A figure shows a uniform metre rule which is pivoted at the 20cm mark and balanced horizontally by an object of weight 3.15N placed at the 10cm mark.
Calculate the weight of the metre rule.
To calculate the weight of the meter rule, we need to use the principle of moments. The principle of moments states that for a body in equilibrium, the sum of the clockwise moments is equal to the sum of the anticlockwise moments.
Let's assume the weight of the meter rule is W (unknown weight). We know that the object of weight 3.15N at the 10cm mark creates a clockwise moment and the meter rule pivoted at the 20cm mark creates an anticlockwise moment.
The clockwise moment is given by the weight of the object multiplied by its distance from the pivot:
Moment clockwise = 3.15N * 10cm = 31.5 Ncm
The anticlockwise moment is given by the weight of the meter rule (W) multiplied by its distance from the pivot:
Moment anticlockwise = W * 20cm = 20W Ncm
Since the meter rule is balanced horizontally, the sum of the clockwise moments should be equal to the sum of the anticlockwise moments:
31.5 Ncm = 20W Ncm
Dividing both sides of the equation by 20cm, we get:
31.5/20 = W
W ≈ 1.575 N
Therefore, the weight of the meter rule is approximately 1.575 Newtons.
To solve this problem, we can use the principle of moments, which states that the total anticlockwise moments about a pivot point equal the total clockwise moments about the same point.
Here's how to calculate the weight of the meter rule:
1. Assign variables:
- Let ```WR``` be the weight of the meter rule (which is what we want to find).
- Let ```WO``` be the weight of the object placed at the 10cm mark, given as 3.15N.
- Let ```DO``` be the distance of the object from the pivot, given as 10cm.
- Let ```DR``` be the distance of the weight of the meter rule from the pivot, which, in this case, is 20cm.
2. Write the equation:
- We can set up an equation based on the principle of moments:
```Clockwise Moment = Anticlockwise Moment```
- The clockwise moment is the product of the weight of the object and its distance from the pivot, which is ```WO x DO```.
- The anticlockwise moment is the product of the weight of the meter rule and its distance from the pivot, which is ```WR x DR```.
- Therefore, the equation becomes ```WO x DO = WR x DR```.
3. Substitute the given values:
- We know that ```WO = 3.15N``` and ```DO = 10cm```.
- We also know that ```DR = 20cm```.
4. Convert the distances into meters:
- Since the weights have units in newtons, it's important to have consistent units.
- Convert the distances from centimeters to meters by dividing them by 100:
- ```DO = 10cm / 100 = 0.10m```
- ```DR = 20cm / 100 = 0.20m```
5. Solve the equation for WR:
- Substitute the values into the equation: ```WO x DO = WR x DR```
- ```3.15N x 0.10m = WR x 0.20m```
- Simplify: ```0.315N = WR x 0.20m```
- Solve for WR: ```WR = 0.315N / 0.20m```
6. Calculate the weight of the meter rule:
- Perform the division: ```WR = 1.575N```
Therefore, the weight of the meter rule is 1.575N.