Question

Um corpo de massa 5kg é abandonado sobre um plano inclinado formando 45° com a horizontal. o coeficiente de atrito entre o bloco e o plano é 0,5. Qual a aceleração do bloco?​

Answer 1

$\large\boxed{\begin{array}{l}\underline{\sf C\acute alculo\,da\,forc_{\!\!\!,}~\!a~peso}\\\rm P=m\cdot g\\\sf P=5\cdot10=50~N\\\underline{\sf C\acute alculo\,da\,forc_{\!\!\!,}~\!a~normal:}\\\rm N=P_y\\\rm N=P\cdot sen(45^\circ)\\\rm N=50\cdot\dfrac{\sqrt{2}}{2}=25\sqrt{2}\\\rm N=25\cdot1,2=30~N\\\underline{\sf C\acute alculo\,da\, forc_{\!\!\!,}~\!a\,de\,atrito}\\\rm F_{at}=\mu\cdot N\\\sf F_{at}=0,5\cdot30=15~N\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\sf C\acute alculo\,da\,componente\,P_x:}\\\rm P_x=P\cdot cos(45^\circ)\\\rm P_x=50\cdot\dfrac{\sqrt{2}}{2}=25\sqrt{2}=30~N\\\underline{\sf C\acute alculo\,da\,acelerac_{\!\!\!,}~\!\tilde ao\!:}\\\rm F_{R}=m\cdot a\\\rm P_x-F_{at}=m\cdot a\longrightarrow a=\dfrac{P_x-F_{at}}{m}\\\\\rm a=\dfrac{30-15}{5}\\\\\rm a=\dfrac{15}{5}\\\\\rm a=3~m/s^2\end{array}}$