A uniform metre rule is balanced at the 30cm mark when a mass of 50g is hanging from its zero cm mark. calculate the weight of the rule?
To calculate the weight of the rule, we need to use the principle of moments. The principle of moments states that the total clockwise moments about a point must be equal to the total anticlockwise moments about the same point in order for the object to be in equilibrium.
In this case, the metre rule is balanced at the 30cm mark. Let's assume the weight of the rule itself is W (unknown) and it acts at its center point, which is at the 50cm mark.
The moment of the weight of the rule (W) about the 30cm mark is given by:
Moment of weight = weight x distance
Since the weight is acting at the 50cm mark and we want the moment about the 30cm mark, the distance is 20cm (50cm - 30cm).
Therefore, the moment of the weight of the rule about the 30cm mark is 20W.
Now, a mass of 50g is hanging from the zero cm mark. The weight of this mass can be calculated using the formula:
Weight = mass x gravitational acceleration
The gravitational acceleration is approximately 9.8 m/s^2. Converting the mass from grams to kilograms, we get 0.05 kg.
Weight = 0.05 kg x 9.8 m/s^2 = 0.49 N
This weight acts at the zero cm mark, so the distance from the 30cm mark is 30cm.
The moment of this weight about the 30cm mark is 30 x 0.49 = 14.7N.
Since the rule is in equilibrium, the total clockwise moment (20W) must be equal to the total anticlockwise moment (14.7N). Therefore:
20W = 14.7N
Now we can solve for W:
W = 14.7N / 20
W = 0.735N
Therefore, the weight of the rule is approximately 0.735 Newtons.