the moment produced by the plank. So:
Moment of the mass = mass of the mass * gravitational acceleration * distance of pivot point from the mass
= mass of the mass * 9.8 m/s² * 0.5m
4. Now, using the principle of moments, we can equate the sum of the clockwise moments to the sum of the anticlockwise moments. In equilibrium, the sum of the moments will be zero. Thus:
Moment of the plank = Moment of the boy + Moment of the mass
8.0kg * 9.8 m/s² * 0.5m = M * 9.8 m/s² * (0.5m + 0.3m) + mass of the mass * 9.8 m/s² * 0.5m
5. Rearranging the equation, we can solve for the mass of the boy:
4.0kg = M * (0.5m + 0.3m) + mass of the mass * 0.5m
6. Substitute the given values into the equation and solve for M:
4.0kg = M * 0.8m + mass of the mass * 0.5m
Since we don't have the mass of the additional weight, we can't solve for the exact mass of the boy. If we have the mass of the additional weight, we can substitute that value into the equation to find the mass of the boy.