Question

Each of the three plates has a mass of $10kg$. If the coefficients of static and kinetic friction at each surface of contact are ${\mu }_s=0.3$ and ${\mu }_k=0.2$, respectively, determine the acceleration of each plate when the three horizontal forces are applied.(Take $g=1m/s^2$)

Answer 1

On plate $D$

$M_{mg}=0.2\times \left(10kg\right)\times \left(9.81m/s^2\right)$

$=2\times 9.81$

$=19.62N$

$F=ma$

$19.62-18N=10\left(a\right)$

$a=0.162m/s^2$

On plate $C$

two opposite forces

$100-2\left(19.62\right)=10\left(a\right)$

$a=\mathrm{6.0.76}m/s^2$

On plate $B$

$A$ is not moving

$Mmg-F=ma$

$0.3\times 10\times 9.81-15N=10\left(a\right)$

$a=2.943m/s^2$