a uniform plank of lenght 5m and a mass1kg support two masses of 500g and 300g . determine the centre of gravity
To determine the center of gravity of the uniform plank with two masses on it, we need to consider the position and weight of each mass relative to the plank. The center of gravity is the point where the overall weight of the object can be considered to act through.
1. First, let's label the positions and weights of the masses:
- Mass 1: 500g (0.5kg) located at position 1m from one end of the plank.
- Mass 2: 300g (0.3kg) located at position 4m from the same end of the plank.
2. Calculate the total weight of the plank by adding the weights of the two masses:
Total weight = Mass 1 + Mass 2 = 0.5kg + 0.3kg = 0.8kg.
3. Next, calculate the total torque (turning force) created by the two masses acting on the plank. Torque is calculated by multiplying the weight of each mass by its distance from the reference point (typically an end or a specific point defined in the problem):
Torque = Mass 1 × Distance 1 + Mass 2 × Distance 2
= (0.5kg × 1m) + (0.3kg × 4m)
= 0.5kgm + 1.2kgm
= 1.7kgm.
4. The next step is to identify the position on the plank where the center of gravity is located. This position can be found by dividing the total torque by the total weight of the plank:
Center of gravity position = Torque / Total weight
= 1.7kgm / 0.8kg
= 2.125m.
Therefore, the center of gravity of the uniform plank with the given masses is located at a distance of 2.125m from one end of the plank.