Answer :
Final answer:
To find the time a clock will show 6 days later when it gains 12 minutes every 12 hours, multiply the number of 12-hour intervals by the gain per interval and add to the original time. For the pendulum problem, a 1.000% change in length affects timekeeping, but without specific physics, we can't calculate exact times.
Explanation:
Clock Pendulum Problem and Time Calculation
Regarding the question about the clock that gains 12 minutes every 12 hours, the mathematics involved in solving it requires understanding time intervals and basic arithmetic operations. To determine what time it will show at 1 pm on the 6th day, we need to calculate the total gain in time over the given period. Since we know the clock gains 12 minutes every 12 hours, and the period from 11 am on the first day to 1 pm on the 6th day spans 114 hours, we can perform the following steps:
- Calculate how many 12-hour intervals are in 114 hours. This gives us 9.5 intervals since 114 / 12 = 9.5.
- Multiply the number of intervals by the gain per interval. Therefore, 9.5 intervals × 12 minutes/interval = 114 minutes of gain.
- Convert the total gain into hours and minutes, which is 1 hour and 54 minutes.
- Add this gain to the original time of 11 am. So after 6 days at 1 pm, the clock will show 2:54 pm because 1 pm + 1 hour and 54 minutes = 2:54 pm.
To address the pendulum length change problem, we need to apply mathematical knowledge about pendulum clocks. The time a pendulum clock keeps is proportional to the square root of its length due to the principles of physics. A change in length by 1.000% would result in a change in the time kept by the clock. There are two possible answers because the clock could either gain time or lose time depending on whether the length was increased or decreased. Without additional physics to establish the relationship between pendulum length and timekeeping, we cannot provide the precise answers to this problem.
As a reminder, when traveling across time zones, the understanding of Earth's rotation and time is crucial. For every 15 degrees of longitudinal difference, there is a one-hour time difference. Practicing problems related to clocks and time zones enhances one's ability to understand timekeeping and the effects of changes in mechanical systems or geographical position.
