

Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Engineering Dynamics Homework solutions
Typology: Exercises
1 / 3
This page cannot be seen from the preview
Don't miss anything!
Homework Assignment 3 Problem 3 - 1
Given:
oh
m
Rough Area (Mn)
Rough Area (Mn)
i
£ 2 : Free Body Diagrams
oh 7 m
oh (^) m
Fgv^ "Ñ my 7 i o ↑ Concentrate on position 2 in particular-
'B'frame
ñ
;^ i
O
Steps- Governing Equations of Motion IF = MBE block OR, Fg→ + FN = m BE^ block. % mgñ + NI = m (Viet + LEG)
But it = ◦ because the loop is perfectly circular.
OR, (^) mg + N = mr¥
(scalar equation along ni )
OR, (^) VE = V 2 = (mg+N)R m Consider the limiting case i.e. when N → o (jcuons^ tta ctlos)tD witI^ h loop Them; mg≥> N Therefore, I^ =^ Vgr ☆^ Time^ to^ invoke^ the^ next^ Governing^ Equation {ÑW = AKE
LHS: Includes work done by all forces acting on the system Contributing forces: ① Gravity 2 ③^ Spring^ force.
② Friction
W gravity = f Fg. ds→ I = (^) f- mgj. [dy;] I = - mg(Yi-Yi)=- 2 mg R
[F. as
[Msmgi. dei
(since dot product only consider motion along 5 )
B (^) Wtriction =
mg?Rough Sfce.
IFFrll.MN' ⇒ N.mg
= - Msmg ( 22 - 21 ) = - Msmg R
c Wspring^ force^ = i
kxi.de? = Skadn I = * ¥!
Eg. l
Revisiting Eq. =^1282 - 2 mg R-Ms Mg R = ±
l mvi-Emre
(start from ◦ rest)
OR, (^) KEI-^2 mg^ R-Ms^ mgr^ =^2 -^ gr
OR, *^ =^5 mg_R+^ Us^ mgr
min
Mgr ( 5 + 2 Mr) k
An rs
Note: This is the minimum value of ± because this is just enough that block loses contact with loop.
If S^ initial^78 min^ :^ Loop^ is^ completed S initial < 8 min :^ Block^ falls^ of^ at^ top. LIMITING CASE!! S initial = 8 min:
Problem 3 - 2
Given:# 11 = 3 m/s To find: IN Solution:
3 m/s
n^ B
c
r
Slept: Reference frames
StepI: FREE BODY DIAGRAMS
ie
3 m/s
r
ñ
3 m/s
e" 1. 2 m A
t
A and C are the positions 1 and 2.
Steps: Governing Equations of motion
r
if^ £ I^ Wiz^ - -^ KE N: No. of contributing forces towards total work done. Here N = 1. "Tension is an internal force".
"d W 9 Ifg. ds {^1 OR WE = - mg ↑. (daitdy ↑) I = - my/ dy § = - mg ( 42 - 41 )
c
Now; FOA = rai and af=-sino it cos 09 04 FOA = - l sinoi - loos 09 So, (^) TY = - loos 0 = Yi Aside... OR, WE = - mg C- 0. 8 + Icoso) = - mg (- 0. 8 + 1. 2. ±) = - my (- 0 - 2 ) = 0. 2 mg
Now, back to RHS in Eq. ①i 0 - 2 mg = ± my (V 27 4 2 )
⇒ Eg.①
OR, 0.^4 g^ =^ VE-(^3 )^2 ☑ = ③. 92 + 9 ) m/s
(Vi = V 1 = 3 m/ 5 )
OR, OR, V.^ =^3.^594 m/s^ And