on a uniform beam of length 5m, hangs a mass 30kg at one end. the beam then balances at a point 1.5m from this end. find the mass of the beam(g=10ms-1)
1(mg) = 1.5(5g)
To find the mass of the beam, we need to use the principle of moments, which states that the sum of the anticlockwise moments about any point is equal to the sum of the clockwise moments about the same point.
In this case, let's take moments about the point where the beam balances, which is 1.5m from the end where the 30kg mass is hanging.
Since the beam balances, the sum of the anticlockwise moments must be equal to the sum of the clockwise moments.
The clockwise moment comes from the mass of the beam itself, while the anticlockwise moment comes from the weight of the 30kg mass.
The weight of an object can be calculated using the formula: weight = mass * acceleration due to gravity.
Given:
- Mass of the hanging mass (m1) = 30 kg
- Length of the beam (L) = 5 m
- Distance from the balancing point (d) = 1.5 m
- Acceleration due to gravity (g) = 10 m/s^2
Let's denote the mass of the beam as m2.
The clockwise moment is given by the formula: clockwise moment = m2 * g * (L - d)
The anticlockwise moment is given by the formula: anticlockwise moment = m1 * g * d
Since the beam balances, the clockwise and anticlockwise moments are equal:
m2 * g * (L - d) = m1 * g * d
To find the mass of the beam (m2), we can rearrange the equation:
m2 = (m1 * g * d) / (g * (L - d))
Plugging in the values:
m2 = (30 * 10 * 1.5) / (10 * (5 - 1.5))
Simplifying:
m2 = (30 * 1.5) / (3.5)
m2 = 12.86 kg
Therefore, the mass of the beam is approximately 12.86 kg.