**Transcription for Educational Website**---Big Ben’s hour hand is 2.7 m long with a mass of 60 kg. The minute hand is 4.5 m long with a mass of 100 kg. For this problem, you may treat each hand as a thin, uniform rod with the center of mass located at the rod’s geometrical center.![Image of Big Ben clock face](Image source: visitlondon.com)Calculate the net torque (magnitude and direction) that the hands exert on their shared rotational axis at the following times.- **12:00**- **3:00**- **7:00**- **9:15** (Note: the hour hand does *not* point directly toward the “9” at this time.)Roughly speaking, at what approximate time(s) do the hands exert maximum net torque on their shared rotational axis? Ignore the direction; focus only on the magnitude for this question.$page number: 2$---Please note the image presents Big Ben's clock, illustrating the hands' positioning, but does not contribute further information beyond what's described in the task above.

Given: Diameter of hour hand Dh=2.7 m Mass of hour hand mh=60 kg Diameter of minute hand Dm=4.5 m Mass of minute hand mm =100 kg To find: Net torque at 12:00 Net torque Mnet=Mh+MmMnet=0At 3:00 Net torque Mnet=Mh+MmMnet=mhg×d2+mmg×0Mnet=60×9.81×2.72Mnet=794.61 N-m At 7:00 Mnet=Mh+MmMnet=mhg×d2sinα+0 Angle made by hour hand with horizontal axis at 7:00 α=60o Mnet=Mh+MmMnet=60×9.81×2.72sin60+0Mnet=688.152 N-m anticlockwise At 9:15 α=30o Mnet=Mh+MmMnet=60×9.81×2.72cos30-100×9.81×4.52cos0Mnet=-1519.1 N-m Mnet=1519.1 N-m CLOCKWISE Maximum net torque will be exerted when angle made by minute hand with horizontal axis will be 0 β=0o This will happen when time 3:15 at 3:15 Mnet=Mh+MmMnet=60×9.81×2.72cos15+100×9.81×4.52cos0Mnet=2974.78 N-m Mnet=2974.78 N-m CLOCKWISE

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Mechanical Engineering

Big Ben's hour hand is 2.7 m long with a mass of 60 kg. The minute hand is 4.5 m long with a mass of 100 kg. For this problem, you may treat each hand as a thin, uniform rod with the center of mass located at the rod's geometrical center. Image source: visitlondon.com Calculate the net torque (magnitude and direction) that the hands exert on their shared rotational axis at the following times. . 12:00 • 3:00 AB FOTOE • 7:00 9:15 (Note: the hour hand does not point directly toward the "9" at this time.) Roughly speaking, at what approximate time(s) do the hands exert maximum net torque on their shared rotational axis? Ignore the direction; focus only on the magnitude for this question.

Big Ben's hour hand is 2.7 m long with a mass of 60 kg. The minute hand is 4.5 m long with a mass of 100 kg. For this problem, you may treat each hand as a thin, uniform rod with the center of mass located at the rod's geometrical center. Image source: visitlondon.com Calculate the net torque (magnitude and direction) that the hands exert on their shared rotational axis at the following times. . 12:00 • 3:00 AB FOTOE • 7:00 9:15 (Note: the hour hand does not point directly toward the "9" at this time.) Roughly speaking, at what approximate time(s) do the hands exert maximum net torque on their shared rotational axis? Ignore the direction; focus only on the magnitude for this question.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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**Transcription for Educational Website**

---

Big Ben’s hour hand is 2.7 m long with a mass of 60 kg. The minute hand is 4.5 m long with a mass of 100 kg. For this problem, you may treat each hand as a thin, uniform rod with the center of mass located at the rod’s geometrical center.

![Image of Big Ben clock face](Image source: visitlondon.com)

Calculate the net torque (magnitude and direction) that the hands exert on their shared rotational axis at the following times.

- **12:00**

- **3:00**

- **7:00**

- **9:15** (Note: the hour hand does *not* point directly toward the “9” at this time.)

Roughly speaking, at what approximate time(s) do the hands exert maximum net torque on their shared rotational axis? Ignore the direction; focus only on the magnitude for this question.

$page number: 2$

---

Please note the image presents Big Ben's clock, illustrating the hands' positioning, but does not contribute further information beyond what's described in the task above.

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