a large jar contains 500 identical marbles. Suppose you have an identical empty jar, a set of standard masses and balance scales. How would you find the mass of one marble without opening or breaking the jar? Explain
Thanks for your help, this stumped me for sure.
I would weigh the empty jar. then weigh the jar with marbles. Subtract the weight of the empty jar from the weight of the full jar. divide the remaining weight by 500 to find how much each marble weighs.
This helped so much I really need help on this question
To find the mass of one marble without opening or breaking the jar, you can follow these steps:
1. Set up the balance scales: Place the empty jar on one side of the balance scales and leave the other side empty.
2. Start adding marbles: Begin adding marbles one by one to the empty jar. Each time you add a marble, compare the balance scales. You will notice that the jar with the marbles becomes heavier than the empty jar.
3. Continue adding marbles: Add marbles until the two sides of the balance scales are perfectly balanced. This means that the total mass of the marbles in the jar is equal to the mass of the empty jar.
4. Divide the total mass: Once the balance scales are balanced, count the number of marbles in the jar. Let's say there are "X" marbles in the jar.
5. Divide the total mass by the number of marbles: Divide the total mass of the marbles (which is equal to the mass of the empty jar) by the number of marbles in the jar (X). This will give you the mass of one marble.
So, by following these steps and using the balance scales, you can find the mass of one marble without opening or breaking the jar.
To find the mass of one marble without opening or breaking the jar, you can use a mathematical approach called differential weighing. Here's how you can do it:
1. Divide the 500 marbles into two equal groups of 250 marbles each. Place 250 marbles in each jar, making sure that the jars are identical in every way.
2. Weigh both jars using the balance scales. Let's say Jar A weighs more than Jar B.
3. Now, take out one marble from Jar A and place it in Jar B. Keep the remaining marbles in Jar A.
4. Weigh both jars again. This time, let's assume Jar B weighs more than Jar A.
5. The difference in weight between the two weighings gives us the weight of one marble.
Explanation:
By dividing the marbles into two equal groups, we are effectively canceling out their collective weight. Each group of 250 marbles should weigh the same because they are identical. Therefore, the difference in weight between Jar A and Jar B can be attributed to the single marble that was transferred.
For instance, if Jar A weighed 500 grams and Jar B weighed 499 grams initially, and after transferring one marble from A to B, Jar A weighed 499 grams and Jar B weighed 500 grams, then the weight of one marble would be 1 gram.
If you repeat this process multiple times, each time taking out one marble from Jar A and placing it in Jar B, and consistently observing the same difference in weight, you can be more confident about the accuracy of your measurement.
It is important to note that the accuracy of this method relies on the assumption that the marbles are all identical in weight. Additionally, the balance scales being used should be accurate and precise for reliable results.