A uniform metre rule Mass 80kg is pivoted at the 30cm mark. Find the mass that would be placed at the 50cm mark for the metre rule to be in equilibrium.
We can start by using the principle of moments, which states that the sum of the clockwise moments must be equal to the sum of the anticlockwise moments for the metre rule to be in equilibrium.
Let x be the mass placed at the 50cm mark.
Clockwise moment:
80kg × 0.3m = 24Nm (due to the pivot at 30cm)
Anticlockwise moment:
x kg × 0.2m = 0.2x Nm (due to the pivot at 50cm)
To be in equilibrium:
24 Nm = 0.2x Nm
Solving for x:
x = 120kg
Therefore, a mass of 120kg would need to be placed at the 50cm mark for the metre rule to be in equilibrium.
To find the mass that would be placed at the 50cm mark for the meter rule to be in equilibrium, we can use the principle of lever (or torque) equilibrium.
The principle of lever equilibrium states that the sum of the clockwise (CW) torques about a pivot point is equal to the sum of the counterclockwise (CCW) torques about the same pivot point.
In this case, we have a uniform meter rule that is pivoted at the 30cm mark. Let's assume that the mass at the 50cm mark is M kg.
To determine the mass needed at the 50cm mark for equilibrium, we need to calculate the torques on each side of the pivot point and set them equal to each other.
Clockwise torque (CW) = Mass x Distance
Counterclockwise torque (CCW) = Mass x Distance
The distance of the mass at the 50cm mark from the pivot point is (50 - 30) = 20 cm = 0.2 m.
Now we can set up the torque equilibrium equation:
80 kg x 0.3 m = M kg x 0.2 m
Simplifying the equation:
24 = 0.2M
Now we can solve for M by dividing both sides of the equation by 0.2:
M = 24 / 0.2 = 120 kg
Therefore, to maintain equilibrium, a mass of 120 kg should be placed at the 50cm mark on the meter rule.