In the figure below PT is a uniform meter rule pivoted at R,the 70cm mark two forces 0.1N and 0.4N are applied at Q, the 60cm mass and S,the 85cm mark. If the meter rule is kept in equilibrium by the forces and it's weight, calculate the rate of the meter rule.
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calculate the rate of the meter rule. ?????
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To calculate the rate of the meter rule, we need to understand the concept of moments and equilibrium.
The moment of a force about a pivot point is the force multiplied by its perpendicular distance from the pivot. The principle of equilibrium states that if a body is in equilibrium, the sum of the clockwise moments about any point must be equal to the sum of the anticlockwise moments about the same point.
In this case, we have two forces, 0.1N at Q and 0.4N at S, acting on the meter rule. The distance between the pivot R and Q is 70cm, and the distance between the pivot R and S is 85cm.
The meter rule is also affected by its weight, which we can assume acts at the center of mass of the meter rule.
Since the meter rule is in equilibrium, the sum of the clockwise moments about R must be equal to the sum of the anticlockwise moments about R.
Clockwise moments about R:
Moment of 0.1N at Q = 0.1N × 70cm
Moment of 0.4N at S = 0.4N × 85cm
Moment of weight of the meter rule = weight × distance from R to the center of mass
Anticlockwise moments about R:
None mentioned in the question.
As the meter rule is in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments. Since there are no mentioned anticlockwise moments, we can assume they are zero.
Therefore, the equation becomes:
0.1N × 70cm + 0.4N × 85cm + Weight × Distance from R to the center of mass = 0
To find the weight of the meter rule, we need to consider the distribution of mass along the meter rule. Since it is a uniform meter rule, we can assume that the center of mass is at the midpoint of the rule. Therefore, the weight can be calculated by multiplying the mass of the meter rule by the acceleration due to gravity (weight = mass × gravity).
Once the weight is calculated, we can substitute it back into the equation and solve for the unknown, which is the rate of the meter rule.