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 a 2.0kg mass is placed 0.5m from B in order to balanced the plank horizontal. Calculate the mass of the boy.
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I don't know how to solve this question so please send me the solution
20kg and reaction is 300N.
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I don't know it !!!!!! Why will i ask if I know it
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Please ,solve me the solution
Where is pivoted ?
To solve this problem, we can 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.
Here's how we can approach this problem step by step:
1. Determine the moment due to the wooden plank:
- Mass of the wooden plank, m1 = 8.0 kg
- Distance from the pivot point to the center of mass of the plank, d1 = 0.5 m
- The moment due to the plank is given by M1 = m1 * d1
2. Determine the moment due to the 2.0 kg mass:
- Mass of the 2.0 kg mass, m2 = 2.0 kg
- Distance from the pivot point to the 2.0 kg mass, d2 = 0.5 m
- The moment due to the 2.0 kg mass is given by M2 = m2 * d2
3. Determine the moment due to the boy:
- Let the mass of the boy be m3 (which we need to find).
- Distance from the pivot point to the boy, d3 = 0.3 m
- The moment due to the boy is given by M3 = m3 * d3
4. Apply the principle of moments:
According to the principle of moments, the sum of clockwise moments is equal to the sum of anticlockwise moments:
M1 + M2 = M3
Plugging in the values we know:
(m1 * d1) + (m2 * d2) = (m3 * d3)
5. Solve for the mass of the boy (m3):
Rearrange the equation:
m3 = ((m1 * d1) + (m2 * d2)) / d3
Substituting the given values:
m3 = ((8.0 kg * 0.5 m) + (2.0 kg * 0.5 m)) / 0.3 m
Calculating:
m3 = (4.0 Nm + 1.0 Nm) / 0.3 m
m3 = 15 kg
Therefore, the mass of the boy is 15 kg.