A uniform harf metre rule is freely pivoted at the 15cm mark and it balances horizontally when a body of mass 40g is hung from the 2cm mark
You want the mass of the rule maybe?
I suppose you mean half a meter long and center of gravity at 25 cm
then moments about pivot point:
40 (15-2) = m (25-15)
40 * 13 = 10 m
m = 52 grams
Well, that's quite a balancing act! I guess the 40g body is like the star performer on this circus-themed ruler. Hanging from the 2cm mark, it's defying gravity and balancing the entire ruler horizontally. It must be a tiny weightlifting champion! I wonder if it knows any tricks? Maybe it can do a handstand while hanging from the ruler?
To solve this problem, we can use the principle of moments, which states that for an object in equilibrium, the total clockwise moment is equal to the total anticlockwise moment.
1. Determine the distances from the pivot point:
- The distance from the pivot to the 40g mass is 2 cm.
- The distance from the pivot to the center of the ruler is 15 cm.
2. Determine the masses and the corresponding distances:
- The mass of the 40g object is 40g.
- The mass of the ruler is assumed to be negligible.
3. Calculate the clockwise moment:
Moment = Mass * Distance
Clockwise Moment = 40g * 2 cm
4. Calculate the anticlockwise moment:
Moment = Mass * Distance
Anticlockwise Moment = 0g * 15 cm
(Since the mass of the ruler is negligible)
5. Set the clockwise moment equal to the anticlockwise moment:
Clockwise Moment = Anticlockwise Moment
40g * 2 cm = 0g * 15 cm
80 g·cm = 0 g·cm
Since the equation is not balanced, there seems to be an error or missing information in the question. Please double-check the given data or provide further details if available.
To solve this problem, we need to take into account the principle of moments. When an object is in equilibrium, the sum of the moments acting on it is zero.
In this case, the uniform half-meter rule is freely pivoted at the 15 cm mark. Let's assume the total length of the ruler is L. The mass of the object is given as 40 g, which can be converted to 0.04 kg.
The moment of the mass hanging at the 2 cm mark can be calculated as follows:
Moment = Force × Distance
The force acting on the mass is its weight, which is given by:
Force = mass × gravitational acceleration
Here, the gravitational acceleration is approximately 9.8 m/s^2. So, the force is:
Force = 0.04 kg × 9.8 m/s^2
Next, we need to calculate the distance of this force from the pivot point at 15 cm. The distance can be determined by finding the difference between the 15 cm pivot point and the 2 cm mark where the mass is hanging:
Distance = 15 cm - 2 cm
Now that we have the force and distance, we can calculate the moment:
Moment = Force × Distance
Substituting the values, we get:
Moment = (0.04 kg × 9.8 m/s^2) × (15 cm - 2 cm)
Simplifying this expression, we convert centimeters to meters by dividing by 100:
Moment = (0.04 kg × 9.8 m/s^2) × (0.15 m - 0.02 m)
Calculating this expression, we find:
Moment = (0.04 kg × 9.8 m/s^2) × (0.13 m)
Finally, we can determine the unknown mass at the 0 cm mark by setting the sum of the moments to zero:
Total Moment = Moment of Unknown Mass
Since the ruler is in equilibrium, the total moment is zero. Therefore, the equation becomes:
0 = (0.04 kg × 9.8 m/s^2) × (0.13 m) - (mass × 9.8 m/s^2 × 0.15 m)
By rearranging this equation, we can solve for the unknown mass:
mass × 9.8 m/s^2 × 0.15 m = (0.04 kg × 9.8 m/s^2) × (0.13 m)
mass = [(0.04 kg × 9.8 m/s^2) × (0.13 m)] / (9.8 m/s^2 × 0.15 m)
Simplifying further, we get:
mass = 0.04 kg × (0.13 m / 0.15 m)
mass = 0.04 kg × (13/15)
mass = 0.04 kg × 0.867
mass ≈ 0.03468 kg
Therefore, the mass of the object at the 0 cm mark is approximately 34.68 g.