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16.
Vectorial: F1+F2+G+N+Ff=0
Scalar: Ox:F1+F2*cosα-Ff=0 (1)
Oy:N-m*g+F2*sinα=0 (2)
(2)=>N=m*g-F2*sinα=6*10-10√3*1/2=60-8,66≈51,34 N
(1)=>Ff=F1+F2*cosα
Ff=μ*N=μ(m*g-F2*sinα)
μ(m*g-F2*sinα)=F1+F2*cosα=>μ=(F1+F2*cosα)/(mg-F2*sinα)=(20+10√3*√3/2)/(60-10√3*1/2)=35/51,34≈0,68
Vectorial: F1+F2+G+N+Ff=m*a
Scalar: Ox:F1+F2*cosα-Ff=m*a
a={[F1+F2(cosα+μ*sinα)]/m}-μg={[20+10√3(√3/2+0,34*1/2)]/6}-0,34*10=[(20+
17,3*1,03)/6]-3,4=37,92/6-3,4=6,32-3,4≈2,92 m/s²
17.Vectorial: F1+F2+F3+G+N+Ff=m*a
Scalar: Ox:F1+F2*sinα2-F3*sinα3-Ff=m*a (1)
Oy:N+F2*cosα2+F3*cosα3-mg=0 (2)
(1)=>Ff=F1+F2*sinα2-F3*sinα3-m*a=12+4√3*1/2-8√2*√2/2-2*2=12+3,46-8-4=3,46 N
(2)=> N=mg-F2*cosα2-F3*cosα3=2*10-4√3*√3/2-8√2*√2/2=20-6-8=6 N
Ff=μ*N=>μ=Ff/N=3,46/6=0,567
Vectorial: F1+F2+G+N+Ff=0
Scalar: Ox:F1+F2*cosα-Ff=0 (1)
Oy:N-m*g+F2*sinα=0 (2)
(2)=>N=m*g-F2*sinα=6*10-10√3*1/2=60-8,66≈51,34 N
(1)=>Ff=F1+F2*cosα
Ff=μ*N=μ(m*g-F2*sinα)
μ(m*g-F2*sinα)=F1+F2*cosα=>μ=(F1+F2*cosα)/(mg-F2*sinα)=(20+10√3*√3/2)/(60-10√3*1/2)=35/51,34≈0,68
Vectorial: F1+F2+G+N+Ff=m*a
Scalar: Ox:F1+F2*cosα-Ff=m*a
a={[F1+F2(cosα+μ*sinα)]/m}-μg={[20+10√3(√3/2+0,34*1/2)]/6}-0,34*10=[(20+
17,3*1,03)/6]-3,4=37,92/6-3,4=6,32-3,4≈2,92 m/s²
17.Vectorial: F1+F2+F3+G+N+Ff=m*a
Scalar: Ox:F1+F2*sinα2-F3*sinα3-Ff=m*a (1)
Oy:N+F2*cosα2+F3*cosα3-mg=0 (2)
(1)=>Ff=F1+F2*sinα2-F3*sinα3-m*a=12+4√3*1/2-8√2*√2/2-2*2=12+3,46-8-4=3,46 N
(2)=> N=mg-F2*cosα2-F3*cosα3=2*10-4√3*√3/2-8√2*√2/2=20-6-8=6 N
Ff=μ*N=>μ=Ff/N=3,46/6=0,567
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