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Document Title
Fundamentals of Stress and Vibration Chapter Title
[A Practical guide for aspiring Designers / Analysts] 2. Engineering Mechanics

Š‡ ƒ ‡š–‡”ƒŽ ˆ‘” ‡ ƒ – ‘ –Š‡ ‘„Œ‡ –ǡ –Š‡ ‘„Œ‡ – ‡‹–Š‡” †‡ˆ‘”• ‘” ƒ ‡Ž‡”ƒ–‡•Ǥ Š‹• ”‡•—Ž–• ‹
™‘” †‘‡ „› –Š‡ ‡š–‡”ƒŽ ˆ‘” ‡ ‘ –Š‡ ‘„Œ‡ –Ǥ

 ƒ•‡ ‘ˆ ‡Žƒ•–‹ †‡ˆ‘”ƒ–‹‘ǡ –Š‡ „‘†› •–‘”‡• ’‘–‡–‹ƒŽ ‡‡”‰›Ǥ –Š‡”™‹•‡ǡ –Š‡ „‘†› †‡˜‡Ž‘’•
‹‡–‹ ‡‡”‰› „‡ ƒ—•‡ ‘ˆ –Š‡ ˜‡Ž‘ ‹–› ‹†— ‡†Ǥ ‹‡–‹ ‡‡”‰› ‹• ƒ—•‡† †—‡ –‘ ‘–‹‘ ƒ••‘ ‹ƒ–‡†
™‹–Š –Š‡ „‘†›Ǥ Ž•‘ ‘–‡ –Šƒ–ǡ ‘•– ‘ˆ –Š‡ „‘†‹‡• ™‡ †‡ƒŽ ™‹–Šǡ ‹ –Š‹• „‘‘ǡ ƒ”‡ ”‹‰‹†ǡ ‡ƒ‹‰ǡ
–Š‡› Šƒ˜‡ œ‡”‘ ‡Žƒ•–‹ ‹–›Ǥ ‘™‡˜‡”ǡ –‘ ”‡’”‡•‡– –Š‡ ‡Žƒ•–‹ ‹–›ǡ •’”‹‰• ƒ”‡ —•‡†ǡ ™Š‹ Š ‘
‘’”‡••‹‘ǡ •–‘”‡ ’‘–‡–‹ƒŽ ‡‡”‰›ǡ ƒ• •Š‘™ ‹ ȏ ‹‰ ʹǤͳȐǤ

‘–Š‡” ˆ‘” ‘ˆ ’‘–‡–‹ƒŽ ‡‡”‰›ǡ ‹• –Š‡ ‡‡”‰› †—‡ –‘ ‰”ƒ˜‹–›ǡ –Šƒ– ‹•ǡ ™Š‡ –Š‡ „‘†› ‹• ‘˜‡†
ˆ”‘ ’‘•‹–‹‘ Ǯ ǯ –‘ Ǯ ǯ ƒ‰ƒ‹•– ‰”ƒ˜‹–›ǡ ™‘” ‹• •–‘”‡† ƒ• ‰”ƒ˜‹–ƒ–‹‘ƒŽ ’‘–‡–‹ƒŽ ‡‡”‰›ǡ ƒ• •Š‘™
‹ ȏ ‹‰ ʹǤʹȐǤ

[Fig 2.2: work done in displacing the car from position ‘A’ to position ‘B’]

‘–‡ –Šƒ–ǡ ‰”ƒ˜‹–ƒ–‹‘ƒŽ ϐ‹‡Ž† ‹• ‘•‡”˜ƒ–‹˜‡ ƒ† –Š‡ ™‘” †‘‡ ‹• ‹†‡’‡†‡– ‘ˆ –Š‡ ’ƒ–ŠǤ Š‡
™‘” †‘‡ ‹• ƒŽ —Žƒ–‡† „› –Š‡ •Š‘”–‡•– †‹•–ƒ ‡ǡ –Šƒ– ‹•ǡ –Š‡ †‹•’Žƒ ‡‡– „‡–™‡‡ –™‘ ’‘‹–• ‹
–Š‡ ˜‡”–‹ ƒŽ †‹”‡ –‹‘ ȋƒ‰ƒ‹•– ‰”ƒ˜‹–›ȌǤ
‡– —• ‘™ †‡”‹˜‡ –Š‡ ‡š’”‡••‹‘ ˆ‘” ‹‡–‹ ǡ ’‘–‡–‹ƒŽ ƒ† •’”‹‰ ‡‡”‰‹‡•Ǥ

Kinetic Energy: A force (F) acts on a mass (m) for (t-seconds), as shown in [Fig 2.1]. Find the
kinetic energy of the mass.

Let the displacement of the body, during (t-seconds) be ‘d’. therefore, the work done by the force is
given by: work done = Force ∗ average displacement
Average displacement is considered, as the body is accelerating uniformly, and travels different
displacements in different intervals of time. Mathematically, we have:

s
Work done = F ∗ s avg = ma ∗ - - - - (2.11)
2
Let us assume that the velocity of the body is ‘v’, after an interval of time ‘t’. Therefore, equation
(2.11) can be rewritten as:

velocity mv (v + 0) 1
2
Work done = ma ∗ s avg = m ∗ velocity avg ∗ time = ∗ t = mv
time t 2 2

Page 10 QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries,