A uniform rule balances horizontally on a knife edge at 55cm mark,when an object of mass 1.0kg is placed at the 5cm mark,it balances at 35cm mark.calculate the magnitude of the weight of the metre rule (g=10m/s^2)
Hum
To solve this problem, we can use the principle of moments, which states that for an object in equilibrium (balanced), the sum of the anticlockwise moments is equal to the sum of the clockwise moments.
Let's assign some variables:
- W = weight of the meter rule
- M = weight of the 1.0 kg object
- L1 = distance from the knife edge to the 55 cm mark (L1 = 55 cm = 0.55 m)
- L2 = distance from the knife edge to the 5 cm mark (L2 = 5 cm = 0.05 m)
- L3 = distance from the knife edge to the 35 cm mark (L3 = 35 cm = 0.35 m)
- g = acceleration due to gravity = 10 m/s^2
We can start by calculating the moment due to the weight of the meter rule about the knife edge when it balances at the 55 cm mark:
Moment1 = W * L1
Similarly, we can calculate the moment due to the weight of the 1.0 kg object about the knife edge when it balances at the 35 cm mark:
Moment2 = M * L3
Since the ruler is balanced in both cases, these two moments must be equal:
Moment1 = Moment2
Substituting the values, we have:
W * L1 = M * L3
W * 0.55 = 1.0 * 0.35
Now we can calculate the weight of the meter rule:
W = (1.0 * 0.35) / 0.55
W = 0.35 / 0.55
W ≈ 0.636 kg
Finally, we can calculate the magnitude of the weight of the meter rule:
Weight = mass * acceleration due to gravity
Weight = 0.636 kg * 10 m/s^2
Weight ≈ 6.36 N
Therefore, the magnitude of the weight of the meter rule is approximately 6.36 N.
To calculate the magnitude of the weight of the meter rule, we can use the principle of moments. The principle of moments states that for an object to be in rotational equilibrium, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments.
First, let's consider the moments exerted by the object placed at the 5cm mark. The weight of the object is given by W = mg, where m is the mass of the object (1.0 kg) and g is the acceleration due to gravity (10 m/s^2). The distance between the 5cm mark and the knife edge is 55 cm - 5 cm = 50 cm = 0.50 m.
The moment exerted by the object is given by the formula:
Moment = weight x distance
Moment = mg x distance
Moment = (1.0 kg)(10 m/s^2)(0.50 m)
Moment = 5.0 Nm
Now, let's consider the moment exerted by the weight of the meter rule itself. Let's assume the weight of the meter rule is W_rule. The distance between the 55cm mark and the knife edge is 0.55 m.
The moment exerted by the meter rule is given by the formula:
Moment = weight x distance
Moment = W_rule x distance
Since the meter rule balances horizontally, the total clockwise moment must be equal to the total counterclockwise moment. Therefore, we have:
5.0 Nm = W_rule x 0.55 m
To find W_rule, we can rearrange the equation:
W_rule = 5.0 Nm / 0.55 m
W_rule ≈ 9.09 N
Therefore, the magnitude of the weight of the meter rule is approximately 9.09 N.