Final answer:
To find which barrel contains the heavy golf balls, take an increasing number of balls from each barrel, weigh them, and the excess weight over the expected total reveals the barrel with heavy balls.
Step-by-step explanation:
Identifying the Barrel with Heavy Golf Balls
To determine which barrel contains the heavy golf balls using only one weighing on a scale, you can use the following method:
Label each barrel with a number from 1 to 10.
From the first barrel, take one golf ball. From the second barrel, take two golf balls, and continue in this manner so that from the tenth barrel, you take ten golf balls.
Use a balance or a scale to weigh the total number of golf balls you have collected. This should be done in ounces since the weights of the balls are given in ounces.
Calculate the expected weight if all balls were 1 ounce each. This would be the sum of the first 10 natural numbers (1+2+3+...+10 = 55 ounces).
Any excess weight over the expected 55 ounces indicates which barrel contained the 2-ounce balls. For example, if the total weight is 56 ounces, the first barrel has the heavy balls. If the weight is 57 ounces, the second barrel has the heavy balls, and so on.
The density of the golf balls is not directly relevant, but understanding mass-to-volume ratios is a useful concept when comparing objects of different weights and sizes.