A uniform metre rule is balanced at the 35cm mark when a mass of 500g is placed at the 20cm mark .determine the mass of the rule ..
To determine the mass of the rule, we can use the principle of moments. The principle of moments states that for an object in equilibrium, the sum of the clockwise moments is equal to the sum of the anticlockwise moments.
We can consider two moments in this scenario: the moment caused by the mass at the 35cm mark (M1) and the moment caused by the mass at the 20cm mark (M2). Since the metre rule is balanced, these two moments must be equal.
Let's calculate the moments:
M1 = Force1 × Distance1
= Mass1 × g × Distance1
= 500g × 9.8m/s^2 × (35cm / 100cm/m)
= 500g × 9.8m/s^2 × 0.35m
= 1715 Nm
M2 = Force2 × Distance2
= Mass2 × g × Distance2
= Mass of the rule × g × (20cm / 100cm/m)
= Mass of the rule × 9.8m/s^2 × 0.20m
= 1.96 Nm × Mass of the rule
Since the moments are equal, we can set up an equation:
M1 = M2
1715 Nm = 1.96 Nm × Mass of the rule
Solving for the mass of the rule:
Mass of the rule = 1715 Nm / 1.96 Nm
≈ 875 grams
Therefore, the mass of the rule is approximately 875 grams.
To determine the mass of the rule, we can use the principle of moments. The principle of moments states that for an object in equilibrium, the sum of the anti-clockwise moments is equal to the sum of the clockwise moments.
In this case, we have two forces acting on the metre rule: the weight of the rule itself and the weight of the 500g mass. Let's assign variables to represent the different forces:
- Mass of the rule: M
- Distance of mass of the rule from the pivot (35 cm mark): D
- Mass of the 500g weight: 500g = 0.5 kg
- Distance of the 500g weight from the pivot (20 cm mark): d
Now we can set up the equation using the principle of moments:
Anti-clockwise moments = Clockwise moments
(M x D) = (0.5 kg x d)
We are given that the rule is balanced at the 35 cm mark when a mass of 500g is placed at the 20 cm mark. This means that the rule is in equilibrium and the moments are equal:
(M x 35 cm) = (0.5 kg x 20 cm)
To perform the calculation, we need to convert the distances to meters:
(M x 0.35 m) = (0.5 kg x 0.2 m)
Now we can solve for the mass of the rule (M):
M = (0.5 kg x 0.2 m) / 0.35 m
M = 0.1 kg / 0.35
M ≈ 0.29 kg
Therefore, the mass of the rule is approximately 0.29 kg.