Unit 1 : Mechanics (summary) by Wook 16

Work

linasalahelddine — 2023-12-29 13:39:13 UTC

W_f= F x d x cos()

W_f= ME_f-ME_i= -f x d

W_net= KE_f-KE_i (work-energy theorem)

W_g= Peg_i-Peg_f

W_net=W_g(when only Peg)

linasalahelddine — 2023-12-29 13:51:33 UTC

Energy is not created nor destroyed

linasalahelddine — 2023-12-29 13:52:51 UTC

h=L(1-cosα)

linasalahelddine — 2023-12-29 13:53:58 UTC

linasalahelddine — 2023-12-29 13:54:27 UTC

ME = KE + PEg

KE= 1/2 M V²

PEg= mgh

linasalahelddine — 2023-12-29 13:56:42 UTC

linasalahelddine — 2023-12-29 14:00:38 UTC

PEe= 1/2 Kx²(J)

Stiffness:

F=-K X (X_f-X_i) (N.M^-1)

Rectilinear Motion

linasalahelddine — 2023-12-29 14:08:57 UTC

URM (Uniform Rectilinear Motion):

a=0

V= constant

X= Vt+ X0

X-X0=d=Vt

UVRM (Uniform Varied Rectilinear Motion):

UARM: accelerated ( a>0)
UDRM: deccelerated (a<0)

V=at + V₀
X=1/2at² + V⁰t + X₀
V² = V₀² + 2ad

3 laws

linasalahelddine — 2023-12-29 14:14:57 UTC

Newtons 1^st law:

∑Fext= 0 (no acceleration)

Newtons 2^nd law:

∑Fext= ma

Newtons 3^rd law:

F_1/2=-F_2/1

_{principle of interaction:}

equal magnitudes
opposite direction
same line of action

linasalahelddine — 2023-12-29 14:40:44 UTC

Particle:

P = m x v (kg.m.s-1)

System:

P= mi vi = mV_G

Newtons second law

linasalahelddine — 2023-12-29 14:48:51 UTC

∑Fext=dp/dt

in a short time:

∑Fext=dp/dt=

p_f-p_i/t_f-t_i

conservation

linasalahelddine — 2023-12-29 14:50:00 UTC

Linear momentum is conserved when system is isolated/sum of external forced applied on system =0

Types of collision

linasalahelddine — 2023-12-29 14:51:45 UTC

Elastic: conservation of KEsys (KE=KE')

Inelastic: No conservation of KEsys