Determining mass of balance bar

In summary, the problem involves a meter stick with a fulcrum at 50cm and masses A and B located at 12.3cm and 86.1cm respectively. After removing mass B and shifting the fulcrum 14cm to the left, the center of mass is still at 50cm and the bar needs to be balanced. Using torque calculations, the mass of the bar is determined to be 169 grams.
  • #1
izmeh
Here's the situation proposed in a problem.
I have a balance bar that is a meter stick.
It has a fulcrum at 50cms. Mass A(100gms[.98nt]) is at 12.3cms and mass B(1.02nt) is located at 86.1cms.
Mass B has been removed and the fulcrum C shifts fo the left by 14cms.
I need to determine the mass of the meter stick. How do i do this?
 
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  • #2
The first part "It has a fulcrum at 50cms. Mass A(100gms[.98nt]) is at 12.3cms and mass B(1.02nt) is located at 86.1cms." just tells you that the bar itself has center of mass located at its center (since A is 50-12.3= 37.7 cm from the center and B is 86.1-50= 36.1 cm from the center- 37.7*.98= 36.1*1.02 (well, close enough for experimental error)).

After B is moved, the fulcrum shifts "14 cm to the left" so it is now at 36 cm. We still have mass A at 12.3 cm, 23.7 cm from the fulcrum. Its torque is .98*23.7= 23.226 (actually 0.23226 N-m). The center of mass of the bar is still at 50, 14 cm from the fulcrum so, taking the weight of the bar to be W, the torque around the fulcrum is
14W. To be balanced we must have 14W= 23.226 or W= 1.659 N. That means that the mass of the bar is 1.659/9.81= 0.169 kg or 169 grams.
 
  • #3
thank you
 

1. How do you determine the mass of a balance bar?

To determine the mass of a balance bar, you will need a triple beam balance or a digital scale. First, make sure the balance bar is clean and free of any debris or substances. Place the balance bar on the balance and make sure it is level. Adjust the weights on the balance until the pointer is at zero. Then, place the object whose mass you want to measure on one side of the balance bar. Adjust the weights on the other side until the pointer is once again at zero. The total mass of the object is equal to the sum of the weights on the balance bar.

2. What is the purpose of determining the mass of a balance bar?

The purpose of determining the mass of a balance bar is to accurately measure the mass of an object. This information is important in many scientific experiments and calculations, as mass is a fundamental property of matter. It can also help in determining the density and volume of an object.

3. How accurate is the measurement of mass using a balance bar?

The accuracy of the measurement of mass using a balance bar depends on the quality and calibration of the balance. A well-calibrated balance can provide measurements with a precision of up to 0.01 grams. However, it is important to note that external factors, such as air currents, can affect the accuracy of the measurement.

4. What are the limitations of using a balance bar to determine mass?

One limitation of using a balance bar to determine mass is that it can only measure the mass of solid objects. Liquids, gases, and substances with irregular shapes cannot be accurately measured using a balance bar. Additionally, the balance bar can only measure mass up to a certain capacity, so objects that are too heavy may require a different method of measurement.

5. Are there any safety precautions to keep in mind when using a balance bar?

When using a balance bar, it is important to handle it with care and avoid touching the weights or moving parts. Always make sure the balance is properly calibrated before use. If handling hazardous materials, be sure to wear appropriate protective gear. It is also important to make sure the balance is placed on a stable and level surface to avoid any accidents.

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