in order to weight a boy in the laboratory a uniform plane of wood ab 3cm long having a mass of 8.0kg is pivoted about a point. 5m from a. the boy stands 0.3m from a and a mass is placed 0.5m from b in order to balance the plane horizontally. calculate the mass of the boy
To calculate the mass of the boy, we need to apply the principle of moments, which states that the sum of the moments acting on an object in equilibrium is zero.
First, let's understand the given information:
- The plane of wood is 3 cm long and has a mass of 8.0 kg. Its length AB is given as 3 cm, but we need to convert it to meters (1 m = 100 cm). Therefore, AB = 3 cm/100 = 0.03 m.
- The boy stands at a distance of 0.3 m from pivot point A.
- A mass is placed at a distance of 0.5 m from pivot point B to balance the plane horizontally.
Now, let's use the principle of moments to solve for the mass of the boy:
The moment of an object is defined as the product of its mass and its distance from the pivot point. Mathematically, moment is calculated as:
Moment = Mass * Distance
Considering clockwise moments as negative and counterclockwise moments as positive, we can write the equation based on the principle of moments:
Moment about pivot A = Moment about pivot B
(Mass of the boy * Distance of the boy from pivot A) = (Mass of the plane * Distance of the plane from pivot B)
(m * 0.3) = (8.0 kg * 0.5)
Rearranging the equation, we can solve for the mass of the boy:
m = (8.0 kg * 0.5) / 0.3
m = 4.0 kg
Therefore, the mass of the boy is 4.0 kg.