a) -Gt-Ff=ma=>-mgsinα-Ff=ma
N-Gn=0=>N=mgcosα
Ff=μN=μmgcosα
-mgsinα-μmgcosα=ma|:m=>a=-gsinα-gμcosα=-g(sinα+μcosα)
Gt-Ff=ma'=>mgsinα-Ff=ma'
N-Gn=0=>N=mgcosα
Ff=μN=μmgcosα
mgsinα-μmgcosα=ma'|:m=>a'=gsinα-gμcosα=g(sinα-μcosα)
|a|=2a'=>|-g(sinα+μcosα)|=2g(sinα-μcosα) =>g(sinα+μcosα)=2g(sinα-μcosα)|:g=>-sinα=-3μcosα=>μ=tgα/3=1/3=0,33
b) ΔEc=L_G+L_Ff+L_N
ΔEc=mv²/2-mv₀²/2=-mv₀²/2
L_N=0;L_G=-mgh=-mgxsinα
L_Ff=-Ff*x=-μNx=-μmgxcosα
-mv₀²/2=-mgxsinα-μmgxcosα|:m=>v₀²=2gxsinα+2μgxcosα=2gx(gsinα+μcosα)
v₀²=2gx(sinα+μcosα)<=>4²=2*10x(0,7+0,33*0,7)<=>16=20x*0,931<=>16=18,62x=>x=16/18,62=0,85 m
c) η=1/(1+μctgα)=1/(1+0,33*1)=1/1,33=0,75=>η=75%
