Beams and pans of a balance weight ,when a object measure w1 in one pan and measures w2 placed in other pan what is the actual weoght

When using a balance scale, the readings you see on each pan represent the weights of the objects being compared. If you have an object that measures \( w_1 \) in one pan and another weight \( w_2 \) in the opposite pan, the actual weight of the object can be determined by understanding how balance scales work.

Understanding the Balance Scale

A balance scale operates on the principle of equilibrium. It compares the weight of an object in one pan to the weight of another object in the opposite pan. When the scale is balanced, it indicates that the weights are equal. Thus, if you have an object weighing \( w_1 \) in one pan and a known weight \( w_2 \) in the other pan, the balance tells us that:

• If the scale is balanced, then \( w_1 = w_2 \).
• If the scale tips towards the pan with \( w_1 \), then \( w_1 > w_2 \).
• If the scale tips towards the pan with \( w_2 \), then \( w_1 < w_2 \).

Calculating the Actual Weight

To find the actual weight of the object, we can use the following reasoning:

• If the scale is balanced, the actual weight of the object is simply \( w_1 \) (or \( w_2 \), since they are equal).
• If the scale is not balanced, you can determine the actual weight by adjusting the weights until equilibrium is achieved. For example, if \( w_1 \) is greater than \( w_2 \), you would need to add more weight to the \( w_2 \) pan until it equals \( w_1 \).

Example Scenario

Let’s say you place a rock in one pan, and it measures \( w_1 = 300 \) grams. In the other pan, you have a standard weight that measures \( w_2 = 300 \) grams as well. Since both pans are equal, the actual weight of the rock is 300 grams.

Now, if you have a different scenario where the rock measures \( w_1 = 350 \) grams and the standard weight is \( w_2 = 300 \) grams, the scale will tip towards the rock. This indicates that the rock is heavier. To find the actual weight, you would need to add weights to the \( w_2 \) pan until it balances with the rock. If you add 50 grams to the \( w_2 \) pan, making it 350 grams, the scale will balance, confirming that the actual weight of the rock is indeed 350 grams.

Final Thoughts

In summary, the actual weight of an object measured on a balance scale can be directly read when the scale is balanced. If not, adjustments can be made to find the weight by achieving equilibrium. This method is fundamental in physics and provides a clear understanding of weight measurement through balance.