Chapter-2 Q022 - Physics For Engineers And Scientists - Solutions

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Question 22 - Problems - Chapter 2

Problem:

On a particular wristwatch, the tips of the minute and second hands are each 0.90 cm from the center, whereas the tip of the hour hand is 0.50 cm from the center.

Question:

What is the average speed of each of these three tips?

Solution:

The distance the tip of the second- and minutehand is traveling is the circumference of a circle.

Distance minute and second $s_{ms} = 2.\pi.r$ where $r=9.0mm$

Distance hour hand is $s_h = 2.\pi.r$ where $r=5.0mm$

The time to travel the wole circle is

Time second hand $t_s = 1$ min.

Time minute hand $t_m = 1$ hour.

Time hour hand $t_h = 12$ hours.

In [1]:
import numpy as np
import pint
u = pint.UnitRegistry()
r_ms = 9 * u.mm
r_h = 5 * u.mm
s_ms = 2 * np.pi * r_ms
s_h = 2 * np.pi * r_h
t_s = 1 * u.min
t_m = 1 *u.hour
t_h = 12 * u.hour
Speed_s = s_ms / t_s
Speed_m = s_ms / t_m
Speed_h = s_h / t_h
print(f'- the average speed of the second hand is {Speed_s.to(u.m / u.s):.2e}.')
print(f'- the average speed of the minute hand is {Speed_m.to(u.m / u.s):.2e}.')
print(f'- the average speed of the hour hand is {Speed_h.to(u.m / u.s):.2e}.')
- the average speed of the second hand is 9.42e-04 meter / second.
- the average speed of the minute hand is 1.57e-05 meter / second.
- the average speed of the hour hand is 7.27e-07 meter / second.

سُوۡرَةُ حٰمٓ السجدة / فُصّلَت
ثُمَّ اسْتَوَىٰ إِلَى السَّمَاءِ وَهِيَ دُخَانٌ فَقَالَ لَهَا وَلِلْأَرْضِ ائْتِيَا طَوْعًا أَوْ كَرْهًا قَالَتَا أَتَيْنَا طَائِعِينَ ﴿١١
فَقَضَاهُنَّ سَبْعَ سَمَاوَاتٍ فِي يَوْمَيْنِ وَأَوْحَىٰ فِي كُلِّ سَمَاءٍ أَمْرَهَا ۚ وَزَيَّنَّا السَّمَاءَ الدُّنْيَا بِمَصَابِيحَ وَحِفْظًا ۚ ذَٰلِكَ تَقْدِيرُ الْعَزِيزِ الْعَلِيمِ ﴿١٢


Surah Fussilat: Thereafter turned He to the heaven and it was as smoke, and said Unto it and Unto the earth: come ye twain, willingly or loth. They said: we come willingly. (11) Then He decreed them as seven heavens in two days, and revealed Unto each heaven the command thereof; and We bedecked the nether heaven with lamps and placed therein a guard. That is the ordinance of the Mighty, the Knower. (12)

De hemelen en aarde (waren) een samenhangende massa. Wij hebben ze toen van elkaar gescheiden… Wij hebben de hemel tot een beschermend dak gemaakt … en de dag en de nacht, de zon en de maan geschapen. (Koran 41 11:12)


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