S1
1. Ec₁=mv₁²/2
Ec₂=mv₂²/2
Ec₁/Ec₂=mv₁²/2/mv₂²/2=v₁²/v₂²=4²/8²=16/64=1/4=>Ec₂=4Ec₁
a crescut de 4 ori
2.m=200 g=0,2 kg
m*v=2=>v=2/m=2/0,2=10 m/s
Ec=mv²/2=0,2*10²/2=0,1*100=10 J
3.F₁=(F₀+F₀₁)/2=
F₀=0
F₀₁=-kΔl/3
F₁=-kΔl/3/2=-kΔl/6
L₁=-F₁*Δl/3=-(-kΔl/6)*Δl/3=kΔl²/18
F₂=(F₀₂+F)/2
F₀₂=-k*2Δl/3
F=-kΔl
F₂=(-k*2Δl/3-kΔl)/2=-5kΔl/6
L₂=-F₂*Δl/3=-(-5kΔl/6)*Δl/3=5kΔl²/18
L₁/L₂=kΔl²/18/5kΔl²/18=1/5
4.m₁=fm
m₂=(1-f)m
G₁=m₁g=fmg
G₁-Ff=0=>G₁=Ff
N₂-G₂=0=>N₂=G₂=m₂g=(1-f)mg
Ff=μN₂=μ(1-f)mg
G₁=Ff=>fmg=μ(1-f)mg |:mg=>f=μ(1-f)<=>f=μ-μf<=>f(1+μ)=μ=>f=μ/(1+μ)=0,25/(0,25+1)=0,25/1,25=0,2
x₀=(1-f)l=(1-0,2)*20=0,8*20=16 cm
5.N₂-mgcosβ=0=>N₂=mgcosβ=0,5*10*cos30°=5*0,866=4,33 N
N₁-mgcosα=0=>N₁=mgcosα=0,5*10*cos60°=5*0,5=2,5 N
N₁=2,5 N
N₂=4,33 N
S2.
b) Tr=Fel<=>Tr=kΔl=>Δl=Tr/k=2/200=0,01 m=1 cm
c) Vectorial:F+G+N+Ff=ma
Ox:Fx-Ff=ma<=>Fcosα-Ff=ma
Oy:N+Fy-mg=0<=>N+Fsinα-mg=0=>N=mg-Fsinα
Ff=μN=μmg-μFsinα
Fcosα-μmg+μFsinα=ma=>a=(Fcosα-μmg+μFsinα)/m=(3√2*√2/2-0,25*1*10+0,25*3√2*√2/2)/1=3-2,5+0,75=0,5+0,75=1,25 m/s²
d) Vectorial:G+N+Ff=ma'
Ox:-Ff=ma'
Oy:N'-mg=0=>N'=mg
Ff'=μN'=μmg
-μmg=ma'=>a'=-μg=-0,25*10=-2,5 m/s²
vf=v+a't<=>0=6-2,5t=>t=6/2,5=2,4 s
