A uniform meter rule is freely pivoted at 30cm mark and balances horizontally when a mass is 80g is hung from 2cm mark. Draw a diagram of the meter rule showing all the forces acting on the meter rule. Calculate the mass of the meter rule?
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Answer
To draw a diagram of the meter rule showing all the forces acting on it, we need to consider the forces at the pivot and the forces due to the weight of the hanging mass.
Here is a step-by-step guide to drawing the diagram:
1. Draw a straight line to represent the meter rule. Label it as "Meter Rule."
2. Mark a point at the 30cm position on the meter rule and label it as "Pivot."
3. Draw a small circle or dot to represent the pivot point at the 30cm mark.
4. At the 2cm mark, draw a vertical line that represents the direction of the hanging mass. Label this point as "Hanging Mass."
5. At the end of the vertical line, draw a small arrow pointing downward to represent the force of gravity acting on the hanging mass. Label it as "Weight of Hanging Mass."
6. Draw a horizontal line from the pivot point to the vertical line representing the hanging mass.
7. At the intersection of the horizontal line and the vertical line, draw a small arrow pointing to the right. Label this arrow as "Reaction Force at Pivot."
The diagram should now show the meter rule with the pivot, the hanging mass, the weight of the hanging mass, and the reaction force at the pivot.
To calculate the mass of the meter rule, we can use the principle of moments. The principle of moments states that the sum of the clockwise moments around a pivot point is equal to the sum of the anticlockwise moments around the same pivot point.
In this case, since the meter rule is balanced horizontally, the clockwise moments and anticlockwise moments are equal.
The clockwise moment is given by the formula: Clockwise Moment = Weight of Hanging Mass * Distance from Pivot to Hanging Mass
The anticlockwise moment is given by the formula: Anticlockwise Moment = Mass of Meter Rule * Distance from Pivot to Meter Rule
Setting the clockwise moment equal to the anticlockwise moment, we have:
Weight of Hanging Mass * Distance from Pivot to Hanging Mass = Mass of Meter Rule * Distance from Pivot to Meter Rule
Given:
Weight of Hanging Mass = 80g = 0.08 kg (converting grams to kilograms)
Distance from Pivot to Hanging Mass = 2 cm = 0.02 m
Distance from Pivot to Meter Rule = 30 cm = 0.3 m
Solving for the Mass of the Meter Rule:
0.08 kg * 0.02 m = Mass of Meter Rule * 0.3 m
Mass of Meter Rule = (0.08 kg * 0.02 m) / 0.3 m
Mass of Meter Rule = 0.005333 kg
Therefore, the mass of the meter rule is approximately 0.005333 kg.
To draw a diagram of the meter rule and calculate the mass, we need to analyze the forces acting on the rule.
Diagram:
1. Draw a straight line to represent the meter rule.
2. Mark the pivot point at the 30cm mark.
3. On the left side of the pivot (0-30cm), draw an arrow pointing upwards to represent the weight (W) of the meter rule acting at the center of mass.
4. On the right side of the pivot (30-100cm), draw an arrow pointing downwards to represent the weight (W) of the 80g mass acting at the 2cm mark.
5. At the 30cm mark, draw an arrow pointing towards the pivot to represent the reaction force (R) acting at the pivot point.
6. Make sure that all the arrows are appropriately labeled.
Now, to calculate the mass of the meter rule, we will use the principle of moments. The principle states that the sum of the clockwise moments (moments acting in the opposite direction of the anticlockwise moments) is equal to zero for an object in rotational equilibrium.
The clockwise moment (M1) is given by the formula: M1 = weight x distance
The anticlockwise moment (M2) is also given by the formula: M2 = weight x distance
In this case:
M1 = 80g x 98cm (weight of the mass x distance from the pivot)
M2 = W x 30cm (weight of the meter rule x distance from the pivot)
Since the meter rule is balanced horizontally, M1 = M2. Therefore, we can equate the two moments and solve for the unknown weight (W) of the meter rule.
80g x 98cm = W x 30cm
To solve for W, we need to convert grams to kilograms (1kg = 1000g):
80g ÷ 1000 = 0.08kg
0.08kg x 98cm = W x 30cm
Simplifying:
7.84kg·cm = W x 30cm
W = 7.84kg·cm ÷ 30cm
W ≈ 0.26kg
Hence, the mass of the meter rule is approximately 0.26kg.