A uniform meterstick pivoted at its center has a 80.0g mass suspended at the 28.0cm position.At what position should a 80.0g mass be suspended to put the system in equilibrium?What mass would have to be suspended at the 90.0cm position for the system to be in equilibrium?
http://gmanacheril.com/PHY2048/Text%20Materials/Lesson%204.4%20Conditions%20of%20Equilibrium.pdf
Example #2
To determine the position at which a 80.0g mass should be suspended to put the system in equilibrium, we need to consider the principle of moments.
The principle of moments states that the total sum of clockwise moments about a pivot point is equal to the total sum of counterclockwise moments about the same pivot point, in a system in equilibrium.
Let's denote the pivot point as P, the 80.0g mass at the 28.0cm position as M1, and the unknown mass at the unknown position as M2. We want to find the position of M2 where the system is in equilibrium.
To solve this, we can set up an equation based on the principle of moments. The moment of M1 about P is given by the product of its mass (m1 = 80.0g) and its distance from the pivot point (d1 = 28.0cm). Similarly, the moment of M2 about P is given by the product of its mass (m2 = M2) and its distance from the pivot point (d2).
According to the principle of moments, the clockwise moment should be equal to the counterclockwise moment:
m1 * d1 = m2 * d2
Plugging in the given values:
(80.0g) * (28.0cm) = (M2) * (d2)
Now we can solve for the unknown position, d2:
d2 = (80.0g * 28.0cm) / M2
To determine the mass required to be suspended at the 90.0cm position for the system to be in equilibrium, we can again apply the principle of moments.
Using the same principle, we can set up another equation. Let's denote the unknown mass required to be suspended at the 90.0cm position as M3.
m1 * d1 = m3 * d3
Plugging in the given values:
(80.0g) * (28.0cm) = (M3) * (90.0cm)
Solving for the unknown mass, M3:
M3 = (80.0g * 28.0cm) / (90.0cm)
Keep in mind that in order to convert the distance in centimeters to meters, divide by 100 (1m = 100cm). Also, if you are dealing with forces rather than masses, you need to consider the acceleration due to gravity (9.8 m/s^2) and convert the mass to weight by multiplying by g.
To summarize:
1. To find the position where a 80.0g mass should be suspended to put the system in equilibrium, use the equation d2 = (80.0g * 28.0cm) / M2, where d2 is the unknown position and M2 is the unknown mass to be suspended.
2. To find the mass required to be suspended at the 90.0cm position for the system to be in equilibrium, use the equation M3 = (80.0g * 28.0cm) / (90.0cm), where M3 is the unknown mass to be suspended.