+ 1/2 points | Previous Answers SerPSE9 15.AE.005 Example 15.5 A Connection Between Length and Time Christian Huygens (1629-1695), the greatest clockmaker in history, suggested that an international unit of length could be defined as the length of a simple pendulum having a period of exactly 1 s. How much shorter would our length unit be if his suggestion had been followed? SOLVE IT Conceptualize Imagine a pendulum that swings back and forth in exactly 1 second. Based on your experience in observing swinging objects, can you make an estimate of the required length? Hang a small object from a string and simulate the 1-s pendulum Categorize This example involves a simple pendulum, so we categorize it as a substitution problem that applies the concepts introduced in this section. Solve the equation for the length and substitute the known values: T2 2(9.80 m/s). = 1.2482 The meter’s length would be slightly less than one-fourth of its current length. Also, the number of significant digits depends only on how precisely we know g because the time has been defined to be exactly 1 s MASTER IT HINTS: GETTING STARTED I IMSTUCKI A grandfather clock is found to gain 22.0 s every 24 hours. If the current length of the pendulum is 0.640 m, how much should the length be changed to make the clock accurate? Let a positive value correspond to an increase in length, and a negative value correspond to a decrease