A horizontal wooden plank is pivoted at one end, as shown.4 m10 mplankcentre of gravitypivotThe plank has a mass of 100 kg and a length of 10 m. The centre of gravity of the plank is adistance of 4 m from the pivot.What is the moment of the weight of the plank about the pivot?A 4 10 2 N m B 5 10 2 N m C 4 10 3 N m D 5 10 3 N m
Question
A horizontal wooden plank is pivoted at one end, as shown.4 m10 mplankcentre of gravitypivotThe plank has a mass of 100 kg and a length of 10 m. The centre of gravity of the plank is adistance of 4 m from the pivot.What is the moment of the weight of the plank about the pivot?A 4 10 2 N m B 5 10 2 N m C 4 10 3 N m D 5 10 3 N m
Solution
The moment of a force is calculated by multiplying the force by the distance from the pivot point. In this case, the force is the weight of the plank, which can be calculated by multiplying the mass of the plank by the acceleration due to gravity.
Step 1: Calculate the weight of the plank The weight (force) of the plank is its mass times the acceleration due to gravity. Assuming the acceleration due to gravity is approximately 9.8 m/s^2, the weight of the plank is 100 kg * 9.8 m/s^2 = 980 N.
Step 2: Calculate the moment of the weight of the plank about the pivot The moment is the weight of the plank times the distance from the pivot to the center of gravity. So, the moment is 980 N * 4 m = 3920 N m.
Therefore, the moment of the weight of the plank about the pivot is 3920 N m. This is closest to option C, 4 x 10^3 N m.
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