In order to weigh a child in a laboratory ,a plank of wood AB. Is 3.0m long .A mass of 8.0kg is pivoted about a point 0.5m from A .The boy stands 0.3m from A and a mass is placed 0.5m from B in order to balance the plank horizontally .Calculate the mass of the boy.
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 is equal to the sum of the anticlockwise moments.
Let's break down the information given step by step:
1. The plank of wood AB is 3.0 meters long.
2. The mass of 8.0 kg is placed at a point 0.5 meters from point A.
3. The boy stands 0.3 meters from point A.
4. A mass is placed 0.5 meters from point B to balance the plank horizontally.
To find the mass of the boy, we need to create an equation using the principle of moments.
Clockwise moments:
The clockwise moment of the 8.0 kg mass is equal to 8.0 kg * 0.5 meters (as the distance from the pivot point is 0.5 meters).
Anticlockwise moments:
The anticlockwise moment of the boy's mass is equal to the mass of the boy multiplied by the distance from the pivot point.
Since the plank is balanced horizontally, the sum of the clockwise moments should equal the sum of the anticlockwise moments:
8.0 kg * 0.5 m = mass of the boy * (3.0 m - 0.3 m).
Simplifying the equation:
4.0 kg*m = mass of the boy * 2.7 m.
Now, we can solve for the mass of the boy by rearranging the equation:
mass of the boy = (4.0 kg*m) / (2.7 m).
By calculating this, we find that the mass of the boy is approximately 1.48 kg.