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 bo
To solve this problem, we can use the principle of conservation of moments. The total moment on the plank should be zero to keep it balanced.
First, let's calculate the moment due to the plank itself. The moment is calculated as the product of the mass and the perpendicular distance from the pivot point.
Moment of the plank = mass of the plank × distance from pivot = 8.0 kg × 0.5 m = 4.0 kg·m
Next, let's calculate the moment due to the boy. We'll assume the boy's mass is M kg.
Moment of the boy = mass of the boy × distance from pivot = M kg × 0.3 m = 0.3M kg·m
Finally, let's calculate the moment due to the mass placed on the other end of the plank.
Moment of the mass = mass placed × distance from pivot = mass placed × 0.5 m
Since the plank is balanced horizontally, the total moment should be zero. Thus, we have the equation:
Total moment = Moment of the plank + Moment of the boy + Moment of the mass = 0
Since we want to find the mass of the boy, let's rearrange the equation:
0 = 4.0 kg·m + 0.3M kg·m - mass placed × 0.5 m
Now, we substitute the given values:
0 = 4.0 kg·m + 0.3M kg·m - mass placed × 0.5 m
0 = 4.0 kg·m + 0.3M kg·m - mass placed × 0.5 m
0 = 0.3M kg·m - mass placed × 0.5 m - 4.0 kg·m
0.3M kg·m = mass placed × 0.5 m + 4.0 kg·m
0.3M kg·m = (mass placed × 0.5 m) + (4.0 kg·m)
Now, let's plug in the values given in the problem. The mass placed is not given, so we'll use M for it.
0.3M kg·m = (M × 0.5 m) + (4.0 kg·m)
Simplifying the equation:
0.3M kg·m = 0.5M kg·m + 4.0 kg·m
Now, let's solve for M:
0.3M kg·m - 0.5M kg·m = 4.0 kg·m
-0.2M kg·m = 4.0 kg·m
M kg·m = 4.0 kg·m / -0.2
M kg·m = -20.0 kg
Since mass cannot be negative, we reject the negative solution.
Thus, there is no valid solution for the mass of the boy in this scenario.