Let's tackle your questions one at a time, starting with the first one about the false balance. This scenario involves understanding how a false balance can misrepresent the weight of an object. When you place a body on one pan and it shows a weight of 8 grams, while on the other pan it shows 18 grams, we need to analyze the situation carefully.
Analyzing the False Balance
In a false balance, the weights displayed can be misleading due to the imbalance in the scale. Since the beam is horizontal when both pans are empty, we can infer that the scale is not calibrated correctly. The key here is to find the true weight of the body based on the readings from the scale.
Understanding the Readings
When the body is placed on one pan, it shows 8 grams, and when placed on the other pan, it shows 18 grams. This discrepancy indicates that the scale is biased. To find the true weight, we can set up an equation based on the principle of balance:
- Let the true weight of the body be W.
- When the body is on the first pan, the scale reads 8 grams, which means:
- W = 8 + x (where x is the error in the scale when the body is on this pan).
- When the body is on the second pan, the scale reads 18 grams, which means:
- W = 18 - y (where y is the error in the scale when the body is on this pan).
Since both expressions equal W, we can set them equal to each other:
8 + x = 18 - y
To find the true weight, we need to determine the errors x and y. However, since the scale is false, we can assume that the average of the two readings gives us a better estimate of the true weight:
True Weight (W) = (8 + 18) / 2 = 26 / 2 = 13 grams.
Thus, the true weight of the body is 13 grams.
Swimming Across a River: Energy Expenditure
Now, let’s discuss your second question regarding swimming across a river and why maximum energy is spent in the last third of the distance. This concept involves understanding the dynamics of swimming against a current.
Breaking Down the Swim
When you swim across a river, you are not only moving through water but also contending with the current of the river. The energy expenditure can be analyzed in terms of distance and the forces acting on the swimmer.
- In the first third of the swim, the swimmer is likely adjusting to the current and finding a rhythm.
- In the second third, the swimmer has established a pace and is effectively using energy to maintain their position against the current.
- However, in the last third, fatigue sets in, and the swimmer must exert more effort to overcome the cumulative effects of the current and their own fatigue.
As the swimmer approaches the opposite bank, the current may also push them downstream, requiring them to swim harder to maintain their trajectory. This combination of fatigue and the need to counteract the current leads to maximum energy expenditure in the final third of the swim.
Visualizing the Effort
Think of it like climbing a hill. At first, you have energy and can manage the incline easily. As you climb higher, you become tired, and the last stretch requires more effort than the initial ascent. Similarly, in swimming, the last part of the swim demands more energy due to both physical fatigue and the need to counteract the river's current.
In summary, the maximum energy is spent in the last third of the swim due to fatigue and the increasing challenge of overcoming the current as the swimmer approaches the opposite bank.
