A uniform meter stick balances on a fulcrum placed at the 40 cm mark when a weight W is placed at 30 cm mark. What is the weight of the meter stick? How to calculator it ?
To calculate the weight of the meter stick, you can use the principle of lever equilibrium. In a balanced lever system, the product of the weight on one side of the fulcrum and its distance from the fulcrum is equal to the product of the weight on the other side and its distance from the fulcrum.
In this case, the weight of the meter stick can be considered to act at its center of mass, which is at the 50 cm mark (halfway between the 0 cm and 100 cm ends).
Here's how you can calculate the weight of the meter stick:
1. Determine the distance of the weight W from the fulcrum. In this case, the weight W is placed at the 30 cm mark, which means it is 10 cm away from the fulcrum (40 cm - 30 cm = 10 cm).
2. Calculate the distance of the center of mass (50 cm mark) from the fulcrum. The center of mass is at a distance of 10 cm from the fulcrum on the other side (50 cm - 40 cm = 10 cm).
3. Set up the lever equilibrium equation:
Weight of the meter stick * Distance of the meter stick's center of mass from the fulcrum = Weight of the weight * Distance of the weight from the fulcrum.
In this case, let's assume the weight of the meter stick is Wm and the weight of the weight is Ww. The equation becomes:
Wm * 10 cm = Ww * 10 cm
4. Since the distances are equal, the weights must also be equal:
Wm = Ww
Therefore, the weight of the meter stick is equal to the weight of the weight placed at the 30 cm mark.
To calculate the weight of the meter stick, we need to consider the concept of torque. Torque is the measure of how effectively a force can rotate an object around a fixed axis, and it depends on both the force applied and the distance from the axis.
In this scenario, the meter stick is balanced on a fulcrum, which acts as the axis of rotation. The weight of the meter stick itself will create a torque that balances out the torque exerted by the weight W at the 30 cm mark.
We can use the equation for torque:
Torque = Force × Distance
Since the meter stick is balanced, the torques on either side of the fulcrum are equal. Therefore, we can express the torque created by the meter stick as:
Torque of meter stick = Weight of meter stick × Distance from fulcrum to center of mass of the meter stick
Similarly, we can express the torque created by weight W as:
Torque of weight W = Weight of W × Distance of W from fulcrum
Since the meter stick is balanced, the torques on either side of the fulcrum are equal:
Torque of meter stick = Torque of weight W
Now let’s substitute the given values into these equations. The distance from the fulcrum to the 40 cm mark is 10 cm (40 cm - 30 cm).
Let's assume the weight of the meter stick is M (in newtons) and the weight of W is W (in newtons).
Therefore, the equation becomes:
M × 10 cm = W × 30 cm
Now we can solve for the weight of the meter stick (M).
M = (W × 30 cm) / 10 cm
Remember to make sure that the units of distance are the same (both in centimeters or both in meters) to get the correct answer.
So, to calculate the weight of the meter stick, you need to know the weight of weight W and the distances of the weight W and the fulcrum from the center of mass of the meter stick.
W(40-30)=Mg(100/2)
Mg=W