A metre rule is balanced by masses of 24g and 16g suspended from its ends.Find the position of the pivot.
24 x = 16 (100-x)
the pivot is x cm from the 24g weight, where
24x = 16(100-x)
3 x= 200 - 2x
5 x = 200
x = 40
assuming that we can ignore the mass of the rule itself.
To find the position of the pivot, we need to consider the concept of equilibrium. In an equilibrium situation, the sum of clockwise moments (torques) is equal to the sum of anticlockwise moments.
Let's denote the position of the pivot (the center of the metre rule) as P. We'll also denote the position of the 24g mass as A and the position of the 16g mass as B.
The general formula for calculating a moment (torque) is:
Moment = Force x Distance
First, we need to consider the forces acting at positions A and B. The weight of each mass creates a downward force that is balanced by an upward force applied by the pivot.
For mass 24g:
The weight of the mass is given by the formula:
Weight = mass x gravity
Using the gravitational acceleration of approximately 9.8 m/s², we can calculate the weight of the 24g mass:
Weight = 24g x 9.8 m/s²
Similarly, for the 16g mass:
Weight = 16g x 9.8 m/s²
Since the metre rule is balanced, the clockwise and anticlockwise moments should be equal.
Clockwise moments:
The clockwise moment is calculated by multiplying the weight of the 24g mass by its distance from the pivot:
Clockwise Moment = Weight of 24g mass x Distance AP
Anticlockwise moments:
The anticlockwise moment is calculated by multiplying the weight of the 16g mass by its distance from the pivot:
Anticlockwise Moment = Weight of 16g mass x Distance BP
In equilibrium, the sum of the clockwise moments must equal the sum of the anticlockwise moments:
Clockwise Moment = Anticlockwise Moment
Substituting the formulas we derived:
Weight of 24g mass x Distance AP = Weight of 16g mass x Distance BP
Now that we have the equation above, we can find the position of the pivot, which is the value of Distance AP.
Since we know the masses (24g and 16g) and the gravitational acceleration (9.8 m/s²), we need to determine the distances AP and BP to solve the equation.
Measure the distances AP and BP on the ruler and substitute the values into the equation:
Weight of 24g mass x Distance AP = Weight of 16g mass x Distance BP
Once you have the distances, you can solve the equation to find the position of the pivot, Distance AP.