Question

N ° 7 ............................

Answer 1

Peso do corpo:

$P_y=F_n = 174\,N \\ cos\,\theta=0,\!87 \\ \\ P_y = P\,cos\,\theta \\ \\ 174 = P\cdot0,\!87 \\ \\ P = \frac{174}{0,\!87} \\ \\ \boxed{P = 200\,N}$

Massa do corpo:

$P=200\,N \\ g=10\,m\!/\!s^2 \\ \\ \vec{P}=m\,\vec{g} \\ \\ 200 = \,m\cdot10 \\ \\ m = \frac{200}{10} \\ \\ \boxed{m=20\,kg}$

Intensidade da força de atrito:

$F_n=174\,N \\ \mu=0,\!2 \\ \\ F_{at}=\mu\,F_n \\ \\ F_{at}=0,\!2\cdot174 \\ \\ \boxed{F_{at}=34,\!8\,N}$

Aceleração:

$F=194\,N \\ F_{at}=34,\!8\,N\\ m=20\,kg \\ P=200\,N \\ sen\,\theta=0,\!5 \\ \\ \vec{F}-\vec{P}_x-\vec{F}_{at}=m\,\vec{a} \\ \\ \vec{F}-\vec{P}\,sen\,\theta - \vec{F}_{at}=m\,\vec{a} \\ \\ 194-200\cdot0,\!5-34,\!8=20\,a \\ \\ 194-100-34,\!8=20\,a \\ \\ 59,\!2=20\,a \\ \\ \boxed{a=2,\!96\,m\!/\!s^2}$