13.
Vectorial:F+N+G+Ff=0
Ox:F-Ff=0=>F=Ff
Oy:N-mg=0=>N=mg
Ff=μN=μmg
F=μmg=>μ=F/mg=50/40•10=5/40=0,125
14.Vectorial:F+N+G+Ff=ma
Ox:F-Ff=ma
Oy:N-mg=0=>N=mg
Ff=μN=μmg
F-μmg=ma=>a=(F-μmg)/m=(16-0,2•6•10)/6=(16-12)/6=4/6=0,66 m/s^2
Vectorial:F+N'+G'+Ff'=0
Ox:F-Ff'=0=>F=Ff'
Oy:N'-m'g=0=>N'=m'g
Ff'=μN'=μm'g
F=μm'g=>m'=F/μg=16/0,2•10=16/2=8 kg
m'=m+m1=>m1=m'-m=8-6=2 kg
15.m=15 t=15000 kg
Ff=1,2%F=1,2F/100
F-Ff=ma<=>F-1,2F/100=15000•0,6<=>98,8F/100=900=>F=100•9000/98,8=9109,3 N
16.F=ma=>a=F/m=24/6=4 m/s^2
v=3vo
v=vo+at<=>3vo=vo+at<=>2vo=at=>t=2vo/a=2•1,2/4=0,6 s
d=vot+at^2/2=1,2•0,6+4•0,6^2/2=0,72+2•0,36=0,72+0,72=1,44 m
17.Vectorial:F+N+G+Ff=0
Ox:Fcosa-Ff=0=>Fcosa=Ff
Oy:N-mg+Fsina=0=>N=mg-Fsina
Ff=μN=μmg-μFsina
Fcosa=μmg-μFsina<=>Fcosa+μFsina=μmg<=>F(cosa+μsina)=μmg=>F=μmg/(cosa+μsina)
sin^2a+cos^2a=1=>cos^2a=1-0,64=0,36=>cosa=0,6
F=μmg/(cosa+μsina)=0,2•0,38•10/(0,6+0,2•0,8)=
0,76/0,76=1 N
